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Article overview
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Multiple Change Point Analysis: Fast Implementation And Strong Consistency | | Jie Ding
; Yu Xiang
; Lu Shen
; Vahid Tarokh
; | | Date: |
2 May 2016 | | Abstract: | Change point analysis is about identifying structural changes for stochastic
processes. One of the main challenges is to carry out analysis for time series
with dependency structure in a computationally tractable way. Another challenge
is that the number of true change points is usually unknown. It therefore is
crucial to apply a suitable model selection criterion to achieve informative
conclusions. To address the first challenge, we model the data generating
process as a segment-wise autoregression, which is composed of several segments
(time epochs), each of which modeled by an autoregressive model. We propose a
multi-window method that is both effective and efficient for discovering the
structure changes. The proposed approach was motivated by transforming a
segment-wise autoregression into a multivariate time series that is
asymptotically segment-wise independent and identically distributed. To address
the second challenge, we further derive theoretical guarantees for almost
surely selecting the true num- ber of change points of segment-wise independent
multivariate time series. Specifically, under mild assumptions we show that a
Bayesian information criterion (BIC)-like criterion gives a strongly consistent
selection of the optimal number of change points, while an Akaike informa- tion
criterion (AIC)-like criterion cannot. Finally, we demonstrate the theory and
strength of the proposed algorithms by experiments on both synthetic and
real-world data, including the eastern US temperature data and the El Nino data
from 1854 to 2015. The experiment leads to some interesting discoveries about
temporal variability of the summer-time temperature over the eastern US, and
about the most dominant factor of ocean influence on climate. | | Source: | arXiv, 1605.0346 | | Services: | Forum | Review | PDF | Favorites | |
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