We want to apply extreme value theory to the maximum yearly temperatures. Before we choose the model we want to test whether or not we can assume independence. First we made a plot of the autocorrelation function: acf plot. Thereafter, we applied the Ljung-Box and/or Box-Pierce test. However we find that if we only include one lag, there is no statistical evidence of dependence on the 5% level (our p-value is about 0.1) but if we include 2 or more lags, the p-values are significantly lower than our significance level. Can anyone help us understand what we can conclude from these results?
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