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I am trying to identify the optimal lag for my multivariate time series and currently I am getting the optimal AIC at lag 98. I have never seen such large optimal lag is this correct?

Note that my data is hourly concentrations of carbon monoxide and the other variables are atmospheric measurements: temperature, wind speed, humidity and wind direction. Also the time series has been differenced for lag=1 to be stationary. After a couple of trial as I increased the lag.max for VARselect() I noticed that the AIC trends downward until lag 98 and then back up and that has been my criteria for optimal lag selection. Is this correct?

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  • $\begingroup$ Welcome to Cross Validated! How long is your time series? If it is very long (tens of housands of observations), 98 might not seem too extreme. Also, 98 is close to 96, and 96 is a multiple of 24. If there is seasonality with a period of 4 days (96 hours), it could be that only the 96th lag (and maybe a few other intermediate lags associated with different periods) are relevant while the majority are superfluous. Or maybe there is seasonality of 98 hours for some reason. I would look at ACF and PACF graphs to inspect potential seasonal variation. $\endgroup$ – Richard Hardy Mar 29 '20 at 19:02
  • $\begingroup$ A side note: when you change lagmax in VARselect, I suspect the dataset on which the likelihood (and thus AIC) is evaluated is changed: some of the initial data points are chopped off because they are used up for forming lagged series. When likelihood is evaluated on different datasets, AIC values are incomparable. So to do it properly, you should only compare AICs within any one application of VARselect, not across applications with different lag.max values. $\endgroup$ – Richard Hardy Mar 29 '20 at 19:02
  • $\begingroup$ Thanks a lot this does makes sense. $\endgroup$ – Sally_ar Mar 29 '20 at 20:10
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or maybe the dominant seasonality is deterministic in form …. think 23 possible hourly effects .. think 6 possible daily indicators …..think possible monthly effects … think possible day-in-the-month effects...think possible interactions .. think of not differencing the data as the non-stationarity might be due to deterministic trends or changing levels over time … think using the data to identify the model rather than trying to fit a presumed auto-projective model.

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  • $\begingroup$ Actually you might be right because when I did ADF test on the original dataset (without differencing) it did indicate stationary with p-value 0.01. $\endgroup$ – Sally_ar Mar 29 '20 at 20:11
  • $\begingroup$ If you want to post your data I might be able to help further . I f you don't know how to post your data as a csv file then feel free to email it to me BUT I would prefer others to be able to access it also. $\endgroup$ – IrishStat Mar 29 '20 at 21:51
  • $\begingroup$ That is mighty kind of you. I don't know how to post the csv file here, but I uploaded it to my Github. This is the full data but I am using one pollutant (for example CO) at a time with the atmospheric data (Temp, Humid, Wind Dir, Wind Speed) for this analysis. Thank you so much!! github.com/arshisal/Capstone-Project/blob/master/Pollutants.csv $\endgroup$ – Sally_ar Mar 29 '20 at 22:04
  • $\begingroup$ had tons of issues trying to sort out your data ,,, couldn't get GitHub to download. I suggest that you send me an email so we can set up a SKYPE session to enable me to get to your data $\endgroup$ – IrishStat Mar 30 '20 at 0:35

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