# Optimal Lag Selection Indicates Lag 98

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?

• 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. – Richard Hardy Mar 29 '20 at 19:02
• 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. – Richard Hardy Mar 29 '20 at 19:02
• Thanks a lot this does makes sense. – Sally_ar Mar 29 '20 at 20:10