The chief tools in identification of ARIMA model are the autocorrelation function (ACF), the partial autocorrelation function (PACF) plots. The Figure below shows that ACF and PACF plots after first difference of a series. Therefore, What are the tentative or candidate ARIMA models of this series?
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Have a look at https://towardsdatascience.com/time-series-forecasting-arima-models-7f221e9eee06
https://towardsdatascience.com/significance-of-acf-and-pacf-plots-in-time-series-analysis-2fa11a5d10a8
https://rstudio-pubs-static.s3.amazonaws.com/303786_f1b99d6b7e9346c4b1488a174bab839a.html
Your data plots do not reveal stationarity of your series. This is because under stationaraity both ACF and PACF should decay after lags of p and q for ARIMA(p,d,q).
In practice, the correlogram do not always adequately identify the best values of p and q for AR and MA parts of the ARIMA (p,d,q) model.
It is only meant to detect the possible orders of p and q respectively after which selection criteria such as the AIC and BIC will be used to determine the best values of p and q based on the results reported by the correlogram. For instance, from your correlogram there are three significant spikes of the Partial Autocorrelation (PACF) which occured at. p=1,2 & 5 while the Autocorrelation Function (ACF) has no significant spikes at all. In this case, ARIMA (1, d, 0), ARIMA (2, d, 0) and ARIMA (5, d, 0) are suggested to fit the series. The "d" there denotes the level of differencing.
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