Interaction between stock indices via changepoint analysis

Abstract

Stock market indices from several countries are modelled as discretely sampled diffusions whose parameters change at certain times. To estimate these times of parameter changes we employ both a sequential likelihood-ratio test and a non-parametric, spectral algorithm designed specifically for time series with multiple changepoints. Finally, we use point-process techniques to model relationships between changepoints of different financial time series.Suppose for simplicity we have observations of X t at times t ¼ 1; . . . ; n: Our goal will be to detect times at which the parameters y 1 and y 2 change. Intuitively, to decide if there is a change at time k we can maximize the log likelihood on t ¼ 1; . . . ; k À 1 and on t ¼ k; . . . ; n and M. J. LENARDON AND A. AMIRDJANOVA 576 Both the likelihood-based and the spectral-based sliding window methods of changepoint detection provide an entire time series of test statistics. To decide to what extent changes in one STOCK INDICES 577

Bayesian Inference for High Dimensional Changing Linear Regression with Application to Minnesota House Price Index Data

“…Such homogeneity assumptions may be violated in systems where the variables involved exhibit dynamic behavior and interactions. Common examples include economic time series (Chen and Gupta 1997;Kezim and Pariseau 2004;Lenardon and Amirdjanova 2006), climate change data (Reeves et al 2007), DNA micro-array data (Baladandayuthapani et al 2010) and so on. Change point models provide a convenient depiction of such complex relationships by splitting the data based on a threshold variable and using a homogeneous model for each segment.…”