I have been working on a forecast model in Excel extrapolating from a small (150 data points) monthly time series. I've converted into a year/year percentage change series to get it stationary, deseasonalized it with monthly dummies, and accounted for serial-correlation (it has a two period error correlation).

However, after graphing the residuals like so...

Graph of actual vs. predicted errors ...it's very clear that there is non-seasonal, semi-regular periodicity that still needs to be removed. What is the recommended approach for modeling this kind of error (hopefully one that doesn't require R)?

Edit: The PACF for the first two lags were (1) -0.481, and (2) -0.2786. PACF values for lags greater than were not significant.

  • $\begingroup$ pacf(1) was -0.481, and the pacf(2) was -0.2786. pacf (>2) were not significant. $\endgroup$
    – Michael M
    Aug 14, 2014 at 0:50

1 Answer 1


The phenomenon is sometimes called pseudo-cyclical behavior.

You sometimes see behavior like that with AR(2) (or higher order) processes.

The PACF values in your comment also suggest an AR(2) as a possible model for your errors.

So my suggestion is: perhaps consider an AR(2) model for your error term.

  • 1
    $\begingroup$ +1 - It is hard to give advice after the series has already been so processed (de-seasonalized with monthly dummies, converted to yearly percentage changes). It could also be the case that the prior transformations are neither sufficient to remove the seasonality or actually introduce the auto-correlation that is shown in the above graph. (Which if the latter is the case they are probably inappropriate to begin with.) $\endgroup$
    – Andy W
    Aug 14, 2014 at 12:28
  • $\begingroup$ @AndyW Yes, all good points. $\endgroup$
    – Glen_b
    Aug 14, 2014 at 13:28

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