I am trying to build ARIMA model, I have 144 terms in my standardized time series, which represent residuals form original time series. This residuals, on which I would like to build ARIMA model, are obtained when I subtracted linear trend and periodical component from original time series, so residuals are stochastic component.

Because of that subtraction I modeled residuals like stationary series (d=0), so model is ARIMA(p,d,q)=ARIMA(?,0,?).

ACF and PACF functions of my residuals are not very clear as cases in literature for identification ARIMA models, and when I choose parameters p and q according to criteria that they are last values outside of confidence interval, I got values p=109, q=97. Matlab gave me error for this case:

Error using arima/estimate (line 386)

Input response series has an insufficient number of observations.

On the other side, when I am looking only to N/4 length of time series for identifying p and q parameters, I got p=36, q=34. Matlab gave me error for this case

Warning: Nonlinear inequality constraints are active; standard errors may be inaccurate.

In arima.estimate at 1113

Error using arima/validateModel (line 1306)

The non-seasonal autoregressive polynomial is unstable.

Error in arima/setLagOp (line 391) Mdl = validateModel(Mdl);

Error in arima/estimate (line 1181) Mdl = setLagOp(Mdl, 'AR' , LagOp([1 -coefficients(iAR)' ], 'Lags', [0 LagsAR ]));

How do I need to correct identify p and q parameters and what is wrong here? And wwhat does it mean in this partial autocorrelation diagram, why are last values so big?

ACF of time series PACF of time series


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