Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price...

This paper develops a wavelet (spectral) approach to test the presence of a unit root in a stochastic process. The wavelet approach is appealing, since it is based directly on the different behavior of the spectra of a unit root process and that of a short memory stationary process. By...

Futures contracts on the New York Mercantile Exchange are the most liquid instruments for trading crude oil, which is the world’s most actively traded physical commodity. Under normal market conditions, traders can easily find counterparties for their trades, resulting in an efficient market...