The 95% confidence intervals are also displayed. While the sorting of the data has no influence on the Jarque-Bera test, it does have an influence with 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 0.01. The bigger 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 as follows: In the options 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 appears. In order to confirm this trend we are going to analyse the autocorrelation function of the series.Īfter opening XLSTAT, select the XLSTAT/XLSTAT-Time/Descriptive analysis command, or click on the corresponding button of the "XLSTAT-Time" toolbar (see below). We notice that on the chart, there is global upward trend, that every year, a similar cycles start while the variability within a year seems to increase over time. Our goal is to show how helpful descriptive analysis can be before a modeling approach. It is widely used as an nonstationary seasonal time series. ![]() The data have been obtained in, and correspond to monthly international airline passengers (in thousands) from January 1949 to December 1960. An Excel sheet with both the data and results can be downloaded by clicking here.
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