How actually my time series models tells me about data behaviour? [closed]

Question

I have different models namely AR, ARMA, ARIMA for different time series (in data set of 4449) stationary-3096, Non stationary-1353 , why this classification appears to be?

If I have $AR(p=1-5)$ and $AR(p >5)$ what does my data tell ?,

I have many time series which follows ARMA-1239 best models, some are AR-90 best model & ARIMA-7 best models out of 3096 stationary data set

Please, kindly tell me in philosophical/non-statistical way (because I didn't understand by term like normal/marginal distribution).

Answer 1

The order of the an AR model tells you how the current value is linearly related to the past p values.
The theory of stationary time series tells us that any stationary model has an infinite autoregressive representation (which could be finite) and also there is an infinite moving average representation (which could be finite). If the AR representation is finite an AR model works. If the MA representation is finite an MA model works.When both representations are infinite you need an ARMA model for a finite parameterization. ARIMA models allow the modeling of a special kind of nonstationary process namely a process that is stationary after differencing of the series. Frist order differencing eliminates a linear trend and higher order differencing eliminates the higher order polynomial trends. The class of ARIMA models therefroe represent a broad class of stationary and nonstationary time series. They do not cover seasonal trends but Box and Jenkins introduced seasonal differencing to deal with seasonal 9or periodic) trends.

Regarding normal distributions, it is commonly assumed for ARIMA models that the random or noise component has the normal (Gaussian) probability distribution usually with zero mean and a common variance. The collection X1, X2, ..., Xn have a multivaraite distribution determined by the model. The individual or univariate distribution of X1 say is called the marginal distribution. If the time series is stationary then all the Xis have the saem marginal distribution.