When validating a time series, one of the first things to check before building an ARIMA model is to verify that the series is stationary. That is, it must be determined that the time series is constant in the mean and that the variance is constant and not time-dependent.
I think you can easily search (using search engine), you must have come across it with examples, especially RPubs's at https://www.google.com/url?sa=t&source=web&rct=j&url=https://rpubs.com/richkt/269797&ved=2ahUKEwjq9-nOg6nuAhWMZxUIHeKmAXgQFjAAegQIARAB&usg=AOvVaw04M4s8_SRlQbSv1Ii-MLQU
R.pub listed Stationarity Testing: Autocorrelation Function (ACF), Ljung-Box test for independence,Augmented Dickey–Fuller (ADF) t-statistic test for unit root, and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity. Indeed, "When investigating a time series, one of the first things to check before building an ARIMA model is to check that the series is stationary."
Adding to that:
1. You can generate the ACF and PACF plots. The ACF plots would show a gradual decrease to zero which implies that the time series is not stationary!
2. The non parametric Mann Kendall test is used to detect monotonic trends.The null hypothesis, H0, is that the data come from a population with independent realizations and are identically distributed.The alternative hypothesis, HA, is that the data follow a monotonic trend. syntax mk.test()
3. ts.stationary.test(tsdata)
Where "tsdata" implies the input univariate time series data. This function tests the deterministic and stochastic trend of the input time series data.
4. Augmented Dickey-Fuller Test is implementated using the adf. test function from the tseries R package. This is a very popular method. And by a rule of thumb, where the p-value is less than 0.05, we decide a statistical strong evidence against the null hypothesis, so we reject the null hypothesis.
Regards, Ibiloye A.C
At first test it graphically by using the plot. Then after you can check it by using Mann-Kendal, Augmented Dickey-Fuller Test, and test for existence of seasonal compartment.
Niyungeko Antoine Thank you Dr.Antoine NIYUNGEKO for being kind enough to answer my question.
Babak Jamshidi Thank you Dr. Babak Jamshidi for being kind enough to answer my question.
Abiodun Christian Ibiloye Thank you Dr. Abiodun Christian Ibiloye for your detailed answers, and for being kind enough to answer my question.
https://nwfsc-timeseries.github.io/atsa-labs/sec-boxjenkins-kpss.html
Stationarity Testing
Andrey Davydenko Thank you Dr. Andrey Davydenko for being kind enough to answer my question.
Kamal M Alsaad Thank you Dr. kamal M.Alsaad for being kind enough to answer my question.
Standard unit root test are weak to distinguish between unit root and its close alternatives (autoregressive coefficient close to unity). It is biased towards accepting null hypothesis. Therefore, when testing for unit root it's useful to employ various unit root test with different null hypothesis. For example ADF test and KPSS test.
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