  In this note we show that the locally stationary wavelet process can be
decomposed into a sum of signals, each of which following a moving average
process with time-varying parameters. We then show that such moving average
processes are equivalent to state space models with stochastic design
components. Using a simple simulation step, we propose a heuristic method of
estimating the above state space models and then we apply the methodology to
foreign exchange rates data.
