Strange SARMAX fit with python statsmodels
Basically, estimation is done using the assumption that pre-sample observations are drawn from the unconditional distribution of the implied SARIMA process.
SARIMAX models are estimated using a state space approach, and if you are a frequentist the this process is referred to as the "initialization" of the first state vector, while if you are a Bayesian then you would think of this as putting a particular prior on the first state vector (the state vector contains all the required lags of the process, so the "initialization", or prior, describes enough pre-sample observations to allow the model to be fit).
While this is a perfectly reasonable approach to setting up the model so that it can be estimated, it doesn't necessarily mean that it is a good idea to specify a model with so many parameters and so few observations. Your estimates will begin to depend more on the prior rather than on the data.
I've a dataset with 48 obs (monthly) and python have been able to fit the SARIMAX ((4, 1, 3), (3, 0, 5)) model... which to me seems quite odd. How does it calculates the B^(12*5) term and the subsequent ones since I have just 48 data points?
I've also tried with ((0, 1, 4), (5, 0, 1)) and it works... Also, I've computed the MAPE agaist the next 12 periods and it's quite good (3% and 6%).
Thoughts?
Thank you