Please, could you advice me a good paper which talks about the ARIMA's state-of-art? I have already searched on google but I have not found anything interesting.

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    $\begingroup$ Welcome to Cross-Validated. This question is too vague. Can you please be more specific? $\endgroup$ – Skander H. - Reinstate Monica Feb 20 '19 at 19:25

You might want to start with material here Time series Forecasting in Python - comparing different models and a primary reference here http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html .

The bottom lime is that arima modelling is an iterative process AND that the simple acf and pacf as the vehicles for model identification requires/presumes that the are no outliers , no step/level shifts , no seasonal pulses , no time trends or any determinstic effects are present (i.e. unadjusted for ) in the series otherwise that structure obfuscates model identification.

Quoting the reflection by AdamO ..."The correlogram (ACF/PACF) should be calculated from residuals using a model that controls for intervention administration, otherwise the intervention effects are taken to be Gaussian noise, underestimating the actual autoregressive effect."

AND I must add for generality purposes there is an unstated assumption that both the candidate model parameters and model error variances are constant over time.


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