A wavelet-based time-varying autoregressive model for non-stationary and irregular time series

Abstract

In this work we propose an autoregressive model with parameters varying in time applied to irregularly spaced non-stationary time series. We expand all the functional parameters in a wavelet basis and estimate the coefficients by least squares after truncation at a suitable resolution level. We also present some simulations in order to evaluate both the estimation method and the model behavior on finite samples. Applications to silicates and nitrites irregularly observed data are provided as well.

Keywords:

• irregularly spaced time series
• locally stationary processes
• autoregressive model
• multiresolution analysis
• wavelets

Acknowledgement

We would especially like to thank PhD. Marcelo Pablo Hernando, Facultad de Medicina, Universidad de Buenos Aires (Argentina) for providing the irregular time series used in Section 6.