Asymptotic Statistics for the Scalogram of a Time Series
Résumé
The scalogram of a time series is defined as the quadratic mean of a multiscale analysis. The latter can be obtained using a wavelet analysis, or, more generally, using a sequence of filters of increasing scales, each one being followed by a temporal subsampling of order proportional to the analyzing scale. We will describe the asymptotic behavior of the scalogram as the scale and the number of observations tend to infinity, for an increment-stationary linear process with short or long memory, and of some non-linear or/and non-stationary long-memory processes.