## Info First-Differences

To make the series stationary, it is necessary to use the first-differences: (1 -D)cact = cact — cact-1 where D is a shift operator. Once the signal is corrected of its trend by means of first differences (table and graph not presented here), the observation of both correlograms of the series shows that all the terms of the simple and partial correlograms are inside the confidence interval, beyond which it is considered that the values are significantly different from zero. Thus, the terms are not significantly different from zero. Traditional approaches usually said that such an observation is characteristic of a "white noise" process. The Q-statistic of the Ljung-Box (calculated by Matlab or Eviews) confirms this observation: Q-stat = 14.58 (with a delay k = 15) < Xo 05-15 = 25. Thus, we would be led to accept the hypothesis of the nullity of coefficients pk (the critical probability of this test is indicated ac = 0.482 > 0 . 05, therefore one accepts the null hypothesis H0). The Ljung-Box Q-Statistic evoked above is given by:

P r2

j=1 T — j where rj is the j-th autocorrelation and T the number of observations. Below, the first-differences of the series: 