Stationarity in EViews
How to test for the existence of a unit root in EViews - Stationarity of a Series
Greetings everyone! In this video, I will demonstrate how to test for the existence of a unit root in a time series using EViews software. Specifically, I will be using real data for Canada, consisting of the consumer price index. Our objective is to determine whether our series is stationary or non-stationary.
To achieve this, we will use three methods, starting with a visual inspection of the graph, followed by a correlogram analysis, and finally, formal tests including the Augmented-Dickey Fuller, KPSS, and Phillips-Perron tests.
Why do we care about stationarity in time series analysis?
Stationarity is a critical property of a time series that is frequently used in statistical modeling and analysis. When a time series is stationary, its statistical properties, such as the mean, variance, and autocorrelation, remain constant over time. This property allows for more accurate and reliable predictions and forecasts. In contrast, non-stationary time series can exhibit erratic and unpredictable behavior, making it difficult to model and forecast. By identifying and modeling the stationary components of a time series, analysts can better understand the underlying patterns and signals in the data, leading to more effective decision-making and forecasting.
We begin our stationarity analysis by taking a look at the graph. After analyzing the graph, we can observe that the series exhibits a trend and an intercept, indicating that the mean of the series changes over time, further suggesting non-stationarity.
A visual graph of a non-stationary time series can display a changing pattern over time, including trends, seasonality, or cycles. The graph may indicate that the mean or variance of the data changes over time, making it challenging to identify any underlying pattern or signal in the data. Moreover, the graph may demonstrate high and persistent autocorrelations, which suggest a lack of independence between data points. In general, the visual graph of a non-stationary time series may show an inconsistent pattern over time, in contrast to a stationary time series graph that is relatively stable and consistent.
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.
In conclusion, the analysis of the graph, correlogram, and formal tests consistently suggest that the consumer price index time series for Canada exhibits non-stationarity, implying the existence of a unit root. We hope you found this video informative. If you have any questions or comments, please feel free to leave them in the comments section of the YouTube Video. Thank you for your attention.
Watch the video tutorial and download the dataset
Learn how to conduct diverse unit root tests on multiple time series at the same time!
Recommended Literature
To comprehend the significance of stationarity in time series analysis, I recommend reading the renowned paper "Spurious Regressions in Econometrics" by Newbold and Granger (1974). This paper highlights the implications of employing non-stationary time series in regression analysis, specifically in economic and financial data analysis.
The authors explain how non-stationary time series can result in unreliable and misleading regression outcomes, known as "spurious" regression results. They also demonstrate that non-stationary series can appear highly correlated in a regression model, even when they are completely unrelated, leading to false conclusions and potentially harmful decisions.
Reading this paper can help you gain a comprehensive understanding of the concept of stationarity in time series analysis, its importance, and methods to detect and manage non-stationarity in your data. This classic paper is widely cited in the field of econometrics and time series analysis.
You can access the paper by clicking here.
I hope you find this recommendation valuable in your learning journey. Happy reading!