A note on state space representations of locally stationary wavelet time   series
  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. 
K. Triantafyllopoulos and G.P. Nason