Lagged Regression

For starters......

In article <6qbhbu$j0t$1@nnrp1.dejanews.com, mashuha@my-dejanews.com says...

Dear all,

I have developed a model to model a time series data, in SAS/ETS and it's
regression with AR(1) errors.

It looks like this:

Series1 = Seasonal Dummies + Series2 + Series3 + AR(1)

There are 6 dummies, describing weekly seasonality, since the data is
daily.

I need to implement that model in MS Excel, so it will be usable by others
who don't have SAS, i.e. they will be entering values of Series2 and
Series3 and get back prediction for Series1.
I am not sure how to do that, how to put AR(1) in?

I will be really grateful for a advice,

Maria.



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What you have is a particular , and not necessarily optimal , case of a Transfer
Function. A general expression for a single input Transfer Function
is as follows ( without a constant ) is



                       W(B)                 T(B)

           Y(t)   =  --------  X(t)  +  ----------  A(t)

                      D(B)                  P(B)


   You have specified  the following form

                       W(B)                 1

           Y(t)   =  --------  X(t)  +  ----------  A(t)

                        1                  P(B)


   Simply clear fractions using you equation and get


    P(B)  Y(t)   =  W(B)*P(B) *  X(t)  +  A(t)

   where P(B) = 1 -PHI1*B  and B is the backshift operator sometimes referred
   to as L or lag operator

   and W(B) is by your specification simply  W0*B**0 or W0


   In terms of your model

      Y(t) = PHI1*Y(t-1) + W0*X(t) - PHI1*W0*X(t-1)

   where PHI1 is your AR(1) coefficient and W0 is your regression coefficient.


Note also that the constant in the model ( not shown here ) would have to be
modified

   by the multiplier ( 1-PHI1 )


   thus the prediction would be


      Y(t) = PHI1*Y(t-1) + W0*X(t) - PHI1*W0*X(t-1)   + (1-PHI1)*YOURCONSTANT



   Dave Reilly
   Automatic Forecasting Systems

   215-675-0652

P.S. A transfer function can be expressed as a lagged autoregression in
 all variables in the model. Some software packages (AUTOBOX for one)
 reports this form so users can go directly to spreadsheets for
the purposes that you require. Care should be taken to deal with
gaussian violations such as Outliers (pulses) , Level Shifts , Seasonal
Pulses , Local time trends , changes in variance , changes in
 parameters, changes in models ...... just to name a few ..



P.S.S. Of course the form of W(B) , D(B) , T(B) and P(B) should never
be assumed just because your current software is restricted to easy
choices. Aggressively do model diagnostic checking to verify the
assumptions that you are making in order to either augment or reduce
the model form. To get some ideas on how to do that please
go to http://www.autobox.com and pursue Modeling Hints.

CLICK HERE:Home Page For AUTOBOX