I am not quite used to ARIMA's models but I believe I reached the on of the limitations of these autoregressive models, could you please check it out and tell me if I am wrong:
Find the data (with no virus, guaranteed) in the following Gofile link: https://gofile.io/d/RAlgkc
I have a timeseries (monthly aggregated) that looks like the following:
I see NO trend at all and the statistical test confirm stationarity:
ADF Statistic: -4.858951 p-value: 0.000042 Lags used: 12.000000 The nobs or number of observations used for the Critical Values: 479.000000 Critical Values: 1%: -3.444 5%: -2.868 10%: -2.570
KPSS Statistic: 0.064377 p-value: 0.100000. lags: 18.000000 Critical Values: 10%: 0.347 5%: 0.463 2.5%: 0.574 1%: 0.739
Perhaps my only concern is the p-value of the KPSS, which is quite above a 5% threshold... Anyway statistical tests points to stationarity so lets move on.
In autoregression correlograms (ACF and PACF) I can see a clear seasonality (remember, x-axis are months)
High correlation with small lags, so I define the orders of this SARIMA model as (1, 0, 1) - (1, 0, 1, 12). Providing quite a consistent results:
From here on, I do not like the results all, this is the prediction compared to my test (splited data).
ARIMA is just describing the average seasonality for the test period (~ 120 months) WITHOUT taking into consideration the order parameteres in between season... Despite this, the residuals are all uncorrelated
So my question is, is it me (probably), that I am not describing properly the order and the seasonal order of the time series or this is the maximum I should expected from a SARIMA model? What concerns me more is that the residuals are uncorrelated...
Your help, opinions, feedback I much appreciated. Thanks a lot!