A note on state space representations of locally stationary wavelet time series

摘要

In this note we show that the locally stationary wavelet process can bedecomposed into a sum of signals, each of which following a moving averageprocess with time-varying parameters. We then show that such moving averageprocesses are equivalent to state space models with stochastic designcomponents. Using a simple simulation step, we propose a heuristic method ofestimating the above state space models and then we apply the methodology toforeign exchange rates data.