Interpretation of p-values in ARIMA model I am starting my journey in time series analysis and forecasting and I'm currently facing some doubts.
If I fit an ARIMA model to my data and I get for example an ARIMA(2,1,2) in which the p-value for the second AR term is >0.05, should I re-estimate the model without that term?
Also, I must note that I'm using an automatic algorithm that estimates the parameters through maximum likelihood. Could this mean that I misconfigured the algorithm?
Thanks in advance for any help.
 A: If you have an over-parameterized model ( seems to me that this is a likely case ) with possibly self-cancelling structure you can often get a clue about this when you have p values that are not significant AND unfortunately even with p values that are small.. 
Make sure that your model identification procedure takes into account pulses , level/step shifts , seasonal pulses and or local time trends (auto.arima does not) . Perhaps you should follow the guidelines as to how to examine the acf and pacf yourself in order to identify a useful model. https://www.analyticsvidhya.com/blog/2015/12/complete-tutorial-time-series-modeling/ may be initially helpful BUT it also does not concern itself when you have untreated latent deterministic structure.
See @Adamo's words excerpted from here Interrupted Time Series Analysis - ARIMAX for High Frequency Biological Data? pinpointing the need to consider latent deterministic effects while identifying arima structure.
"The correlogram 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 would like to add possibly over-identifying the possible model . 
If you post your data in a csv format , I may be able to help further.
Alternatively see Non sensical results from auto_arima for a detailed walk-through of an iterative approach to forming a useful model.
