Dynamic changepoint detection in count time series: a particle filter approach

We study Bayesian dynamic models for detecting changepoints in count time series that present structural breaks. As the inferential approach, we develop a parameter learning version of the algorithm proposed by Chopin [Chopin N. Dynamic detection of changepoints in long time series. Annals of the Institute of Statistical Mathematics 2007;59:349–366.], called the Chopin filter with parameter learning, which allows us to estimate the static parameters in the model. In this extension, the static parameters are addressed by using the kernel smoothing approximations proposed by Liu and West [Liu J, West M. Combined parameters and state estimation in simulation-based filtering. In: Doucet A, de Freitas N, Gordon N, editors. Sequential Monte Carlo methods in practice. New York: Springer-Verlag; 2001]. The proposed methodology is then applied to both simulated and real data sets and the time series models include distributions that allow for overdispersion and/or zero inflation. Since our procedure is general, robust and naturally adaptive because the particle filter approach does not require restrictive specifications to ensure its validity and effectiveness, we believe it is a valuable alternative for dealing with the problem of detecting changepoints in count time series. The proposed methodology is also suitable for count time series with no changepoints and for independent count data.     

Variable dimension via stochastic volatility model using FX rates

In this paper, changepoint analysis is applied to stochastic volatility (SV) models which aim to understand the locations and movements of high frequency FX financial time series. Bayesian inference using the Markov Chain Monte Carlo method is performed using a process called variable dimension for SV parameters. Interesting results are that FX series have locations where one or more positions of the sequence correspond to systemic changes, and overall non-stationarity, in the returns process. Furthermore, we found that the changepoint locations provide an informative estimate for all FX series. Importantly in most cases, the detected changepoints can be identified with economic factors relevant to the country concerned. This helps support the fact that macroeconomics news and the movement in financial price are positively related.     

Nonparametric statistical procedures for the changepoint problem

Let X₁,…,X_r?1,X_r,X_r+1,…,X_n be independent, continuous random variables such that X_i, i = 1,…,r, has distribution function F(x), and X_i, i = r+1,…,n, has distribution function F(x?Δ), with -∞ <Δ< ∞. When the integer r is unknown, this is refered to as a change point problem with at most one change. The unknown parameter Δ represents the magnitude of the change and r is called the changepoint. In this paper we present a general review discussion of several nonparametric approaches for making inferences about r and Δ.     

Generalized bent-cable methodology for changepoint data: a Bayesian approach

The choice of the model framework in a regression setting depends on the nature of the data. The focus of this study is on changepoint data, exhibiting three phases: incoming and outgoing, both of which are linear, joined by a curved transition. Bent-cable regression is an appealing statistical tool to characterize such trajectories, quantifying the nature of the transition between the two linear phases by modeling the transition as a quadratic phase with unknown width. We demonstrate that a quadratic function may not be appropriate to adequately describe many changepoint data. We then propose a generalization of the bent-cable model by relaxing the assumption of the quadratic bend. The properties of the generalized model are discussed and a Bayesian approach for inference is proposed. The generalized model is demonstrated with applications to three data sets taken from environmental science and economics. We also consider a comparison among the quadratic bent-cable, generalized bent-cable and piecewise linear models in terms of goodness of fit in analyzing both real-world and simulated data. This study suggests that the proposed generalization of the bent-cable model can be valuable in adequately describing changepoint data that exhibit either an abrupt or gradual transition over time.