the plot points out time varying mean of the series and hence the non-stationarity as discussed in the key conceptsdifferencing series helps in achieving stationarity in the following snippetwe prepare first order differenced log series and perform the same tests in [ ]log_series_shift log_series log_series shift(log_series_shift log_series_shift[~np isnan(log_series_shift)ad_fuller_test(log_series_shiftplot_rolling_stats(log_series_shiftthe test statistic at - is lower than even critical valuethus we reject the null hypothesis for ad fuller test the following are the test results test statistic - -value #lags used number of observations used critical value ( %- critical value ( %- critical value ( %- dtypefloat figure - rolling mean and standard deviation plot for log differenced gold price series this exercise points us to the fact that we need to use log differenced series for arima to model the dataset at hand see figure - yet we still need to figure out the order of autoregression and moving average componentsi and