Data-Driven Learning of the Number of States in Multi-State Autoregressive Models
This addresses model selection for non-stationary time-series analysis, but it is incremental as it builds on existing Gap statistics methods.
The authors tackled the problem of selecting the number of states in multi-state autoregressive models for non-stationary time-series, proposing a new model selection technique based on Gap statistics and a distance measure using mean squared prediction error, with numerical results showing improved performance.
In this work, we consider the class of multi-state autoregressive processes that can be used to model non-stationary time-series of interest. In order to capture different autoregressive (AR) states underlying an observed time series, it is crucial to select the appropriate number of states. We propose a new model selection technique based on the Gap statistics, which uses a null reference distribution on the stable AR filters to check whether adding a new AR state significantly improves the performance of the model. To that end, we define a new distance measure between AR filters based on mean squared prediction error (MSPE), and propose an efficient method to generate random stable filters that are uniformly distributed in the coefficient space. Numerical results are provided to evaluate the performance of the proposed approach.