Markov-switching generalized additive models

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• 作者：Roland Langrock ; Thomas Kneib ; Richard Glennie ; Théo Michelot
• 关键词：P ; splines ; Hidden Markov model ; Penalized likelihood ; Time series regression
• 刊名：Statistics and Computing
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：27
• 期：1
• 页码：259-270
• 全文大小：1074KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics and Computing/Statistics Programs; Artificial Intelligence (incl. Robotics); Statistical Theory and Methods; Probability and Statistics in Computer Science;
• 出版者：Springer US
• ISSN：1573-1375
• 卷排序：27

文摘

We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for nonparametrically estimating the functional form of the effect of the covariates in such a regression model, assuming an additive structure of the predictor. The resulting class of Markov-switching generalized additive models is immensely flexible, and contains as special cases the common parametric Markov-switching regression models and also generalized additive and generalized linear models. The feasibility of the suggested maximum penalized likelihood approach is demonstrated by simulation. We further illustrate the approach using two real data applications, modelling (i) how sales data depend on advertising spending and (ii) how energy price in Spain depends on the Euro/Dollar exchange rate.