While the sorting of the data has no influence on the Jarque-Bera test, it does have an influence on the three other tests which are particularly suited for time series analysis.īelow the table that displays the descriptive functions of the time series, two bar charts display the evolution of the **autocorrelation function (ACF)**and of the partial autocorrelation function (PACF). They all agree that the data cannot be assumed to be generated by a white noise process. These tests are also based on the Chi-square distribution. They allow to test if the data could be assumed to be a white noise or not. The three other three tests ( Box-Pierce, Ljung-Box, McLeod-Li) are computed at different time lags. With an alpha=0.05 significance level, one should reject the null hypothesis. Here the p-value, which corresponds to the probability of being wrong when rejecting the null hypothesis, is close to 0.012. The higher the value of the Chi-square statistic, the more unlikely the null hypothesis that the data are normally distributed.
The Jarque-Bera test is a normality test, based on the skewness and kurtosis coefficients. Then the Normality test and white noise tests table is displayed. The first table displays the summary statistics. Interpreting the descriptive statistics of a time series The computations begin once you have clicked on OK. The Outputs and Charts tabs are parameterized as follows: In the O ptions tab, automatic time steps are selected: The option Series labels is activated because the first row of the selected data contains the header of the variable. The Time series corresponds to the series of interest, the Passengers. Once you've clicked on the button, the Descriptive analysis dialog box appears.
Setting up a descriptive analysis of time seriesĪfter opening XLSTAT, select the XLSTAT / Time / Descriptive analysis command. In order to confirm this trend we are going to analyze the autocorrelation function of the series. Every year, a similar cycle starts while the variability within a year seems to increase over time. We notice a global upward trend on the chart. Our goal is to show how helpful a descriptive analysis can be prior to a modeling approach. It is widely used as a non-stationary seasonal time series. The data have been obtained in, and correspond to monthly international airline passengers (in thousands) from January 1949 to December 1960. Dataset for the differencing transformation This tutorial will help you describing a time series and transforming it so that it becomes stationary, in Excel using the XLSTAT software.