Identifying Nonstationarities

The wavelet stationarity test can additionally indicate where the nonstationarities are located in the series. This is because the test knows the scale and location of the Haar wavelet coefficients whose null hypotheses were rejected. The estimated nonstationarities can be plotted by locits by simple application of plot by:

plot(ans)

which results in the plot shown to the left.

The plot shows the exP time series in grey. Each red double-headed arrow corresponds to one of the 11 FDR nonstationarities identified by the test. The length of the arrow corresponds to the scale of the Haar wavelet coefficient whose null hypothesis was rejected and the location of that Haar wavelet coefficient is fixed by the mid-point of the arrow. The numbers 6, 7, 8 on the right-hand side of the plot correspond to the scale of the wavelet periodogram, j where the nonstationarity was found. It is particularly noticeable that most of the nonstationarities seem centred around the t=100 point where there appears to be a significant burst of power.

If not Stationary, then what?

The explosion data set is an extreme example of a time series that is almost certainly not stationary. It would be clearly inappropriate to use methods designed for stationary series on the explosion P wave. For example, the autocovariance structure of the series is clearly different at the beginning and end of the series. Also, it would not be appropriate to apply the regular spectrum (periodogram) estimator to the whole series as it would erroneously average out the differences in the series.

In this case, and others of nonstationarity, it would be better to use local methods of autocovariance or local spectral quantities to estimate the second-order structure of the series. Information on how to do this can be found in the sections on local autocovariance and local autocorrelation or local spectral analysis. Local Autocovariance>