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

TL;DR

This paper demonstrates that locally stationary wavelet processes can be represented as sums of moving average signals with time-varying parameters, which are equivalent to state space models, and proposes a heuristic estimation method applied to exchange rate data.

Contribution

It introduces a novel decomposition of locally stationary wavelet processes into state space models with stochastic design, along with a heuristic estimation approach.

Findings

Successful application to foreign exchange rates data

Effective heuristic estimation method demonstrated

Theoretical link between wavelet processes and state space models

Abstract

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.