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I am using multivariate autoregressive (MAR) models to fit my long-term dataset of species abundances and environmental variables but when I use only the data from a specific period of the year (e.g., summer) instead of all of it, some coefficients from the resulting model are greater than 1. What does this mean? Should I reject these values from the final model? Why do I have this problem? Could it be caused by the small number of data? When I use all the data I don't have coefficients >1 or <-1.

gung - Reinstate Monica
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Carmen
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    Autoregressive parameters can be greater than 1 but sometimes there are constraints on the coefficients when stationarity is required or if the process should not be explosive. – Michael R. Chernick May 24 '17 at 16:18
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    Well yes, of course they can. This means the process is explosive. Whether the model makes any real world sense is a other question. – Dole May 24 '17 at 16:33
  • Maybe you need to apply a time-varying (TV) MVAR. In a TV MVAR the parameters of the model change with time implying that the interactions between time series are no longer constant. – amanita Aug 01 '17 at 22:42
  • Hi: the algorithms for the estimation of ARIMA models is fairly complex so, if there is no constraint in the alg for enforcing stationarity, you may get AR coefficient estimates greater than but that doesn't mean that roots inside the unit circle wouldn't fit almost as well. I would try a regular arima algorithm from R ( there are many ) and see what happens there. – mlofton Aug 15 '18 at 02:54
  • Oops. didn't see the multivariate aspect of your problem when I replied. There should be multivariate ARIMA algorithms in R but I don't know the package that has them. OTOH, If by multivariate, you just mean a VAR, then vars is the package you want to look at.. – mlofton Aug 15 '18 at 02:56
  • stationary AR(2) have coefficients greater than 1. For example, $y_t = 1.19 y_{t-1} - 0.23 y_{t-2} + e_t$ is stationary! You can check the region from https://stats.stackexchange.com/questions/118019/a-proof-for-the-stationarity-of-an-ar2 – KH Kim Jan 29 '23 at 03:47

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