# Tom Reilly

Waging a war against how to model time series vs fitting

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# Is it a trend or a level shift? Yes, Simpson's Paradox also exists in Time Series Analysis!

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You have data that is decreasing.  You have three areas where the data seems to level off.  Is it a trend or is it two level shifts?

If you have any knowledge about what drives the data then by all means use a causal variable.  What to do if you have none?  It then becomes an interesting and very debatable topic.

How many periods determines a level shift might be a big factor here.

Simpson's Paradox is where you have a global significance, but not local.  From a global perspective, sure there is a trend.  From a local, there is no trend. Who is to say that the overall trend will continue?  Who is to say that the trend won't?  Maybe it will go up?

If you run this without making assumptions, you get two level shifts at period 14 and 25 and some outliers using the following data

20324 19856 19012 17247 18616 17786 20509 19097 19437 18562 17648 18672 17324 16765 16108 14742 16567 16041 15511 15403 16797 13977 15570 16249 14005 16645 14098 12310 15923 13422 13030

Y(T) =  18776.                                monthly

+[X1(T)][(-  2800.9    )]        :LEVEL SHIFT      14                                                    2011/ 10

+[X2(T)][(-  2602.3    )]        :LEVEL SHIFT      25                                                    2012/  9

+[X3(T)][(+  3272.0    )]        :PULSE            26                                                    2012/ 10

+[X4(T)][(-  1998.3    )]        :PULSE            22                                                    2012/  6

+[X5(T)][(+  2550.0    )]        :PULSE            29                                                    2013/  1

+                    +   [A(T)]

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