I have a time series I want to use as a response in a regression model. The problem is that I suspect that the changes in this variable could be due to sampling error. As a result, I created a moving average of this time series in order to smoothed out the shocks. I am now considering using this as the response in my regression model and not the original series. Note: I am not constructing an ARMA type model. My predictors are also time series such as media spend and consumer confidence scores.
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The moving-average will be auto-correlated (even if the original series is not auto-correlated) thus this is a potential violation of the subsequent causal model. I would simply include the variable as a predictor in a Transfer Function also known as Dynamic Regression .
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$\begingroup$ Thank you IrishStat that makes sense! I will put the MA on the RHS of a Dynamic Regression so as to control for the trend changes. I don't have enough reputation points to vote an answer but hopefully some one will. $\endgroup$– RayRCommented Dec 8, 2014 at 14:56
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$\begingroup$ @RayR Someone will, but you do have enough reputation to accept this answer (if it solves your problem) :) $\endgroup$– psarkaCommented Dec 8, 2014 at 15:02
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$\begingroup$ You should identify the form of the polynomials (numerator and denominator) for the error process as it may be an AR structore or an MA structure or some combination of these two. One way ( not necessarily optimal) is to conduct a transfer function with a white noise error (i.e. no ARIMA) and then identify a possible ARIMA structurefrom the residuals. $\endgroup$ Commented Dec 8, 2014 at 15:09