Stationarity in EViews

 This observation is reinforced by the correlogram analysis which reveals a non-immediate decay in the auto-correlation function.
A correlogram is a visual representation of the autocorrelation function (ACF) or partial autocorrelation function (PACF) of a time series. However, for non-stationary time series, where the statistical properties change over time, the correlogram may look distinct from that of a stationary series. In particular, non-stationary time series may exhibit slow or absent decay in autocorrelations, indicating trends or seasonality in the data. As a result, the correlogram of a non-stationary time series may display high and persistent autocorrelations, making it difficult to detect the true signal or pattern within the data. 

Next, we conduct the Augmented-Dickey Fuller test with a trend and intercept, as indicated by the graph. 

The augmented Dickey-Fuller (ADF) test is a statistical method used to determine whether a time series data set is stationary or non-stationary. The ADF test checks for the presence of a trend in the data by testing for the presence of a unit root. If a time series is stationary, its statistical properties such as the mean, variance, and autocorrelation remain constant over time. Conversely, when a time series is non-stationary, it has a trend or pattern that changes over time.

The ADF test is an extension of the Dickey-Fuller test that adds extra lagged terms in the regression equation to account for any serial correlation in the data. The ADF test produces a test statistic and a p-value. A series is considered stationary if the test statistic is less than the critical value and the p-value is less than a chosen significance level, typically 0.05. On the other hand, if the test statistic is greater than the critical value and the p-value is greater than the significance level, we fail to reject the null hypothesis, and conclude that the series is non-stationary.

The test results suggest that we cannot reject the null hypothesis of the series having a unit root, which confirms our suspicion of non-stationarity. 

We obtain similar outcomes from the Phillips-Perron test. 

The Phillips-Perron test is a popular statistical method for detecting stationarity in time series data, much like the Augmented Dickey-Fuller (ADF) test. However, the Phillips-Perron test utilizes a unique approach to account for autocorrelation and heteroscedasticity. By regressing the first difference of the series on a set of lagged differences, the test produces a test statistic and p-value. If the test statistic is less than the critical value and the p-value is less than the chosen significance level (usually 0.05), the null hypothesis that the time series is non-stationary can be rejected, and it can be concluded that the series is stationary. 

Furthermore, we use the KPSS test to determine if the series is stationary. The results of the KPSS test indicate that we can reject the null hypothesis of stationarity, again confirming the non-stationarity of our series.

The KPSS test is a statistical technique used to assess the stationarity of time series data by examining whether its trend is stationary around a mean or linear trend. Unlike the Augmented Dickey-Fuller (ADF) and Phillips-Perron tests, which detect the presence of a unit root indicating non-stationarity, the KPSS test checks the opposite.  Eviews produces a test statistic value, and if the statistical value is above the asymptotic critical values , we reject the null hypothesis of the test (null hypothesis: "the series is stationary"). The KPSS test is named after its inventors Kwiatkowski, Phillips, Schmidt, and Shin.