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I have 44 years of data for 4 variables: Y, X1, X2, X3.

All 4 variables are non-stationary. I plan to run this model: Y= X1 + X2 + X3 + e. I wonder what should I do next, steps by steps, to fit my model?

1.Should I first use log and/or difference on all the 4 variables to make them become stationary, and then run the model?

2.How to decide whether I should put 4 logs and/or difference on all the 4 variables? or on Y, X1, X2, or X3?

3.What time series methods should I use to fit my model? AR, MA, ARMA, ARIMA, ARMAV, Multivariate Time Series?

4.I am using SPSS. Answers about SPSS or not are all appreciated.

Thanks a lot.

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The first thing to do is to determine what level of differencing is required for all of the series and then convert Y, X1, X2 and X3 to y,x1, x2 and x3. The second step is to determine the appropriate ARMA filter for each of these three series x1,x2 and x3. Develop pre-whitened cross-correlations see here https://onlinecourses.science.psu.edu/stat510/node/75 and then identify the appropriate transfer function between Y and X1,X2 AND X3. Add any necessary ARIMA structure and any needed indicators reflecting Pulses, Level Shifts , Seasonal Pulses and/or Time Trends that may be needed . Estimate the model and then delete non-significant structure. Re-examine residuals to possibly augment the model via diagnostic checking procedures.

SPSS is in my opinion ill-suited for your needs BUT you might call their help desk and ask for advice as more recent versions may have an automatic transfer function identification option available to you. Otherwise you might try googling terms like "automatic time series modelling" or "automatic intervention detection" etc ....just make sure that the suggested solutions are multi-variate and single equation

Logs or any other transforms such as weighted modelling should only be used when it is proven that the error variance is not homogenous across time. See When (and why) should you take the log of a distribution (of numbers)? for a good discussion on this topic. Transforms should never be done willy-nilly i.e. without cause.

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  • $\begingroup$ I disagree with your statement on SPSS being ill suited. They do have excellent automatic transfer function modeling. $\endgroup$ – forecaster Aug 30 '17 at 14:59
  • $\begingroup$ but no automatic diagnostics to add possibly needed intervention variables that may have been overlooked by the user OR any automatic transfer function id or any built-in feature to determine an optimum way to deal with non-constant error variance or time-varying parameters or a few other missing items. If you wish we can do an offline comparison of software that I am familiar with and we can possibly both learn the art of the possible. $\endgroup$ – IrishStat Aug 30 '17 at 15:36
  • $\begingroup$ It might not do everything that you are mentioning and not sure if everything is important, i do know spss does automatic outlier detection and automatic transfer function modeling, and it was written by a famous statistician with extensive time series back ground ? Can you make a guess of who wrote their automatic transfer function/outlier detection? $\endgroup$ – forecaster Aug 30 '17 at 16:39
  • $\begingroup$ they don't have an intervention detection procedure in their tf modelling because I didn't give them a license to do that . Theirs is a piece meal very imperfect solution written by RT that is not unified. SPSS does not 't have an automatic procedure to pre-filter the series because I rejected their proposal to acquire AUTOBOX . Beauty is in the eye of the beerholder. (beholder !) $\endgroup$ – IrishStat Aug 30 '17 at 16:46
  • $\begingroup$ @forecaster I am a little shocked and stunned with your comment "not sure if everthing is important" . any and all quality computational aids are a blessing to help those who don't know what you know. $\endgroup$ – IrishStat Aug 30 '17 at 16:54

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