autobox report

TIME=07:55:08 DATE= 3/ 3/97 THE MAXIMUM NUMBER OF OBSERVATIONS ALLOWED IN A SERIES IS: 600 THE MAXIMUM NUMBER OF SERIES ALLOWED IN A MODEL IS: 6 THE SERIAL NUMBER IS: 0 THE PRODUCT NUMBER IS: 6 AUTOBOX 5.02000 60030 6BP90000,A GOOD COMPANY , A GOOD CITY , SOMEWHERE NOTE -> THE PROGRAM IS USING THE STANDARD PROCEDURE FOR COMPUTING THE AUTOCORRELATION AND PARTIAL AUTOCORRELATION FUNCTIONS. PLOT OF THE OBSERVED (ACTUAL) SERIES GRAPH KEY A = INPUT B = OUTPUT 1820.0 20127. DATE ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1992/ 4 B A 9977.0 1992/ 5 B A 12417. 1992/ 6 B A 9129.0 1992/ 7 B A 9613.0 1992/ 8 B A 8528.0 1992/ 9 B A 10008. 1992/ 10 B A 9208.0 1992/ 11 A B 10624. 1992/ 12 A B 7106.0 1993/ 1 B 10870. 1993/ 2 B A 16577. 1993/ 3 B A 20127. 1993/ 4 B A 15691. 1993/ 5 A B 14206. 1993/ 6 A B 12079. 1993/ 7 A B 7958.0 1993/ 8 A B 9924.0 1993/ 9 A B 9311.0 1993/ 10 B A 10046. 1993/ 11 A B 6766.0 1993/ 12 A B 6202.0 1994/ 1 A B 4802.0 1994/ 2 A B 4201.0 1994/ 3 A B 5540.0 1994/ 4 A B 4244.0 1994/ 5 A B 4192.0 1994/ 6 A B 3776.0 1994/ 7 A B 3918.0 1994/ 8 A B 4351.0 1994/ 9 A B 3902.0 1994/ 10 A B 3845.0 1994/ 11 B 4923.0 1994/ 12 B A 4283.0 1995/ 1 B A 7261.0 1995/ 2 B A 4471.0 1995/ 3 AB 3814.0 1995/ 4 B 2704.0 1995/ 5 AB 3104.0 1995/ 6 A B 3219.0 1995/ 7 BA 3683.0 1995/ 8 B 2841.0 1995/ 9 BA 3062.0 1995/ 10 AB 3126.0 1995/ 11 A B 3277.0 1995/ 12 AB 1820.0 1996/ 1 AB 2950.0 1996/ 2 A B 2439.0 1996/ 3 AB 2659.0 1996/ 4 AB 2588.0 1996/ 5 AB 2594.0 1996/ 6 A B 2146.0 1996/ 7 A B 2524.0 1996/ 8 A B 2242.0 1996/ 9 A B 2640.0 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Analysis for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT SERIES NAME IS : INPUT THE FILTER APPLIED TO THE INPUT SERIES MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS -885.5719 2 Autoregressive-Factor # 1 3 -.6971897 3 Autoregressive-Factor # 2 6 -.4953457 [(1-B1)]Y(T) = -348.94 + [(1+ .697B 3)(1 + .495B 6)]-1 [A(T)] THE FILTER APPLIED TO THE OUTPUT SERIES MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS 41.23572 2 Autoregressive-Factor # 1 3 -.6971897 3 Autoregressive-Factor # 2 6 -.4953457 [(1-B1)]Y(T) = 16.248 + [(1+ .697B 3)(1 + .495B 6)]-1 [A(T)] CROSS CORRELATIONS BETWEEN: FILTERED INPUT AND FILTERED OUTPUT SERIES Mean of X1 444.32 Mean of Y -310.75 Variance of X1 .42844E+07 Variance of Y .21881E+07 St. Deviation of X1 2069.9 St. Deviation of Y 1479.2 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 .148 .151 .98 0 .148 .151 .98 1 .122 .152 .80 -1 .112 .152 .74 2 .183 .154 1.19 -2 -.184 .154 -1.20 3 .323 .156 2.07 -3 .207 .156 1.32 4 .188 .158 1.19 -4 -.119 .158 -.75 5 .242 .160 1.51 -5 -.085 .160 -.53 6 -.009 .162 -.06 -6 -.105 .162 -.65 7 .162 .164 .99 -7 -.130 .164 -.79 8 .030 .167 .18 -8 -.198 .167 -1.19 9 -.091 .169 -.54 -9 -.213 .169 -1.26 10 .212 .171 1.24 -10 -.103 .171 -.60 11 .032 .174 .19 -11 -.229 .174 -1.31 LAG IMPULSE STANDARD T-RATIO RESPONSE WEIGHT ERROR 0 .10597 .1077 .984 1 .87353E-01 .1090 .802 2 .13112 .1103 1.19 3 .23052 .1116 2.07 4 .13429 .1130 1.19 5 .17263 .1144 1.51 6 -.66255E-02 .1159 -.572E-01 7 .11590 .1175 .986 8 .21452E-01 .1191 .180 9 -.65284E-01 .1208 -.540 10 .15168 .1226 1.24 11 .23123E-01 .1244 .186 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 .148 .98 { } .148 .98 { } 1 .122 .80 { } .112 .74 { } 2 .183 1.19 { } -.184 -1.20 { } 3 .323 2.07 { } .207 1.32 { } 4 .188 1.19 { } -.119 -.75 { } 5 .242 1.51 { } -.085 -.53 { } 6 -.009 -.06 { * } -.105 -.65 { } 7 .162 .99 { *} -.130 -.79 { ** } 8 .030 .18 { * } -.198 -1.19 {* } 9 -.091 -.54 { } -.213 -1.26 {* } 10 .212 1.24 { *} -.103 -.60 { ** } 11 .032 .19 { * } -.229 -1.31 {* } ACF & PACF OF TENTATIVELY IDENTIFIED NOISE PROCESS LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 -.689 .144 -4.78 24.26 .0000 -.689 .144 -4.78 2 .666 .202 3.30 47.37 .0000 .363 .144 2.51 3 -.570 .243 -2.34 64.69 .0000 -.060 .144 -.42 4 .580 .269 2.15 83.06 .0000 .170 .144 1.18 5 -.516 .294 -1.75 97.89 .0000 -.023 .144 -.16 6 .425 .313 1.36 108.21 .0000 -.131 .144 -.91 7 -.440 .324 -1.36 119.57 .0000 -.119 .144 -.83 8 .308 .337 .92 125.27 .0000 -.189 .144 -1.31 9 -.308 .342 -.90 131.10 .0000 .000 .144 .00 10 .153 .348 .44 132.58 .0000 -.194 .144 -1.35 11 -.132 .350 -.38 133.71 .0000 .077 .144 .53 12 .104 .351 .30 134.44 .0000 .092 .144 .64 13 -.044 .351 -.13 134.58 .0000 .069 .144 .48 14 .094 .351 .27 135.20 .0000 .199 .144 1.38 15 -.038 .352 -.11 135.30 .0000 -.059 .144 -.41 16 .072 .352 .21 135.69 .0000 .016 .144 .11 17 -.034 .352 -.10 135.78 .0000 -.106 .144 -.73 18 .109 .352 .31 136.72 .0000 .110 .144 .76 19 -.111 .353 -.32 137.75 .0000 -.050 .144 -.34 20 .084 .354 .24 138.36 .0000 -.089 .144 -.61 21 -.153 .354 -.43 140.44 .0000 -.041 .144 -.29 22 .102 .356 .29 141.40 .0000 -.116 .144 -.80 23 -.170 .356 -.48 144.19 .0000 .026 .144 .18 24 .129 .358 .36 145.86 .0000 .000 .144 .00 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 -.689 -4.78 {* } -.689 -4.78 **{* } 2 .666 3.30 { **}* .363 1.80 { ***}* 3 -.570 -2.34 { } -.060 -.25 { } 4 .580 2.15 { ***}* .170 .63 { *} 5 -.516 -1.75 {**** } -.023 -.08 { * } 6 .425 1.36 { * } -.131 -.42 { } 7 -.440 -1.36 { * } -.119 -.37 { } 8 .308 .92 { ** } -.189 -.56 {* } 9 -.308 -.90 { **** } .000 .00 { * } 10 .153 .44 { * } -.194 -.56 {* } 11 -.132 -.38 { } .077 .22 { } 12 .104 .30 { } .092 .26 { } 13 -.044 -.13 { * } .069 .20 { } 14 .094 .27 { } .199 .57 { ***} 15 -.038 -.11 { * } -.059 -.17 { } 16 .072 .21 { } .016 .04 { * } 17 -.034 -.10 { * } -.106 -.30 { } 18 .109 .31 { } .110 .31 { } 19 -.111 -.32 { } -.050 -.14 { * } 20 .084 .24 { } -.089 -.25 { } 21 -.153 -.43 { *** } -.041 -.12 { * } 22 .102 .29 { } -.116 -.33 { } 23 -.170 -.48 { *** } .026 .07 { * } 24 .129 .36 { ** } .000 .00 { * } THE STARTING MODEL FOR THIS VARIABLE MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 34.15595 2 Autoregressive-Factor # 1 1 -.4174977 3 2 .3362784 4 3 -.6013446E-01 INPUT SERIES X1 INPUT Lambda Value 5 Omega (input) -Factor # 2 3 .2305243 6 4 -.1342935 7 5 -.1726309 Y(T) = 29.926 +[X1(T)][(+ .231B 3+ .134B 4+ .173B 5)] + [(1+ .417B 1- .336B 2+ .060B 3)]-1 [A(T)] THE STARTING MODEL FOR THIS VARIABLE MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS .1000000 2 Autoregressive-Factor # 1 1 -.4174977 3 2 .3362784 4 3 -.6013446E-01 INPUT SERIES X1 INPUT Lambda Value 5 Omega (input) -Factor # 2 3 .2305243 6 4 -.1342935 7 5 -.1726309 Y(T) = .87615E-01 +[X1(T)][(+ .231B 3+ .134B 4+ .173B 5)] + [(1+ .417B 1- .336B 2+ .060B 3)]-1 [A(T)] Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 46 Number of Degrees of Freedom =n-m 39 Residual Mean = R/n -.142398E-01 Sum of Squares = R .344519E+08 Variance var= R /(n) 748955. Adjusted Variance = R /(n-m) 883383. Standard Deviation = 939.884 Standard Error of the Mean = / (n-m) 150.502 Mean / its Standard Error = /[ / (n-m)] -.946153E-04 Mean Absolute Deviation = R /n 676.829 AIC Value ( Uses var ) =nln +2m 636.216 SBC Value ( Uses var ) =nln +m*lnn 649.016 BIC Value ( Uses var ) =see Wei p153 599.104 R Square =1-[ R / (A- A) ] .949617 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 249.0943 252.316 .9872 2 Autoregressive-Factor # 1 1 .4699459 .102532 4.583 3 2 .7700131 .844354E-01 9.120 4 3 -.3429049 .100057 -3.427 INPUT SERIES X1 INPUT Lambda Value 5 Omega (input) -Factor # 2 3 .2040171 .728315E-01 2.801 6 4 -.2015528 .703371E-01 -2.866 7 5 -.1060601 .711927E-01 -1.490 Y(T) = 2419.7 +[X1(T)][(+ .204B 3+ .202B 4+ .106B 5)] + [(1- .470B 1- .770B 2+ .343B 3)]**-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .025 -.012 -.060 -.201 -.273 -.120 2 .025 1.000 .410 -.444 -.232 -.083 .184 3 -.012 .410 1.000 -.416 .023 .039 -.027 4 -.060 -.444 -.416 1.000 .065 .091 .008 5 -.201 -.232 .023 .065 1.000 -.276 -.620 6 -.273 -.083 .039 .091 -.276 1.000 -.339 7 -.120 .184 -.027 .008 -.620 -.339 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 249.1 Significant 2 4.583 Significant 3 9.120 Significant 4 -3.427 Significant 5 2.801 Significant 6 -2.866 Significant * 7 -1.490 Not Significant * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 .213 .147 1.44 2.23 NA .213 .147 1.44 2 -.075 .154 -.49 2.51 NA -.127 .147 -.86 3 .015 .155 .10 2.52 NA .064 .147 .43 4 .061 .155 .40 2.72 NA .036 .147 .24 5 -.123 .155 -.79 3.54 NA -.149 .147 -1.01 6 -.341 .157 -2.17 9.97 NA -.291 .147 -1.97 7 -.234 .173 -1.35 13.06 NA -.147 .147 -1.00 8 -.041 .180 -.23 13.16 .0003 -.032 .147 -.22 9 -.008 .180 -.05 13.16 .0014 -.006 .147 -.04 10 -.052 .180 -.29 13.33 .0040 -.031 .147 -.21 11 .111 .180 .62 14.11 .0070 .097 .147 .66 12 .134 .182 .74 15.28 .0092 -.037 .147 -.25 13 .176 .184 .96 17.35 .0081 .083 .147 .56 14 .128 .187 .68 18.48 .0100 .055 .147 .37 15 .085 .189 .45 19.00 .0149 .060 .147 .40 16 -.140 .190 -.74 20.44 .0154 -.204 .147 -1.38 17 -.134 .192 -.70 21.80 .0162 -.045 .147 -.31 18 .013 .194 .07 21.81 .0259 .089 .147 .60 19 -.092 .194 -.47 22.50 .0323 -.035 .147 -.24 20 -.117 .195 -.60 23.66 .0344 .036 .147 .24 21 -.108 .197 -.55 24.70 .0377 -.054 .147 -.36 22 .002 .198 .01 24.70 .0542 -.083 .147 -.56 23 -.003 .198 -.02 24.70 .0753 -.112 .147 -.76 24 -.005 .198 -.03 24.70 .1016 -.012 .147 -.08 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 .213 1.44 { } .213 1.44 { } 2 -.075 -.49 { } -.127 -.82 { } 3 .015 .10 { * } .064 .41 { } 4 .061 .40 { } .036 .23 { * } 5 -.123 -.79 { } -.149 -.96 { } 6 -.341 -2.17 {* } -.291 -1.85 {* } 7 -.234 -1.35 {* } -.147 -.85 { } 8 -.041 -.23 { * } -.032 -.18 { * } 9 -.008 -.05 { * } -.006 -.03 { * } 10 -.052 -.29 { ** } -.031 -.17 { * } 11 .111 .62 { } .097 .54 { } 12 .134 .74 { ** } -.037 -.21 { * } 13 .176 .96 { * } .083 .45 { } 14 .128 .68 { } .055 .29 { } 15 .085 .45 { } .060 .32 { } 16 -.140 -.74 { } -.204 -1.07 {* } 17 -.134 -.70 { ** } -.045 -.24 { * } 18 .013 .07 { * } .089 .46 { } 19 -.092 -.47 { } -.035 -.18 { * } 20 -.117 -.60 { ** } .036 .18 { * } 21 -.108 -.55 { } -.054 -.27 { } 22 .002 .01 { * } -.083 -.42 { ** } 23 -.003 -.02 { * } -.112 -.56 { ** } 24 -.005 -.03 { * } -.012 -.06 { * } SERIES NAME IS : INPUT THE CROSS CORRELATIONS BETWEEN THE FILTERED INPUT AND THE RESIDUALS (R) Mean of X1 444.32 Mean of R 35.583 Variance of X1 .42844E+07 Variance of R .74159E+06 St. Deviation of X1 2069.9 St. Deviation of R 861.16 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 .008 .151 .05 0 .008 .151 .05 1 .041 .152 .27 -1 -.018 .152 -.12 2 .112 .154 .73 -2 -.096 .154 -.62 3 -.096 .156 -.62 -3 .092 .156 .59 4 -.082 .158 -.52 -4 -.106 .158 -.67 5 .051 .160 .32 -5 .033 .160 .21 6 -.124 .162 -.76 -6 -.007 .162 -.04 7 .026 .164 .16 -7 .013 .164 .08 8 .100 .167 .60 -8 .030 .167 .18 9 -.021 .169 -.12 -9 -.081 .169 -.48 10 .147 .171 .86 -10 -.078 .171 -.45 11 .102 .174 .58 -11 -.117 .174 -.67 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 .008 .05 { * } .008 .05 { * } 1 .041 .27 { * } -.018 -.12 { * } 2 .112 .73 { } -.096 -.62 { } 3 -.096 -.62 { } .092 .59 { } 4 -.082 -.52 { } -.106 -.67 { } 5 .051 .32 { ** } .033 .21 { * } 6 -.124 -.76 { ** } -.007 -.04 { * } 7 .026 .16 { * } .013 .08 { * } 8 .100 .60 { ** } .030 .18 { * } 9 -.021 -.12 { * } -.081 -.48 { } 10 .147 .86 { } -.078 -.45 { } 11 .102 .58 { } -.117 -.67 { ** } DIAGNOSTIC CHECK #2B: THE INVERTIBILITY TEST FACTOR # TEST RESULT 1 Invertible DIAGNOSTIC CHECK #3: THE SUFFICIENCY TEST The Critical Value used for this test : 1.96 For the NOISE model : ACF lags that are significant 6, CCF lags that are significant NONE Since the automatic model fixup option for the Sufficiency Test is enabled, the program will now add the new parameter(s) to the model and return to the estimation stage in order to complete this iterative step. Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 40 Number of Degrees of Freedom =n-m 32 Residual Mean = R/n -.151110E-01 Sum of Squares = R .184605E+08 Variance var= R /(n) 461512. Adjusted Variance = R /(n-m) 576890. Standard Deviation = 759.533 Standard Error of the Mean = / (n-m) 134.268 Mean / its Standard Error = /[ / (n-m)] -.112544E-03 Mean Absolute Deviation = R /n 532.930 AIC Value ( Uses var ) =nln +2m 537.691 SBC Value ( Uses var ) =nln +mlnn 551.202 BIC Value ( Uses var ) =see Wei p153 526.500 R Square =1-[ R / (A- A) ] .964603 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR 1 PURE RIGHT-HAND SIDE CONS 163.7929 240.924 .6799 2 Autoregressive-Factor # 1 1 .4105241 .109321 3.755 3 2 .8019495 .621546E-01 12.90 4 3 -.2846337 .107722 -2.642 5 Autoregressive-Factor # 2 6 -.4482155 .124472 -3.601 INPUT SERIES X1 INPUT Lambda Value 6 Omega (input) -Factor # 3 3 .7802320E-01 .698496E-01 1.117 7 4 -.2141471 .600509E-01 -3.566 8 5 -.1670831E-01 .546059E-01 -.3060 Y(T) = 1567.3 +[X1(T)][(+ .078B 3+ .214B 4+ .017B 5)] + [(1- .411B 1- .802B 2+ .285B 3)(1 + .448B 6)]-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 -.135 -.030 .019 .098 -.235 -.226 .201 2 -.135 1.000 .547 -.585 -.218 .090 .201 -.284 3 -.030 .547 1.000 -.522 .265 .031 -.248 -.257 4 .019 -.585 -.522 1.000 .122 .089 -.157 .106 5 .098 -.218 .265 .122 1.000 -.267 -.841 .133 6 -.235 .090 .031 .089 -.267 1.000 -.219 -.216 7 -.226 .201 -.248 -.157 -.841 -.219 1.000 -.106 8 .201 -.284 -.257 .106 .133 -.216 -.106 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 163.8 Significant 2 3.755 Significant 3 12.90 Significant 4 -2.642 Significant 5 -3.601 Significant 6 1.117 Not Significant 7 -3.566 Significant 8 -.3060 Not Significant * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 .119 .158 .75 .61 NA .119 .158 .75 2 -.298 .160 -1.86 4.53 NA -.317 .158 -2.00 3 .099 .174 .57 4.98 NA .206 .158 1.31 4 .245 .175 1.40 7.78 NA .111 .158 .70 5 .126 .183 .68 8.54 NA .177 .158 1.12 6 -.031 .186 -.16 8.58 NA .011 .158 .07 7 -.191 .186 -1.03 10.45 NA -.194 .158 -1.23 8 -.186 .191 -.98 12.27 NA -.253 .158 -1.60 9 .044 .195 .23 12.37 .0004 -.073 .158 -.46 10 -.049 .195 -.25 12.51 .0019 -.166 .158 -1.05 11 -.083 .196 -.42 12.90 .0049 .117 .158 .74 12 -.123 .196 -.63 13.81 .0079 -.052 .158 -.33 13 -.170 .198 -.86 15.61 .0081 -.062 .158 -.39 14 -.006 .202 -.03 15.61 .0160 -.026 .158 -.16 15 .124 .202 .61 16.64 .0199 .038 .158 .24 16 -.153 .204 -.75 18.29 .0192 -.214 .158 -1.36 17 -.163 .207 -.79 20.24 .0165 -.032 .158 -.20 18 .112 .210 .53 21.20 .0198 -.005 .158 -.03 19 .044 .211 .21 21.35 .0299 -.029 .158 -.18 20 -.136 .212 -.64 22.90 .0286 -.156 .158 -.98 21 -.018 .214 -.09 22.93 .0426 .004 .158 .02 22 .079 .214 .37 23.51 .0525 -.019 .158 -.12 23 -.019 .215 -.09 23.55 .0732 -.052 .158 -.33 24 -.019 .215 -.09 23.58 .0990 -.066 .158 -.42 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 .119 .75 { } .119 .75 { } 2 -.298 -1.86 {* } -.317 -1.97 {* } 3 .099 .57 { } .206 1.19 { } 4 .245 1.40 { } .111 .64 { } 5 .126 .68 { } .177 .97 { } 6 -.031 -.16 { } .011 .06 { * } 7 -.191 -1.03 { * } -.194 -1.04 {* } 8 -.186 -.98 { * } -.253 -1.33 {* } 9 .044 .23 { * } -.073 -.37 { ** } 10 -.049 -.25 { * } -.166 -.85 {* } 11 -.083 -.42 { } .117 .60 { } 12 -.123 -.63 { } -.052 -.27 { } 13 -.170 -.86 { * } -.062 -.31 { ** } 14 -.006 -.03 { * } -.026 -.13 { * } 15 .124 .61 { ** } .038 .19 { * } 16 -.153 -.75 { * } -.214 -1.05 {* } 17 -.163 -.79 { *** } -.032 -.16 { * } 18 .112 .53 { ** } -.005 -.02 { * } 19 .044 .21 { * } -.029 -.14 { * } 20 -.136 -.64 { } -.156 -.74 {* } 21 -.018 -.09 { * } .004 .02 { * } 22 .079 .37 { ** } -.019 -.09 { * } 23 -.019 -.09 { * } -.052 -.24 { ** } 24 -.019 -.09 { * } -.066 -.31 { } SERIES NAME IS : INPUT THE CROSS CORRELATIONS BETWEEN THE FILTERED INPUT AND THE RESIDUALS (R) Mean of X1 188.34 Mean of R -.15111E-01 Variance of X1 .29010E+07 Variance of R .46151E+06 St. Deviation of X1 1703.2 St. Deviation of R 679.35 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 -.234 .158 -1.48 0 -.234 .158 -1.48 1 -.107 .160 -.67 -1 -.052 .160 -.32 2 -.115 .162 -.71 -2 -.040 .162 -.25 3 -.045 .164 -.27 -3 -.072 .164 -.44 4 -.068 .167 -.41 -4 -.060 .167 -.36 5 -.036 .169 -.21 -5 .020 .169 .12 6 -.111 .171 -.65 -6 -.119 .171 -.69 7 .131 .174 .75 -7 .118 .174 .68 8 .170 .177 .96 -8 .116 .177 .66 9 -.056 .180 -.31 -9 -.088 .180 -.49 10 .175 .183 .96 -10 -.045 .183 -.24 11 -.018 .186 -.10 -11 .030 .186 .16 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 -.234 -1.48 {* } -.234 -1.48 {* } 1 -.107 -.67 { } -.052 -.32 { } 2 -.115 -.71 { } -.040 -.25 { * } 3 -.045 -.27 { * } -.072 -.44 { } 4 -.068 -.41 { } -.060 -.36 { ** } 5 -.036 -.21 { * } .020 .12 { * } 6 -.111 -.65 { } -.119 -.69 { } 7 .131 .75 { } .118 .68 { } 8 .170 .96 { *} .116 .66 { } 9 -.056 -.31 { } -.088 -.49 { } 10 .175 .96 { *** } -.045 -.24 { * } 11 -.018 -.10 { * } .030 .16 { * } NOTE -> The program is REPLACING ARMA STRUCTURE WITH A DIFFERENCING FACTOR (A) Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 48 Number of Degrees of Freedom =n-m 44 Residual Mean = R/n -.180900E-04 Sum of Squares = R .118230E+09 Variance var= R /(n) .246313E+07 Adjusted Variance = R /(n-m) .268705E+07 Standard Deviation = 1639.22 Standard Error of the Mean = / (n-m) 247.122 Mean / its Standard Error = /[ / (n-m)] -.732025E-07 Mean Absolute Deviation = R /n 1165.92 AIC Value ( Uses var ) =nln +2m 714.413 SBC Value ( Uses var ) =nln +m*lnn 721.898 BIC Value ( Uses var ) =see Wei p153 598.973 R Square =1-[ R / (A- A) ] .832531 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS -.5277499 229.326 -.2301E-02 INPUT SERIES X1 INPUT Lambda Value Differencing 1 2 Omega (input) -Factor # 1 3 .1400341E-01 .121344 .1154 3 4 -.3662981 .118224 -3.098 4 5 .1564846 .116035 1.349 [(1-B1)]Y(T) = -.52775 +[X1(T)][(1-B1)][(+ .014B 3+ .366B 4 - .156B** 5)] + [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .077 -.113 -.083 2 .077 1.000 -.023 .031 3 -.113 -.023 1.000 .068 4 -.083 .031 .068 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 -.5277 Not Significant * 2 .1154 Not Significant 3 -3.098 Significant 4 1.349 Not Significant * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 -.501 .144 -3.47 12.83 NA -.501 .144 -3.47 2 .494 .177 2.79 25.58 NA .325 .144 2.25 3 -.374 .204 -1.83 33.03 NA -.065 .144 -.45 4 .426 .218 1.96 42.92 NA .187 .144 1.30 5 -.372 .234 -1.59 50.64 .0000 -.083 .144 -.57 6 .333 .246 1.35 56.99 .0000 .008 .144 .05 7 -.373 .255 -1.46 65.12 .0000 -.138 .144 -.96 8 .268 .267 1.01 69.44 .0000 -.068 .144 -.47 9 -.212 .272 -.78 72.21 .0000 .102 .144 .70 10 .201 .276 .73 74.77 .0000 .024 .144 .16 11 -.251 .279 -.90 78.85 .0000 -.085 .144 -.59 12 .195 .283 .69 81.37 .0000 -.029 .144 -.20 13 -.116 .286 -.41 82.30 .0000 .098 .144 .68 14 .094 .287 .33 82.93 .0000 -.044 .144 -.31 15 -.032 .288 -.11 83.00 .0000 .094 .144 .65 16 -.002 .288 -.01 83.00 .0000 -.069 .144 -.48 17 .015 .288 .05 83.02 .0000 .011 .144 .08 18 .006 .288 .02 83.02 .0000 .006 .144 .04 19 .004 .288 .02 83.03 .0000 -.025 .144 -.17 20 -.084 .288 -.29 83.63 .0000 -.060 .144 -.41 21 -.059 .288 -.20 83.94 .0000 -.221 .144 -1.53 22 -.015 .288 -.05 83.96 .0000 -.011 .144 -.08 23 -.054 .289 -.19 84.24 .0000 -.062 .144 -.43 24 .007 .289 .02 84.24 .0000 .051 .144 .36 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 -.501 -3.47 {* } -.501 -3.47 {* } 2 .494 2.79 { } .325 1.83 { } 3 -.374 -1.83 { } -.065 -.32 { } 4 .426 1.96 { **} .187 .86 { } 5 -.372 -1.59 { } -.083 -.35 { } 6 .333 1.35 { ** } .008 .03 { * } 7 -.373 -1.46 {* } -.138 -.54 { } 8 .268 1.01 { } -.068 -.26 { } 9 -.212 -.78 { * } .102 .37 { } 10 .201 .73 { *** } .024 .09 { * } 11 -.251 -.90 { } -.085 -.31 { } 12 .195 .69 { * } -.029 -.10 { * } 13 -.116 -.41 { } .098 .34 { } 14 .094 .33 { ** } -.044 -.15 { * } 15 -.032 -.11 { * } .094 .33 { ** } 16 -.002 -.01 { * } -.069 -.24 { ** } 17 .015 .05 { * } .011 .04 { * } 18 .006 .02 { * } .006 .02 { * } 19 .004 .02 { * } -.025 -.09 { * } 20 -.084 -.29 { } -.060 -.21 { } 21 -.059 -.20 { } -.221 -.77 {* } 22 -.015 -.05 { * } -.011 -.04 { * } 23 -.054 -.19 { } -.062 -.22 { } 24 .007 .02 { * } .051 .18 { } SERIES NAME IS : INPUT THE CROSS CORRELATIONS BETWEEN THE FILTERED INPUT AND THE RESIDUALS (R) Mean of X1 444.32 Mean of R -131.22 Variance of X1 .42844E+07 Variance of R .18504E+07 St. Deviation of X1 2069.9 St. Deviation of R 1360.3 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 -.108 .151 -.71 0 -.108 .151 -.71 1 .077 .152 .51 -1 .182 .152 1.19 2 .048 .154 .31 -2 -.171 .154 -1.11 3 .199 .156 1.27 -3 .139 .156 .89 4 -.246 .158 -1.55 -4 -.034 .158 -.21 5 .289 .160 1.80 -5 .098 .160 .61 6 -.155 .162 -.96 -6 -.056 .162 -.35 7 .094 .164 .57 -7 -.014 .164 -.08 8 -.141 .167 -.85 -8 .100 .167 .60 9 .106 .169 .63 -9 -.153 .169 -.90 10 -.022 .171 -.13 -10 .061 .171 .35 11 .051 .174 .30 -11 -.115 .174 -.66 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 -.108 -.71 { } -.108 -.71 { } 1 .077 .51 { } .182 1.19 { ***} 2 .048 .31 { * } -.171 -1.11 {* } 3 .199 1.27 { } .139 .89 { } 4 -.246 -1.55 { } -.034 -.21 { * } 5 .289 1.80 { } .098 .61 { } 6 -.155 -.96 { } -.056 -.35 { } 7 .094 .57 { ** } -.014 -.08 { * } 8 -.141 -.85 { } .100 .60 { } 9 .106 .63 { } -.153 -.90 {* } 10 -.022 -.13 { * } .061 .35 { } 11 .051 .30 { } -.115 -.66 { ** } DIAGNOSTIC CHECK #3: THE SUFFICIENCY TEST The Critical Value used for this test : 1.96 For the NOISE model : ACF lags that are significant 1, 2, CCF lags that are significant NONE Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 48 Number of Degrees of Freedom =n-m 44 Residual Mean = R/n -.579013E-09 Sum of Squares = R .118230E+09 Variance var= R /(n) .246313E+07 Adjusted Variance = R /(n-m) .268705E+07 Standard Deviation = 1639.22 Standard Error of the Mean = / (n-m) 247.122 Mean / its Standard Error = /[ / (n-m)] -.234302E-11 Mean Absolute Deviation = R /n 1165.92 AIC Value ( Uses var ) =nln +2m 714.413 SBC Value ( Uses var ) =nln +m*lnn 721.898 BIC Value ( Uses var ) =see Wei p153 598.973 R Square =1-[ R / (A- A) ] .832531 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS -.5277696 229.326 -.2301E-02 INPUT SERIES X1 INPUT Lambda Value Differencing 1 2 Omega (input) -Factor # 1 3 .1400341E-01 .121344 .1154 3 4 -.3662981 .118224 -3.098 4 5 .1564846 .116035 1.349 [(1-B1)]Y(T) = -.52777 +[X1(T)][(1-B1)][(+ .014B 3+ .366B 4 - .156B** 5)] + [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .077 -.113 -.083 2 .077 1.000 -.023 .031 3 -.113 -.023 1.000 .068 4 -.083 .031 .068 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 -.5278 Not Significant * 2 .1154 Not Significant 3 -3.098 Significant 4 1.349 Not Significant * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 -.501 .144 -3.47 12.83 NA -.501 .144 -3.47 2 .494 .177 2.79 25.58 NA .325 .144 2.25 3 -.374 .204 -1.83 33.03 NA -.065 .144 -.45 4 .426 .218 1.96 42.92 NA .187 .144 1.30 5 -.372 .234 -1.59 50.64 .0000 -.083 .144 -.57 6 .333 .246 1.35 56.99 .0000 .008 .144 .05 7 -.373 .255 -1.46 65.12 .0000 -.138 .144 -.96 8 .268 .267 1.01 69.44 .0000 -.068 .144 -.47 9 -.212 .272 -.78 72.21 .0000 .102 .144 .70 10 .201 .276 .73 74.77 .0000 .024 .144 .16 11 -.251 .279 -.90 78.85 .0000 -.085 .144 -.59 12 .195 .283 .69 81.37 .0000 -.029 .144 -.20 13 -.116 .286 -.41 82.30 .0000 .098 .144 .68 14 .094 .287 .33 82.93 .0000 -.044 .144 -.31 15 -.032 .288 -.11 83.00 .0000 .094 .144 .65 16 -.002 .288 -.01 83.00 .0000 -.069 .144 -.48 17 .015 .288 .05 83.02 .0000 .011 .144 .08 18 .006 .288 .02 83.02 .0000 .006 .144 .04 19 .004 .288 .02 83.03 .0000 -.025 .144 -.17 20 -.084 .288 -.29 83.63 .0000 -.060 .144 -.41 21 -.059 .288 -.20 83.94 .0000 -.221 .144 -1.53 22 -.015 .288 -.05 83.96 .0000 -.011 .144 -.08 23 -.054 .289 -.19 84.24 .0000 -.062 .144 -.43 24 .007 .289 .02 84.24 .0000 .051 .144 .36 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 -.501 -3.47 {* } -.501 -3.47 {* } 2 .494 2.79 { } .325 1.83 { } 3 -.374 -1.83 { } -.065 -.32 { } 4 .426 1.96 { **} .187 .86 { } 5 -.372 -1.59 { } -.083 -.35 { } 6 .333 1.35 { ** } .008 .03 { * } 7 -.373 -1.46 {* } -.138 -.54 { } 8 .268 1.01 { } -.068 -.26 { } 9 -.212 -.78 { * } .102 .37 { } 10 .201 .73 { *** } .024 .09 { * } 11 -.251 -.90 { } -.085 -.31 { } 12 .195 .69 { * } -.029 -.10 { * } 13 -.116 -.41 { } .098 .34 { } 14 .094 .33 { ** } -.044 -.15 { * } 15 -.032 -.11 { * } .094 .33 { ** } 16 -.002 -.01 { * } -.069 -.24 { ** } 17 .015 .05 { * } .011 .04 { * } 18 .006 .02 { * } .006 .02 { * } 19 .004 .02 { * } -.025 -.09 { * } 20 -.084 -.29 { } -.060 -.21 { } 21 -.059 -.20 { } -.221 -.77 {* } 22 -.015 -.05 { * } -.011 -.04 { * } 23 -.054 -.19 { } -.062 -.22 { } 24 .007 .02 { * } .051 .18 { } SERIES NAME IS : INPUT THE CROSS CORRELATIONS BETWEEN THE FILTERED INPUT AND THE RESIDUALS (R) Mean of X1 444.32 Mean of R -131.22 Variance of X1 .42844E+07 Variance of R .18504E+07 St. Deviation of X1 2069.9 St. Deviation of R 1360.3 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 -.108 .151 -.71 0 -.108 .151 -.71 1 .077 .152 .51 -1 .182 .152 1.19 2 .048 .154 .31 -2 -.171 .154 -1.11 3 .199 .156 1.27 -3 .139 .156 .89 4 -.246 .158 -1.55 -4 -.034 .158 -.21 5 .289 .160 1.80 -5 .098 .160 .61 6 -.155 .162 -.96 -6 -.056 .162 -.35 7 .094 .164 .57 -7 -.014 .164 -.08 8 -.141 .167 -.85 -8 .100 .167 .60 9 .106 .169 .63 -9 -.153 .169 -.90 10 -.022 .171 -.13 -10 .061 .171 .35 11 .051 .174 .30 -11 -.115 .174 -.66 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 -.108 -.71 { } -.108 -.71 { } 1 .077 .51 { } .182 1.19 { ***} 2 .048 .31 { * } -.171 -1.11 {* } 3 .199 1.27 { } .139 .89 { } 4 -.246 -1.55 { } -.034 -.21 { * } 5 .289 1.80 { } .098 .61 { } 6 -.155 -.96 { } -.056 -.35 { } 7 .094 .57 { ** } -.014 -.08 { * } 8 -.141 -.85 { } .100 .60 { } 9 .106 .63 { } -.153 -.90 {* } 10 -.022 -.13 { * } .061 .35 { } 11 .051 .30 { } -.115 -.66 { ** } DIAGNOSTIC CHECK #3: THE SUFFICIENCY TEST The Critical Value used for this test : 1.96 For the NOISE model : ACF lags that are significant 1, 2, CCF lags that are significant NONE KENDALL RANK CORRELATION ( TEST) FOR SUFFICIENCY SERIES NAME TAU( ) P VALUE INPUT .047 .803 ADVISORY THE TEST FOR CONSTANCY OF PARAMETERS WILL NOT BE EXECUTED. Analysis for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT DIAGNOSTIC CHECK #4: THE OUTLIER TEST The Critical Value used for this test : .10 TYPE OF THE PATTERN CYCLE TIME DATE REGRESSION P VALUE INTERVENTION (T) WEIGHT (OUTLIER) Additive SeasPulse 12 9 1992/ 12 -2267.6 .0384 Additive Pulse NA 8 1992/ 11 4150.1 .0321 Additive Pulse NA 19 1993/ 10 -3221.2 .0734 Additive Pulse NA 16 1993/ 7 3117.7 .0641 Additive Pulse NA 15 1993/ 6 -2957.1 .0574 Additive Pulse NA 17 1993/ 8 -2738.4 .0567 Additive Pulse NA 14 1993/ 5 2623.2 .0495 Additive SeasPulse 12 10 1993/ 1 1317.6 .0381 Additive Pulse NA 7 1992/ 10 2519.7 .0233 Additive Pulse NA 24 1994/ 3 2111.5 .0385 Additive Pulse NA 12 1993/ 3 1972.7 .0338 Additive Pulse NA 20 1993/ 11 1660.5 .0537 Additive Pulse NA 39 1995/ 6 1689.4 .0316 Additive Pulse NA 30 1994/ 9 -1386.0 .0559 Additive Pulse NA 23 1994/ 2 -1421.9 .0315 Since the automatic model fixup option for the Outlier Test is enabled, the program will add variables to the model for the identified outliers, subject to the program maximum. The program will then start the the iterative process of transfer function model identification, estimation and diagnostic checking. The forecasts will include the 'known' future values of the intervention variables in the computation of the output series forecast values. Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MINE X2 = I~AS0009 1992/ 12 SEASP MINE X3 = I~AP0008 1992/ 11 PULSE MINE X4 = I~AP0019 1993/ 10 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 48 Number of Degrees of Freedom =n-m 41 Residual Mean = R/n .293795E-04 Sum of Squares = R .707927E+08 Variance var= R /(n) .147485E+07 Adjusted Variance = R /(n-m) .172665E+07 Standard Deviation = 1314.02 Standard Error of the Mean = / (n-m) 205.216 Mean / its Standard Error = /[ / (n-m)] .143164E-06 Mean Absolute Deviation = R /n 878.994 AIC Value ( Uses var ) =nln +2m 695.795 SBC Value ( Uses var ) =nln +m*lnn 708.894 BIC Value ( Uses var ) =see Wei p153 616.534 R Square =1-[ R / (A- A) ] .899725 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS 178.1350 188.491 .9451 INPUT SERIES X1 INPUT Lambda Value Differencing 1 2 Omega (input) -Factor # 1 3 -.3273223E-01 .993871E-01 -.3293 3 4 -.3295056 .929305E-01 -3.546 4 5 .1490819 .934446E-01 1.595 INPUT SERIES X2 I~AS0009 1992/ 12 SEASP Lambda Value 5 Omega (input) -Factor # 2 0 -2372.004 640.367 -3.704 INPUT SERIES X3 I~AP0008 1992/ 11 PULSE Lambda Value 6 Omega (input) -Factor # 3 0 3831.689 1271.58 3.013 INPUT SERIES X4 I~AP0019 1993/ 10 PULSE Lambda Value 7 Omega (input) -Factor # 4 0 -3552.552 1319.46 -2.692 [(1-B1)]Y(T) = 178.13 +[X1(T)][(1-B1)][(- .033B 3+ .330B 4 - .149B** 5)] +[X2(T)][(- 2372.0 )] +[X3(T)][(+ 3831.7 )] +[X4(T)][(- 3552.6 )] + [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .038 -.103 -.003 -.297 -.148 -.115 2 .038 1.000 -.074 -.020 -.035 .081 .318 3 -.103 -.074 1.000 .072 .041 .027 -.166 4 -.003 -.020 .072 1.000 -.108 -.240 -.122 5 -.297 -.035 .041 -.108 1.000 .069 .037 6 -.148 .081 .027 -.240 .069 1.000 .068 7 -.115 .318 -.166 -.122 .037 .068 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 178.1 Significant * 2 -.3293 Not Significant 3 -3.546 Significant 4 1.595 Not Significant 5 -3.704 Significant 6 3.013 Significant 7 -2.692 Significant Since the automatic model fixup option for the Necessity Test is enabled, the program will now delete the parameter with the lowest non-significant T-ratio and return to the estimation stage in order to complete this iterative step. * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. NOTE -> Deleting model structure. Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MINE X2 = I~AS0009 1992/ 12 SEASP MINE X3 = I~AP0008 1992/ 11 PULSE MINE X4 = I~AP0019 1993/ 10 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 48 Number of Degrees of Freedom =n-m 42 Residual Mean = R/n .135351E-01 Sum of Squares = R .709527E+08 Variance var= R /(n) .147818E+07 Adjusted Variance = R /(n-m) .168935E+07 Standard Deviation = 1299.75 Standard Error of the Mean = / (n-m) 200.556 Mean / its Standard Error = /[ / (n-m)] .674880E-04 Mean Absolute Deviation = R /n 879.871 AIC Value ( Uses var ) =nln +2m 693.903 SBC Value ( Uses var ) =nln +mlnn 705.131 BIC Value ( Uses var ) =see Wei p153 613.247 R Square =1-[ R / (A- A) ] .899498 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS 180.4505 188.569 .9569 INPUT SERIES X1 INPUT Lambda Value Differencing 1 2 Omega (input) -Factor # 1 4 .3317036 .927788E-01 3.575 3 5 .1484820 .935317E-01 1.588 INPUT SERIES X2 I~AS0009 1992/ 12 SEASP Lambda Value 4 Omega (input) -Factor # 2 0 -2379.336 640.698 -3.714 INPUT SERIES X3 I~AP0008 1992/ 11 PULSE Lambda Value 5 Omega (input) -Factor # 3 0 3865.822 1268.79 3.047 INPUT SERIES X4 I~AP0019 1993/ 10 PULSE Lambda Value 6 Omega (input) -Factor # 4 0 -3414.561 1252.28 -2.727 [(1-B1)]Y(T) = 180.45 +[X1(T)][(1-B1)][(+ .332B 4- .148B 5)] +[X2(T)][(- 2379.3 )] +[X3(T)][(+ 3865.8 )] +[X4(T)][(- 3414.6 )] + [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .101 -.002 -.296 -.152 -.134 2 .101 1.000 -.071 -.039 -.033 .150 3 -.002 -.071 1.000 -.109 -.240 -.122 4 -.296 -.039 -.109 1.000 .072 .050 5 -.152 -.033 -.240 .072 1.000 .044 6 -.134 .150 -.122 .050 .044 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 180.5 Significant 2 3.575 Significant 3 1.588 Not Significant 4 -3.714 Significant 5 3.047 Significant 6 -2.727 Significant Since the automatic model fixup option for the Necessity Test is enabled, the program will now delete the parameter with the lowest non-significant T-ratio and return to the estimation stage in order to complete this iterative step. * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. NOTE -> Deleting model structure. Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MINE X2 = I~AS0009 1992/ 12 SEASP MINE X3 = I~AP0008 1992/ 11 PULSE MINE X4 = I~AP0019 1993/ 10 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 49 Number of Degrees of Freedom =n-m 44 Residual Mean = R/n -.313082E-05 Sum of Squares = R .749141E+08 Variance var= R /(n) .152886E+07 Adjusted Variance = R /(n-m) .170259E+07 Standard Deviation = 1304.83 Standard Error of the Mean = / (n-m) 196.711 Mean / its Standard Error = /[ / (n-m)] -.159158E-07 Mean Absolute Deviation = R /n 862.092 AIC Value ( Uses var ) =nln +2m 707.762 SBC Value ( Uses var ) =nln +m*lnn 717.221 BIC Value ( Uses var ) =see Wei p153 621.661 R Square =1-[ R / (A- A) ] .894007 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS 193.8718 189.031 1.026 INPUT SERIES X1 INPUT Lambda Value Differencing 1 2 Omega (input) -Factor # 1 4 .3494024 .923095E-01 3.785 INPUT SERIES X2 I~AS0009 1992/ 12 SEASP Lambda Value 3 Omega (input) -Factor # 2 0 -2282.351 646.805 -3.529 INPUT SERIES X3 I~AP0008 1992/ 11 PULSE Lambda Value 4 Omega (input) -Factor # 3 0 4332.017 1252.11 3.460 INPUT SERIES X4 I~AP0019 1993/ 10 PULSE Lambda Value 5 Omega (input) -Factor # 4 0 -3169.693 1264.08 -2.508 [(1-B1)]Y(T) = 193.87 +[X1(T)][(1-B1)][(+ .349B** 4)] +[X2(T)][(- 2282.4 )] +[X3(T)][(+ 4332.0 )] +[X4(T)][(- 3169.7 )] + [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .071 -.293 -.153 -.139 2 .071 1.000 -.037 -.046 .145 3 -.293 -.037 1.000 .046 .038 4 -.153 -.046 .046 1.000 .016 5 -.139 .145 .038 .016 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 193.9 Significant 2 3.785 Significant 3 -3.529 Significant 4 3.460 Significant * 5 -2.508 Significant * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 -.506 .143 -3.54 13.35 NA -.506 .143 -3.54 2 .512 .176 2.91 27.28 NA .344 .143 2.41 3 -.438 .204 -2.15 37.68 NA -.142 .143 -1.00 4 .309 .222 1.39 43.00 NA -.060 .143 -.42 5 -.347 .231 -1.50 49.83 NA -.106 .143 -.74 6 .327 .241 1.35 56.03 .0000 .109 .143 .76 7 -.210 .250 -.84 58.65 .0000 .103 .143 .72 8 .126 .254 .50 59.62 .0000 -.168 .143 -1.17 9 -.181 .255 -.71 61.67 .0000 -.120 .143 -.84 10 .067 .258 .26 61.96 .0000 -.038 .143 -.27 11 -.087 .258 -.34 62.47 .0000 .035 .143 .25 12 .098 .259 .38 63.11 .0000 .035 .143 .25 13 .048 .259 .18 63.27 .0000 .117 .143 .82 14 .051 .259 .20 63.46 .0000 .090 .143 .63 15 .063 .260 .24 63.75 .0000 .121 .143 .84 16 -.166 .260 -.64 65.84 .0000 -.211 .143 -1.47 17 .017 .262 .07 65.86 .0000 -.202 .143 -1.41 18 -.068 .262 -.26 66.23 .0000 .078 .143 .54 19 .037 .263 .14 66.35 .0000 -.009 .143 -.06 20 .041 .263 .16 66.49 .0000 .080 .143 .56 21 -.029 .263 -.11 66.57 .0000 -.086 .143 -.60 22 -.013 .263 -.05 66.58 .0000 -.011 .143 -.08 23 -.044 .263 -.17 66.77 .0000 .100 .143 .70 24 -.033 .263 -.12 66.87 .0000 -.139 .143 -.97 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 -.506 -3.54 {* } -.506 -3.54 {* } 2 .512 2.91 { } .344 1.96 { } 3 -.438 -2.15 { } -.142 -.70 { } 4 .309 1.39 { } -.060 -.27 { } 5 -.347 -1.50 { } -.106 -.46 { } 6 .327 1.35 { ** } .109 .45 { } 7 -.210 -.84 { * } .103 .41 { } 8 .126 .50 { } -.168 -.66 {* } 9 -.181 -.71 { * } -.120 -.47 { } 10 .067 .26 { ** } -.038 -.15 { * } 11 -.087 -.34 { ** } .035 .14 { * } 12 .098 .38 { ** } .035 .14 { * } 13 .048 .18 { * } .117 .45 { } 14 .051 .20 { } .090 .35 { } 15 .063 .24 { } .121 .46 { } 16 -.166 -.64 { * } -.211 -.81 {*** } 17 .017 .07 { * } -.202 -.77 {* } 18 -.068 -.26 { } .078 .30 { ** } 19 .037 .14 { * } -.009 -.03 { * } 20 .041 .16 { * } .080 .30 { ** } 21 -.029 -.11 { * } -.086 -.33 { ** } 22 -.013 -.05 { * } -.011 -.04 { * } 23 -.044 -.17 { * } .100 .38 { ** } 24 -.033 -.12 { * } -.139 -.53 { } SERIES NAME IS : INPUT THE CROSS CORRELATIONS BETWEEN THE FILTERED INPUT AND THE RESIDUALS (R) Mean of X1 444.32 Mean of R -81.935 Variance of X1 .42844E+07 Variance of R .14792E+07 St. Deviation of X1 2069.9 St. Deviation of R 1216.2 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 -.211 .151 -1.40 0 -.211 .151 -1.40 1 .106 .152 .70 -1 .146 .152 .96 2 .059 .154 .38 -2 -.284 .154 -1.84 3 .091 .156 .58 -3 .083 .156 .53 4 -.212 .158 -1.34 -4 -.122 .158 -.77 5 .171 .160 1.07 -5 .111 .160 .69 6 -.233 .162 -1.44 -6 -.097 .162 -.60 7 .219 .164 1.34 -7 .042 .164 .26 8 .019 .167 .12 -8 .095 .167 .57 9 .140 .169 .83 -9 -.130 .169 -.77 10 .112 .171 .65 -10 .073 .171 .43 11 .022 .174 .13 -11 -.100 .174 -.57 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 -.211 -1.40 {* } -.211 -1.40 {* } 1 .106 .70 { } .146 .96 { } 2 .059 .38 { } -.284 -1.84 {* } 3 .091 .58 { } .083 .53 { } 4 -.212 -1.34 {* } -.122 -.77 { } 5 .171 1.07 { } .111 .69 { } 6 -.233 -1.44 { } -.097 -.60 { } 7 .219 1.34 { } .042 .26 { } 8 .019 .12 { * } .095 .57 { } 9 .140 .83 { } -.130 -.77 { } 10 .112 .65 { } .073 .43 { ** } 11 .022 .13 { * } -.100 -.57 { ** } DIAGNOSTIC CHECK #2B: THE INVERTIBILITY TEST FACTOR # TEST RESULT 1 Invertible 2 Invertible 3 Invertible DIAGNOSTIC CHECK #3: THE SUFFICIENCY TEST The Critical Value used for this test : 1.96 For the NOISE model : ACF lags that are significant 1, 2, 3, CCF lags that are significant NONE Since the automatic model fixup option for the Sufficiency Test is enabled, the program will now add the new parameter(s) to the model and return to the estimation stage in order to complete this iterative step. Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MINE X2 = I~AS0009 1992/ 12 SEASP MINE X3 = I~AP0008 1992/ 11 PULSE MINE X4 = I~AP0019 1993/ 10 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 46 Number of Degrees of Freedom =n-m 38 Residual Mean = R/n .381304E-01 Sum of Squares = R .302648E+08 Variance var= R /(n) 657931. Adjusted Variance = R /(n-m) 796443. Standard Deviation = 892.436 Standard Error of the Mean = / (n-m) 144.772 Mean / its Standard Error = /[ / (n-m)] .263382E-03 Mean Absolute Deviation = R /n 617.466 AIC Value ( Uses var ) =nln +2m 632.255 SBC Value ( Uses var ) =nln +m*lnn 646.884 BIC Value ( Uses var ) =see Wei p153 603.716 R Square =1-[ R / (A- A) ] .955740 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS 25.58238 131.765 .1942 2 Autoregressive-Factor # 1 1 -.2774867 .123695 -2.243 3 2 .3863572 .967808E-01 3.992 4 3 -.1170101 .108566 -1.078 INPUT SERIES X1 INPUT Lambda Value Differencing 1 5 Omega (input) -Factor # 2 4 .2611110 .614930E-01 4.246 INPUT SERIES X2 I~AS0009 1992/ 12 SEASP Lambda Value 6 Omega (input) -Factor # 3 0 -1529.225 410.859 -3.722 INPUT SERIES X3 I~AP0008 1992/ 11 PULSE Lambda Value 7 Omega (input) -Factor # 4 0 -1670.435 2174.62 -.7682 INPUT SERIES X4 I~AP0019 1993/ 10 PULSE Lambda Value 8 Omega (input) -Factor # 5 0 -1522.969 777.519 -1.959 [(1-B1)]Y(T) = 25.376 +[X1(T)][(1-B1)][(+ .261B 4)] +[X2(T)][(- 1529.2 )] +[X3(T)][(- 1670.4 )] +[X4(T)][(- 1523.0 )] + [(1+ .277B 1- .386B 2+ .117B 3)]**-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .125 -.275 -.042 -.202 -.016 -.227 -.180 2 .125 1.000 -.020 .025 .044 -.171 -.235 -.019 3 -.275 -.020 1.000 .019 .110 -.276 -.102 .259 4 -.042 .025 .019 1.000 .015 -.517 .313 .408 5 -.202 .044 .110 .015 1.000 .106 .229 -.031 6 -.016 -.171 -.276 -.517 .106 1.000 .115 -.629 7 -.227 -.235 -.102 .313 .229 .115 1.000 .260 8 -.180 -.019 .259 .408 -.031 -.629 .260 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 25.58 Significant 2 -2.243 Significant 3 3.992 Significant * 4 -1.078 Not Significant 5 4.246 Significant 6 -3.722 Significant 7 -.7682 Not Significant 8 -1.959 Not Significant Since the automatic model fixup option for the Necessity Test is enabled, the program will now delete the parameter with the lowest non-significant T-ratio and return to the estimation stage in order to complete this iterative step. * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. NOTE -> Deleting model structure. Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MINE X2 = I~AS0009 1992/ 12 SEASP MINE X3 = I~AP0008 1992/ 11 PULSE MINE X4 = I~AP0019 1993/ 10 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 47 Number of Degrees of Freedom =n-m 40 Residual Mean = R/n .764176 Sum of Squares = R .386711E+08 Variance var= R /(n) 822789. Adjusted Variance = R /(n-m) 966778. Standard Deviation = 983.248 Standard Error of the Mean = / (n-m) 155.465 Mean / its Standard Error = /[ / (n-m)] .491541E-02 Mean Absolute Deviation = R /n 702.629 AIC Value ( Uses var ) =nln +2m 654.161 SBC Value ( Uses var ) =nln +mlnn 667.112 BIC Value ( Uses var ) =see Wei p153 611.438 R Square =1-[ R / (A- A) ] .945224 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS 43.35526 143.053 .3031 2 Autoregressive-Factor # 1 1 -.3139896 .151571 -2.072 3 2 .4674754 .151100 3.094 INPUT SERIES X1 INPUT Lambda Value Differencing 1 4 Omega (input) -Factor # 2 4 .2508902 .679371E-01 3.693 INPUT SERIES X2 I~AS0009 1992/ 12 SEASP Lambda Value 5 Omega (input) -Factor # 3 0 -1633.221 419.866 -3.890 INPUT SERIES X3 I~AP0008 1992/ 11 PULSE Lambda Value 6 Omega (input) -Factor # 4 0 3296.573 904.179 3.646 INPUT SERIES X4 I~AP0019 1993/ 10 PULSE Lambda Value 7 Omega (input) -Factor # 5 0 -1569.306 895.323 -1.753 [(1-B1)]Y(T) = 51.216 +[X1(T)][(1-B1)][(+ .251B 4)] +[X2(T)][(- 1633.2 )] +[X3(T)][(+ 3296.6 )] +[X4(T)][(- 1569.3 )] + [(1+ .314B 1- .467B 2)]-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .151 -.263 .043 -.232 -.241 -.252 2 .151 1.000 -.127 .274 -.047 -.371 -.367 3 -.263 -.127 1.000 -.111 .225 .149 .110 4 .043 .274 -.111 1.000 -.153 -.457 -.382 5 -.232 -.047 .225 -.153 1.000 .324 .399 6 -.241 -.371 .149 -.457 .324 1.000 .713 7 -.252 -.367 .110 -.382 .399 .713 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 43.36 Significant 2 -2.072 Significant 3 3.094 Significant 4 3.693 Significant 5 -3.890 Significant 6 3.646 Significant 7 -1.753 Not Significant Since the automatic model fixup option for the Necessity Test is enabled, the program will now delete the parameter with the lowest non-significant T-ratio and return to the estimation stage in order to complete this iterative step. * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. NOTE -> Deleting model structure. NOTE -> The program is deleting the input series from the model since it does not have any significant parameters. Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MINE X2 = I~AS0009 1992/ 12 SEASP MINE X3 = I~AP0008 1992/ 11 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 47 Number of Degrees of Freedom =n-m 41 Residual Mean = R/n .332499E-02 Sum of Squares = R .418944E+08 Variance var= R /(n) 891370. Adjusted Variance = R /(n-m) .102181E+07 Standard Deviation = 1010.85 Standard Error of the Mean = / (n-m) 157.868 Mean / its Standard Error = /[ / (n-m)] .210618E-04 Mean Absolute Deviation = R /n 737.235 AIC Value ( Uses var ) =nln +2m 655.924 SBC Value ( Uses var ) =nln +mlnn 667.025 BIC Value ( Uses var ) =see Wei p153 607.302 R Square =1-[ R / (A- A) ] .940658 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS 8.686961 143.147 .6069E-01 2 Autoregressive-Factor # 1 1 -.3145004 .143049 -2.199 3 2 .4777480 .136760 3.493 INPUT SERIES X1 INPUT Lambda Value Differencing 1 4 Omega (input) -Factor # 2 4 .2710837 .709015E-01 3.823 INPUT SERIES X2 I~AS0009 1992/ 12 SEASP Lambda Value 5 Omega (input) -Factor # 3 0 -1519.650 425.882 -3.568 INPUT SERIES X3 I~AP0008 1992/ 11 PULSE Lambda Value 6 Omega (input) -Factor # 4 0 3347.436 928.127 3.607 [(1-B1)]Y(T) = 10.382 +[X1(T)][(1-B1)][(+ .271B 4)] +[X2(T)][(- 1519.6 )] +[X3(T)][(+ 3347.4 )] + [(1+ .315B 1- .478B 2)]-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .119 -.225 -.020 -.119 -.121 2 .119 1.000 -.150 .279 -.399 -.384 3 -.225 -.150 1.000 -.106 .133 .095 4 -.020 .279 -.106 1.000 -.440 -.355 5 -.119 -.399 .133 -.440 1.000 .669 6 -.121 -.384 .095 -.355 .669 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 8.687 Significant 2 -2.199 Significant 3 3.493 Significant 4 3.823 Significant 5 -3.568 Significant 6 3.607 Significant * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 .029 .146 .20 .04 NA .029 .146 .20 2 -.029 .146 -.20 .08 NA -.030 .146 -.20 3 -.096 .146 -.66 .57 NA -.094 .146 -.65 4 .007 .147 .05 .57 NA .011 .146 .08 5 -.287 .147 -1.94 5.08 NA -.296 .146 -2.03 6 -.075 .159 -.47 5.39 NA -.073 .146 -.50 7 -.128 .160 -.80 6.34 .0118 -.164 .146 -1.12 8 -.015 .162 -.10 6.35 .0417 -.092 .146 -.63 9 -.043 .162 -.27 6.47 .0910 -.087 .146 -.60 10 .092 .162 .57 7.00 .1361 -.043 .146 -.29 11 .166 .163 1.01 8.75 .1194 .111 .146 .76 12 -.016 .167 -.09 8.77 .1871 -.134 .146 -.92 13 .144 .167 .86 10.17 .1793 .150 .146 1.03 14 .138 .169 .82 11.50 .1749 .115 .146 .79 15 -.044 .172 -.25 11.64 .2345 -.036 .146 -.25 16 -.286 .172 -1.66 17.71 .0600 -.188 .146 -1.29 17 -.086 .182 -.47 18.27 .0754 -.099 .146 -.68 18 .035 .183 .19 18.37 .1049 .130 .146 .89 19 .056 .183 .31 18.63 .1350 .085 .146 .58 20 -.049 .183 -.27 18.84 .1713 -.013 .146 -.09 21 .002 .183 .01 18.84 .2213 -.104 .146 -.72 22 .066 .183 .36 19.23 .2567 .011 .146 .07 23 -.067 .184 -.36 19.66 .2919 -.112 .146 -.77 24 -.062 .184 -.34 20.05 .3302 -.152 .146 -1.04 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 .029 .20 { * } .029 .20 { * } 2 -.029 -.20 { * } -.030 -.20 { * } 3 -.096 -.66 { } -.094 -.65 { } 4 .007 .05 { * } .011 .08 { * } 5 -.287 -1.94 {* } -.296 -2.01 {* } 6 -.075 -.47 { } -.073 -.46 { } 7 -.128 -.80 { } -.164 -1.03 {* } 8 -.015 -.10 { * } -.092 -.57 { ** } 9 -.043 -.27 { * } -.087 -.54 { } 10 .092 .57 { } -.043 -.27 { * } 11 .166 1.01 { } .111 .68 { } 12 -.016 -.09 { } -.134 -.80 { } 13 .144 .86 { } .150 .90 { } 14 .138 .82 { } .115 .68 { ** } 15 -.044 -.25 { * } -.036 -.21 { * } 16 -.286 -1.66 {* } -.188 -1.09 {* } 17 -.086 -.47 { } -.099 -.55 { } 18 .035 .19 { * } .130 .71 { } 19 .056 .31 { } .085 .47 { ** } 20 -.049 -.27 { * } -.013 -.07 { * } 21 .002 .01 { * } -.104 -.57 { } 22 .066 .36 { } .011 .06 { * } 23 -.067 -.36 { } -.112 -.61 { } 24 -.062 -.34 { } -.152 -.82 {* } SERIES NAME IS : INPUT THE CROSS CORRELATIONS BETWEEN THE FILTERED INPUT AND THE RESIDUALS (R) Mean of X1 444.32 Mean of R -17.238 Variance of X1 .42844E+07 Variance of R .76387E+06 St. Deviation of X1 2069.9 St. Deviation of R 874.00 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 .137 .151 .91 0 .137 .151 .91 1 -.014 .152 -.09 -1 -.015 .152 -.10 2 .075 .154 .48 -2 -.234 .154 -1.52 3 .200 .156 1.28 -3 .243 .156 1.56 4 -.052 .158 -.33 -4 -.003 .158 -.02 5 -.074 .160 -.46 -5 -.019 .160 -.12 6 -.141 .162 -.87 -6 .055 .162 .34 7 .052 .164 .31 -7 .151 .164 .92 8 -.042 .167 -.25 -8 -.034 .167 -.20 9 -.021 .169 -.12 -9 -.053 .169 -.31 10 .285 .171 1.66 -10 .044 .171 .26 11 .011 .174 .06 -11 -.137 .174 -.78 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 .137 .91 { } .137 .91 { } 1 -.014 -.09 { * } -.015 -.10 { * } 2 .075 .48 { } -.234 -1.52 {* } 3 .200 1.28 { } .243 1.56 { } 4 -.052 -.33 { ** } -.003 -.02 { * } 5 -.074 -.46 { ** } -.019 -.12 { * } 6 -.141 -.87 { } .055 .34 { } 7 .052 .31 { } .151 .92 { } 8 -.042 -.25 { } -.034 -.20 { * } 9 -.021 -.12 { * } -.053 -.31 { } 10 .285 1.66 { } .044 .26 { } 11 .011 .06 { * } -.137 -.78 { ** } DIAGNOSTIC CHECK #2B: THE INVERTIBILITY TEST FACTOR # TEST RESULT 1 Invertible 2 Invertible 3 Invertible DIAGNOSTIC CHECK #3: THE SUFFICIENCY TEST The Critical Value used for this test : 1.96 For the NOISE model : Recommended Adjustment The model is sufficient CCF lags that are significant NONE KENDALL RANK CORRELATION ( TEST) FOR SUFFICIENCY SERIES NAME TAU( ) P VALUE INPUT .067 .720 ADVISORY THE TEST FOR CONSTANCY OF PARAMETERS WILL NOT BE EXECUTED. Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MINE X2 = I~AS0009 1992/ 12 SEASP MINE X3 = I~AP0008 1992/ 11 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 47 Number of Degrees of Freedom =n-m 41 Residual Mean = R/n .332499E-02 Sum of Squares = R .418944E+08 Variance var= R /(n) 891370. Adjusted Variance = R /(n-m) .102181E+07 Standard Deviation = 1010.85 Standard Error of the Mean = / (n-m) 157.868 Mean / its Standard Error = /[ / (n-m)] .210618E-04 Mean Absolute Deviation = R /n 737.235 AIC Value ( Uses var ) =nln +2m 655.924 SBC Value ( Uses var ) =nln +mlnn 667.025 BIC Value ( Uses var ) =see Wei p153 607.302 R Square =1-[ R / (A- A) ] .940658 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS 8.686961 143.147 .6069E-01 2 Autoregressive-Factor # 1 1 -.3145004 .143049 -2.199 3 2 .4777480 .136760 3.493 INPUT SERIES X1 INPUT Lambda Value Differencing 1 4 Omega (input) -Factor # 2 4 .2710837 .709015E-01 3.823 INPUT SERIES X2 I~AS0009 1992/ 12 SEASP Lambda Value 5 Omega (input) -Factor # 3 0 -1519.650 425.882 -3.568 INPUT SERIES X3 I~AP0008 1992/ 11 PULSE Lambda Value 6 Omega (input) -Factor # 4 0 3347.436 928.127 3.607 [(1-B1)]Y(T) = 10.382 +[X1(T)][(1-B1)][(+ .271B 4)] +[X2(T)][(- 1519.6 )] +[X3(T)][(+ 3347.4 )] + [(1+ .315B 1- .478B 2)]-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .119 -.225 -.020 -.119 -.121 2 .119 1.000 -.150 .279 -.399 -.384 3 -.225 -.150 1.000 -.106 .133 .095 4 -.020 .279 -.106 1.000 -.440 -.355 5 -.119 -.399 .133 -.440 1.000 .669 6 -.121 -.384 .095 -.355 .669 1.000 ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 .029 .146 .20 .04 NA .029 .146 .20 2 -.029 .146 -.20 .08 NA -.030 .146 -.20 3 -.096 .146 -.66 .57 NA -.094 .146 -.65 4 .007 .147 .05 .57 NA .011 .146 .08 5 -.287 .147 -1.94 5.08 NA -.296 .146 -2.03 6 -.075 .159 -.47 5.39 NA -.073 .146 -.50 7 -.128 .160 -.80 6.34 .0118 -.164 .146 -1.12 8 -.015 .162 -.10 6.35 .0417 -.092 .146 -.63 9 -.043 .162 -.27 6.47 .0910 -.087 .146 -.60 10 .092 .162 .57 7.00 .1361 -.043 .146 -.29 11 .166 .163 1.01 8.75 .1194 .111 .146 .76 12 -.016 .167 -.09 8.77 .1871 -.134 .146 -.92 13 .144 .167 .86 10.17 .1793 .150 .146 1.03 14 .138 .169 .82 11.50 .1749 .115 .146 .79 15 -.044 .172 -.25 11.64 .2345 -.036 .146 -.25 16 -.286 .172 -1.66 17.71 .0600 -.188 .146 -1.29 17 -.086 .182 -.47 18.27 .0754 -.099 .146 -.68 18 .035 .183 .19 18.37 .1049 .130 .146 .89 19 .056 .183 .31 18.63 .1350 .085 .146 .58 20 -.049 .183 -.27 18.84 .1713 -.013 .146 -.09 21 .002 .183 .01 18.84 .2213 -.104 .146 -.72 22 .066 .183 .36 19.23 .2567 .011 .146 .07 23 -.067 .184 -.36 19.66 .2919 -.112 .146 -.77 24 -.062 .184 -.34 20.05 .3302 -.152 .146 -1.04 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 .029 .20 { } .029 .20 { * } 2 -.029 -.20 { * } -.030 -.20 { * } 3 -.096 -.66 { } -.094 -.65 { } 4 .007 .05 { * } .011 .08 { * } 5 -.287 -1.94 {* } -.296 -2.01 {* } 6 -.075 -.47 { } -.073 -.46 { } 7 -.128 -.80 { } -.164 -1.03 {* } 8 -.015 -.10 { * } -.092 -.57 { ** } 9 -.043 -.27 { * } -.087 -.54 { } 10 .092 .57 { } -.043 -.27 { * } 11 .166 1.01 { } .111 .68 { } 12 -.016 -.09 { } -.134 -.80 { } 13 .144 .86 { } .150 .90 { } 14 .138 .82 { } .115 .68 { ** } 15 -.044 -.25 { * } -.036 -.21 { * } 16 -.286 -1.66 {* } -.188 -1.09 {* } 17 -.086 -.47 { } -.099 -.55 { } 18 .035 .19 { * } .130 .71 { } 19 .056 .31 { } .085 .47 { ** } 20 -.049 -.27 { * } -.013 -.07 { * } 21 .002 .01 { * } -.104 -.57 { } 22 .066 .36 { } .011 .06 { * } 23 -.067 -.36 { } -.112 -.61 { } 24 -.062 -.34 { } -.152 -.82 {* } SERIES NAME IS : INPUT THE CROSS CORRELATIONS BETWEEN THE FILTERED INPUT AND THE RESIDUALS (R) Mean of X1 444.32 Mean of R -17.238 Variance of X1 .42844E+07 Variance of R .76387E+06 St. Deviation of X1 2069.9 St. Deviation of R 874.00 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 .137 .151 .91 0 .137 .151 .91 1 -.014 .152 -.09 -1 -.015 .152 -.10 2 .075 .154 .48 -2 -.234 .154 -1.52 3 .200 .156 1.28 -3 .243 .156 1.56 4 -.052 .158 -.33 -4 -.003 .158 -.02 5 -.074 .160 -.46 -5 -.019 .160 -.12 6 -.141 .162 -.87 -6 .055 .162 .34 7 .052 .164 .31 -7 .151 .164 .92 8 -.042 .167 -.25 -8 -.034 .167 -.20 9 -.021 .169 -.12 -9 -.053 .169 -.31 10 .285 .171 1.66 -10 .044 .171 .26 11 .011 .174 .06 -11 -.137 .174 -.78 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 .137 .91 { } .137 .91 { } 1 -.014 -.09 { * } -.015 -.10 { * } 2 .075 .48 { } -.234 -1.52 {* } 3 .200 1.28 { } .243 1.56 { } 4 -.052 -.33 { ** } -.003 -.02 { * } 5 -.074 -.46 { ** } -.019 -.12 { * } 6 -.141 -.87 { } .055 .34 { } 7 .052 .31 { } .151 .92 { } 8 -.042 -.25 { } -.034 -.20 { * } 9 -.021 -.12 { * } -.053 -.31 { } 10 .285 1.66 { } .044 .26 { } 11 .011 .06 { * } -.137 -.78 { ** } Analysis for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MINE X2 = I~AS0009 1992/ 12 SEASP MINE X3 = I~AP0008 1992/ 11 PULSE DIAGNOSTIC CHECK #5: THE VARIANCE STABILITY TEST The Critical value used for this test : 90.00 The minimum group or interval size was: 5 DIRECTION TIME DATE F VALUE P VALUE (T) DECREASING 26 1994/ 5 .225697 .0002 DECREASING 49 1996/ 4 .215058 .0301 Since the automatic model fixup option for the variance stability test is enabled, the program will now estimate the parameters of the model with a set of weights that adjusts the residuals to account for the variance change(s). Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MINE X2 = I~AS0009 1992/ 12 SEASP MINE X3 = I~AP0008 1992/ 11 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 47 Number of Degrees of Freedom =n-m 41 Residual Mean = R/n 8.51613 Sum of Squares = R .435502E+08 Variance var= R /(n) 926600. Adjusted Variance = R /(n-m) .106220E+07 Standard Deviation = 1030.63 Standard Error of the Mean = / (n-m) 160.958 Mean / its Standard Error = /[ / (n-m)] .529092E-01 Mean Absolute Deviation = R /n 731.654 AIC Value ( Uses var ) =nln +2m 657.746 SBC Value ( Uses var ) =nln +mlnn 668.847 BIC Value ( Uses var ) =see Wei p153 606.878 R Square =1-[ R / (A- A) ] .938313 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS 4.334560 88.8230 .4880E-01 2 Autoregressive-Factor # 1 1 -.2403839 .133299 -1.803 3 2 .4158580 .128866 3.227 INPUT SERIES X1 INPUT Lambda Value Differencing 1 4 Omega (input) -Factor # 2 4 .2408069 .748353E-01 3.218 INPUT SERIES X2 I~AS0009 1992/ 12 SEASP Lambda Value 5 Omega (input) -Factor # 3 0 -1648.532 380.462 -4.333 INPUT SERIES X3 I~AP0008 1992/ 11 PULSE Lambda Value 6 Omega (input) -Factor # 4 0 3384.565 1277.30 2.650 [(1-B1)]Y(T) = 5.2570 +[X1(T)][(1-B1)][(+ .241B 4)] +[X2(T)][(- 1648.5 )] +[X3(T)][(+ 3384.6 )] + [(1+ .240B 1- .416B 2)]-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .088 -.165 -.016 -.068 -.054 2 .088 1.000 -.057 .120 -.148 -.170 3 -.165 -.057 1.000 -.064 .134 .055 4 -.016 .120 -.064 1.000 -.256 -.159 5 -.068 -.148 .134 -.256 1.000 .359 6 -.054 -.170 .055 -.159 .359 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 4.335 Significant 2 -1.803 Not Significant 3 3.227 Significant 4 3.218 Significant 5 -4.333 Significant 6 2.650 Significant Since the automatic model fixup option for the Necessity Test is enabled, the program will now delete the parameter with the lowest non-significant T-ratio and return to the estimation stage in order to complete this iterative step. * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. NOTE -> Deleting model structure. Estimation/Diagnostic Checking for Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MINE X2 = I~AS0009 1992/ 12 SEASP MINE X3 = I~AP0008 1992/ 11 PULSE MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 47 Number of Degrees of Freedom =n-m 42 Residual Mean = R/n -3.87648 Sum of Squares = R .503705E+08 Variance var= R /(n) .107171E+07 Adjusted Variance = R /(n-m) .119930E+07 Standard Deviation = 1095.12 Standard Error of the Mean = / (n-m) 168.981 Mean / its Standard Error = /[ / (n-m)] -.229403E-01 Mean Absolute Deviation = R /n 760.594 AIC Value ( Uses var ) =nln +2m 662.584 SBC Value ( Uses var ) =nln +m*lnn 671.835 BIC Value ( Uses var ) =see Wei p153 601.915 R Square =1-[ R / (A- A) ] .928652 THE ESTIMATED MODEL PARAMETERS MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS -1.135561 90.8546 -.1250E-01 2 Autoregressive-Factor # 1 2 .4988369 .124075 4.020 INPUT SERIES X1 INPUT Lambda Value Differencing 1 3 Omega (input) -Factor # 2 4 .2285280 .737861E-01 3.097 INPUT SERIES X2 I~AS0009 1992/ 12 SEASP Lambda Value 4 Omega (input) -Factor # 3 0 -1752.774 384.620 -4.557 INPUT SERIES X3 I~AP0008 1992/ 11 PULSE Lambda Value 5 Omega (input) -Factor # 4 0 3154.757 1264.24 2.495 [(1-B1)]Y(T) = -2.2659 +[X1(T)][(1-B1)][(+ .229B 4)] +[X2(T)][(- 1752.8 )] +[X3(T)][(+ 3154.8 )] + [(1- .499B 2)]**-1 [A(T)] CORRELATION MATRIX OF THE PARAMETER ESTIMATES # 1 2 3 4 5 6 7 8 9 10 1 1.000 .040 -.096 -.026 -.035 2 .040 1.000 -.037 .064 -.111 3 -.096 -.037 1.000 .000 .019 4 -.026 .064 .000 1.000 -.025 5 -.035 -.111 .019 -.025 1.000 DIAGNOSTIC CHECK #1: THE NECESSITY TEST PARAMETER # T-VALUE TEST RESULT 1 -1.136 Not Significant 2 4.020 Significant 3 3.097 Significant 4 -4.557 Significant * 5 2.495 Significant * THE ASTERISK INDICATES THE PARAMETER THAT IS BEING CONSIDERED FOR DELETION, UNLESS DIFFERENCING IS INVOKED. ACF & PACF OF RESIDUALS FROM THE ESTIMATED MODEL LAG ACF STND. T- CHI-SQUARE & PACF STND. T- VALUE ERROR RATIO PROBABILITY VALUE ERROR RATIO 1 -.282 .146 -1.94 3.99 NA -.282 .146 -1.94 2 .185 .157 1.17 5.73 NA .114 .146 .78 3 -.351 .162 -2.17 12.19 NA -.301 .146 -2.06 4 .208 .177 1.18 14.51 NA .049 .146 .33 5 -.374 .182 -2.05 22.16 NA -.305 .146 -2.09 6 .148 .198 .75 23.39 .0000 -.124 .146 -.85 7 -.191 .200 -.96 25.50 .0000 -.128 .146 -.88 8 .132 .204 .65 26.54 .0000 -.180 .146 -1.24 9 -.127 .206 -.62 27.51 .0000 -.119 .146 -.81 10 .130 .208 .63 28.56 .0000 -.160 .146 -1.10 11 .087 .209 .41 29.04 .0001 .100 .146 .69 12 -.008 .210 -.04 29.04 .0001 -.151 .146 -1.03 13 .065 .210 .31 29.33 .0003 .057 .146 .39 14 .104 .210 .49 30.08 .0004 .202 .146 1.38 15 -.052 .212 -.25 30.28 .0008 -.034 .146 -.23 16 -.229 .212 -1.08 34.18 .0003 -.138 .146 -.94 17 -.046 .217 -.21 34.34 .0006 -.137 .146 -.94 18 .060 .217 .28 34.63 .0010 .121 .146 .83 19 .055 .218 .25 34.87 .0015 .060 .146 .41 20 -.007 .218 -.03 34.88 .0026 .013 .146 .09 21 -.007 .218 -.03 34.88 .0041 -.076 .146 -.52 22 .066 .218 .30 35.28 .0057 .015 .146 .10 23 -.059 .218 -.27 35.61 .0079 -.013 .146 -.09 24 -.012 .219 -.06 35.63 .0117 -.159 .146 -1.09 LAG ACF T PACF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 1 -.282 -1.94 {* } -.282 -1.94 {* } 2 .185 1.17 { } .114 .73 { } 3 -.351 -2.17 {* } -.301 -1.86 {* } 4 .208 1.18 { ***} .049 .28 { * } 5 -.374 -2.05 {** } -.305 -1.67 {* } 6 .148 .75 { } -.124 -.63 { } 7 -.191 -.96 { * } -.128 -.64 { } 8 .132 .65 { } -.180 -.88 {* } 9 -.127 -.62 { } -.119 -.58 { } 10 .130 .63 { } -.160 -.77 {* } 11 .087 .41 { } .100 .48 { } 12 -.008 -.04 { * } -.151 -.72 {* } 13 .065 .31 { } .057 .27 { } 14 .104 .49 { } .202 .96 { } 15 -.052 -.25 { } -.034 -.16 { } 16 -.229 -1.08 { * } -.138 -.65 { } 17 -.046 -.21 { * } -.137 -.63 { } 18 .060 .28 { } .121 .56 { } 19 .055 .25 { } .060 .28 { ** } 20 -.007 -.03 { * } .013 .06 { * } 21 -.007 -.03 { * } -.076 -.35 { } 22 .066 .30 { } .015 .07 { * } 23 -.059 -.27 { ** } -.013 -.06 { * } 24 -.012 -.06 { * } -.159 -.73 {*** } SERIES NAME IS : INPUT THE CROSS CORRELATIONS BETWEEN THE FILTERED INPUT AND THE RESIDUALS (R) Mean of X1 444.32 Mean of R -18.902 Variance of X1 .42844E+07 Variance of R .92825E+06 St. Deviation of X1 2069.9 St. Deviation of R 963.46 LAG CROSS- STANDARD T-RATIO LAG CROSS- STANDARD T-RATIO CORRELATION ERROR CORRELATION ERROR 0 -.017 .151 -.12 0 -.017 .151 -.12 1 .069 .152 .45 -1 .045 .152 .29 2 -.002 .154 -.01 -2 -.262 .154 -1.70 3 .186 .156 1.19 -3 .226 .156 1.45 4 -.077 .158 -.48 -4 -.060 .158 -.38 5 -.027 .160 -.17 -5 .050 .160 .31 6 -.215 .162 -1.33 -6 .003 .162 .02 7 .127 .164 .77 -7 .109 .164 .66 8 -.098 .167 -.59 -8 .031 .167 .18 9 .034 .169 .20 -9 -.063 .169 -.37 10 .242 .171 1.41 -10 .079 .171 .46 11 -.020 .174 -.11 -11 -.107 .174 -.62 LAG CCF T FB CCF T VALUE RATIO -1 0 +1 VALUE RATIO -1 0 +1 0 -.017 -.12 { * } -.017 -.12 { * } 1 .069 .45 { ** } .045 .29 { * } 2 -.002 -.01 { * } -.262 -1.70 {* } 3 .186 1.19 { } .226 1.45 { } 4 -.077 -.48 { } -.060 -.38 { ** } 5 -.027 -.17 { * } .050 .31 { * } 6 -.215 -1.33 {*** } .003 .02 { * } 7 .127 .77 { } .109 .66 { } 8 -.098 -.59 { ** } .031 .18 { * } 9 .034 .20 { * } -.063 -.37 { } 10 .242 1.41 { *} .079 .46 { ** } 11 -.020 -.11 { * } -.107 -.62 { } DIAGNOSTIC CHECK #2B: THE INVERTIBILITY TEST FACTOR # TEST RESULT 1 Invertible 2 Invertible 3 Invertible DIAGNOSTIC CHECK #3: THE SUFFICIENCY TEST The Critical Value used for this test : 1.96 For the NOISE model : ACF lags that are significant 3, 5, CCF lags that are significant NONE KENDALL RANK CORRELATION ( TEST) FOR SUFFICIENCY SERIES NAME TAU( ) P VALUE INPUT .002 .991 ADVISORY THE TEST FOR CONSTANCY OF PARAMETERS WILL NOT BE EXECUTED. VALUES ARE IN THE ORIGINAL METRIC TIME DATE WEIGHTS TO ACTUAL 1PERIOD AHEAD RESIDUAL % (T) STABILIZE OBSERVATION FORECAST(FIT) ERROR 1 1992/ 4 1.00000 3835.0 NA NA NA 2 1992/ 5 1.00000 3456.0 NA NA NA 3 1992/ 6 1.00000 4424.0 NA NA NA 4 1992/ 7 1.00000 4858.0 NA NA NA 5 1992/ 8 1.00000 4270.0 NA NA NA 6 1992/ 9 1.00000 5788.0 NA NA NA 7 1992/ 10 1.00000 6656.0 NA NA NA 8 1992/ 11 1.00000 11351. 10399. 952. 8.38 9 1992/ 12 1.00000 7937.0 10157. -.222E+04 -27.97 10 1993/ 1 1.00000 10905. 8987.2 .192E+04 17.59 11 1993/ 2 1.00000 9528.0 10016. -488. -5.12 12 1993/ 3 1.00000 12025. 11162. 863. 7.17 13 1993/ 4 1.00000 10359. 10624. -265. -2.56 14 1993/ 5 1.00000 15087. 12302. .278E+04 18.46 15 1993/ 6 1.00000 13721. 15960. -.224E+04 -16.32 16 1993/ 7 1.00000 17215. 16461. 754. 4.38 17 1993/ 8 1.00000 12390. 14868. -.248E+04 -20.00 18 1993/ 9 1.00000 12596. 13388. -792. -6.29 19 1993/ 10 1.00000 8877.0 10208. -.133E+04 -14.99 20 1993/ 11 1.00000 9257.0 8206.1 .105E+04 11.35 21 1993/ 12 1.00000 8054.0 6339.7 .171E+04 21.29 22 1994/ 1 1.00000 9128.0 8572.1 556. 6.09 23 1994/ 2 1.00000 7921.0 9345.0 -.142E+04 -17.98 24 1994/ 3 1.00000 8629.0 7775.9 853. 9.89 25 1994/ 4 1.00000 8912.0 7813.1 .110E+04 12.33 26 1994/ 5 4.43072 9064.0 9318.0 -254. -2.80 27 1994/ 6 4.43072 8835.0 9131.0 -296. -3.35 28 1994/ 7 4.43072 8067.0 9375.3 -.131E+04 -16.22 29 1994/ 8 4.43072 7384.0 7724.0 -340. -4.60 30 1994/ 9 4.43072 6069.0 6835.2 -766. -12.63 31 1994/ 10 4.43072 5576.0 5779.8 -204. -3.66 32 1994/ 11 4.43072 4962.0 4957.3 4.73 .10 33 1994/ 12 4.43072 3081.0 3108.5 -27.5 -.89 34 1995/ 1 4.43072 3510.0 2654.8 855. 24.37 35 1995/ 2 4.43072 3418.0 3382.5 35.5 1.04 36 1995/ 3 4.43072 4072.0 3928.4 144. 3.53 37 1995/ 4 4.43072 2841.0 3885.2 -.104E+04 -36.76 38 1995/ 5 4.43072 3602.0 3723.8 -122. -3.38 39 1995/ 6 4.43072 3703.0 2422.2 .128E+04 34.59 40 1995/ 7 4.43072 3499.0 3591.8 -92.8 -2.65 41 1995/ 8 4.43072 2786.0 3612.6 -827. -29.67 42 1995/ 9 4.43072 2899.0 2849.4 49.6 1.71 43 1995/ 10 4.43072 3438.0 2695.0 743. 21.61 44 1995/ 11 4.43072 3782.0 3553.7 228. 6.04 45 1995/ 12 4.43072 2091.0 2091.4 -.433 -.02 46 1996/ 1 4.43072 3155.0 2259.1 896. 28.40 47 1996/ 2 4.43072 3405.0 3295.3 110. 3.22 48 1996/ 3 4.43072 3062.0 3943.9 -882. -28.80 49 1996/ 4 20.6024 2766.0 2845.3 -79.3 -2.87 50 1996/ 5 20.6024 2864.0 2834.8 29.2 1.02 51 1996/ 6 20.6024 2805.0 2764.5 40.5 1.44 52 1996/ 7 20.6024 3056.0 2774.2 282. 9.22 53 1996/ 8 20.6024 3608.0 3067.5 541. 14.98 54 1996/ 9 20.6024 3223.0 3708.4 -485. -15.06 THE FORECAST MODEL USED FOR THIS VARIABLE MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS -885.5719 2 Autoregressive-Factor # 1 3 -.6971897 3 Autoregressive-Factor # 2 6 -.4953457 [(1-B1)]Y(T) = -348.94 + [(1+ .697B 3)(1 + .495B 6)]**-1 [A(T)] MODEL STATISTICS IN TERMS OF THE ORIGINAL DATA Number of Residuals (R) =n 47 Number of Degrees of Freedom =n-m 42 Residual Mean = R/n -3.87648 Sum of Squares = R .503705E+08 Variance var= R /(n) .107171E+07 Adjusted Variance = R /(n-m) .119930E+07 Standard Deviation = 1095.12 Standard Error of the Mean = / (n-m) 168.981 Mean / its Standard Error = /[ / (n-m)] -.229403E-01 Mean Absolute Deviation = R /n 760.594 AIC Value ( Uses var ) =nln +2m 662.584 SBC Value ( Uses var ) =nln +m*lnn 671.835 BIC Value ( Uses var ) =see Wei p153 601.915 R Square =1-[ R / (A- A) ] .928652 Model Forecasting for Time Series Variable Y = OUTPUT as a f(input var(s)) X1 = INPUT MINE X2 = I~AS0009 1992/ 12 SEASP MINE X3 = I~AP0008 1992/ 11 PULSE THE FORECAST MODEL USED FOR THIS VARIABLE MODEL COMPONENT LAG COEFFICIENT STANDARD T-RATIO # (BOP) ERROR Differencing 1 1 PURE RIGHT-HAND SIDE CONS -1.135561 2 Autoregressive-Factor # 1 2 .4988369 INPUT SERIES X1 INPUT Lambda Value Differencing 1 3 Omega (input) -Factor # 2 4 .2285280 INPUT SERIES X2 I~AS0009 1992/ 12 SEASP Lambda Value 4 Omega (input) -Factor # 3 0 -1752.774 INPUT SERIES X3 I~AP0008 1992/ 11 PULSE Lambda Value 5 Omega (input) -Factor # 4 0 3154.757 [(1-B1)]Y(T) = -2.2659 +[X1(T)][(1-B1)][(+ .229B 4)] +[X2(T)][(- 1752.8 )] +[X3(T)][(+ 3154.8 )] + [(1- .499B 2)]**-1 [A(T)] VALUES ARE IN TERMS OF THE ORIGINAL METRIC TIME DATE LOWER 80% UPPER 80% FORECAST ACTUAL RESIDUAL % (T) LIMIT LIMIT (IF KNOWN) ERROR 55 1996/ 10 2104. 4702. 3403. 56 1996/ 11 1458. 5133. 3295. 57 1996/ 12 -1060. 4295. 1618. 58 1997/ 1 -1700. 4922. 1611. 59 1997/ 2 -2727. 5398. 1336. 60 1997/ 3 -3527. 5863. 1168. 61 1997/ 4 -4355. 6293. 968.7 62 1997/ 5 -4913. 6799. 942.8 63 1997/ 6 -5506. 7244. 869.3 64 1997/ 7 -6050. 7660. 805.2 65 1997/ 8 -6567. 8067. 749.7 66 1997/ 9 -7070. 8433. 681.6 THE AGGREGATE .1179E+05 .2311E+05 .1745E+05 PLOT OF THE OBSERVED (ACTUAL) & THE FORECAST SERIES GRAPH KEY A = OUTPUT F = FORECASTS -7070.1 17215. DATE ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1992/ 4 A 3835.0 1992/ 5 A 3456.0 1992/ 6 A 4424.0 1992/ 7 A 4858.0 1992/ 8 A 4270.0 1992/ 9 A 5788.0 1992/ 10 A 6656.0 1992/ 11 A 11351. 1992/ 12 A 7937.0 1993/ 1 A 10905. 1993/ 2 A 9528.0 1993/ 3 A 12025. 1993/ 4 A 10359. 1993/ 5 A 15087. 1993/ 6 A 13721. 1993/ 7 A 17215. 1993/ 8 A 12390. 1993/ 9 A 12596. 1993/ 10 A 8877.0 1993/ 11 A 9257.0 1993/ 12 A 8054.0 1994/ 1 A 9128.0 1994/ 2 A 7921.0 1994/ 3 A 8629.0 1994/ 4 A 8912.0 1994/ 5 A 9064.0 1994/ 6 A 8835.0 1994/ 7 A 8067.0 1994/ 8 A 7384.0 1994/ 9 A 6069.0 1994/ 10 A 5576.0 1994/ 11 A 4962.0 1994/ 12 A 3081.0 1995/ 1 A 3510.0 1995/ 2 A 3418.0 1995/ 3 A 4072.0 1995/ 4 A 2841.0 1995/ 5 A 3602.0 1995/ 6 A 3703.0 1995/ 7 A 3499.0 1995/ 8 A 2786.0 1995/ 9 A 2899.0 1995/ 10 A 3438.0 1995/ 11 A 3782.0 1995/ 12 A 2091.0 1996/ 1 A 3155.0 1996/ 2 A 3405.0 1996/ 3 A 3062.0 1996/ 4 A 2766.0 1996/ 5 A 2864.0 1996/ 6 A 2805.0 1996/ 7 A 3056.0 1996/ 8 A 3608.0 1996/ 9 A 3223.0 1996/ 10 L F U 3402.9 1996/ 11 L F U 3295.4 1996/ 12 L F U 1617.9 1997/ 1 L F U 1611.0 1997/ 2 L F U 1335.8 1997/ 3 L F U 1168.1 1997/ 4 L F U 968.71 1997/ 5 L F U 942.75 1997/ 6 L F U 869.31 1997/ 7 L F U 805.16 1997/ 8 L F U 749.68 1997/ 9 L F U 681.64 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Click here to EXIT VIEW FULL ANALYSIS REPORT

CLICK HERE:Home Page For AUTOBOX