Piecewise autoregression for general integer-valued time series

2019/11/03 by Diop, Mamadou Lamine, Kengne, William · 1 citation
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1911.00989

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 O(n²) 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.

Cited by

• Modelling time series of counts with hysteresis

Related

• Inference for multiple change-points in generalized integer-valued autoregressive model
• Evaluating Approximations of Count Distributions and Forecasts for Poisson-Lindley Integer Autoregressive Processes
• Integer-valued autoregressive process with flexible marginal and innovation distributions
• BNB autoregressions for modeling integer-valued time series with extreme observations
• Estimating nonlinear time-series models using simulated vector autoregressions