Piecewise autoregression for general integer-valued time series

TL;DR

This paper introduces a piecewise autoregressive model for integer-valued time series with a novel inference method, demonstrating its effectiveness through simulations and real-world financial data applications.

Contribution

It develops a new piecewise autoregression model with a penalized likelihood inference and efficient dynamic programming implementation for integer-valued time series.

Findings

Consistent estimator for piecewise constant parameters.

Effective data-driven penalty calibration using slope heuristic.

Successful application to US recession data and stock trades.

Abstract

This paper proposes a piecewise autoregression for general integer-valued time series. The conditional mean of the process depends on a parameter which is piecewise constant over time. We derive an inference procedure based on a penalized contrast that is constructed from the Poisson quasi-maximum likelihood of the model. The consistency of the proposed estimator is established. From practical applications, we derive a data-driven procedure based on the slope heuristic to calibrate the penalty term of the contrast; and the implementation is carried out through the dynamic programming algorithm, which leads to a procedure of $\mathcal{O}(n^2)$ time complexity. Some simulation results are provided, as well as the applications to the US recession data and the number of trades in the stock of Technofirst.