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I need a tip or two.

I am performing OLS with dynamic factors (4x1 factors each representing a PANEL of 24 series, hence 4 time series).

My OLS has autocorrelation in the error so I want to use OLS with ARIMA errors, therefore I model my initial error and the only model that I have found that kills the autocorrelation is ARMA(3,7).

AR(1) does, OK job but I have some significant residuals in lag 4 and few later lags and everything else makes it worse until ARMA(3,7) which make the error 100% white noise (not a single value with significant Q-statistic).

My concern is that ARMA(3,7) model is crazy complex.. what does MA(7) even mean of the OLS error, I have no explanation behind it.

Should I perform a OLS with AR(1) errors even thought it is not perfect (DW statistic is around 2.1) or should I go for OLS with ARMA(3,7) errors which makes the regression perfect?

Any tips? Thanks :)

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  • $\begingroup$ It sounds to me that there may be deterministic structure in the residuals ( pulses,level shifts,seasonal pulses) or an error variance that is not constant. Post your data in a csv file and I will try and help. $\endgroup$
    – IrishStat
    Commented Feb 17, 2019 at 20:54
  • $\begingroup$ Hi IrishStat, I have filtered the original series for deterministics (but not for outliers). How would advice me to check the residual structure for pulses, level shifts, etc.? $\endgroup$
    – Kiril E. Proykov
    Commented Feb 17, 2019 at 21:20
  • $\begingroup$ tsoutliers my be useful but I am not sure. I apologize for the deletion of my answer as someone didn't recognize that I had actually answered your question. Do you agree ? $\endgroup$
    – IrishStat
    Commented Feb 17, 2019 at 21:31
  • $\begingroup$ I just checked my series and I can identify very strong weekly seasonality (every 7 days). I guess that causes the funky ARMA(3,7). Weird thing is that, when I take diff(x,7) the seasonality still stays in the data. $\endgroup$
    – Kiril E. Proykov
    Commented Feb 17, 2019 at 21:34
  • $\begingroup$ your findings based upon my answer suggest that you add 6 seasonal dummies (6 seasonl pulses) ARiMA doesn't fix determnistic effects $\endgroup$
    – IrishStat
    Commented Feb 17, 2019 at 21:36

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A collection of 4 useful comments should constitute an answer !

It sounds to me that there may be deterministic structure in the residuals ( pulses,level shifts,seasonal pulses) or an error variance that is not constant. Post your data in a csv file and I will try and help.

tsoutliers my be useful to test for deterministic structure.

I suggest that you add 6 seasonal dummies (6 seasonl pulses) AS ARIMA doesn't fix determnistic effects –

I would simply leave them in as they seem to absorb/fix the issue the 6 indicators are being measure/tested on a 1 by 1 basis AND not collectively ...whereas the ar(7) is a global/composite effect.

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I have discovered the issue. It was coming from stationary and non-stationary long-memory dependencies in my series.

After performing fractional differencing I was able to clean my model to perfection!

To estimate the differencing parameter I used Local Whittle methods.

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