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Structural Break Detection in Time Series Models



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Structural Break Detection in Time Series Models Richard A Davis Thomas Lee Gabriel Rodriguez Yam Colorado State University http www stat colostate edu rdavis lectures This research supported in part by an IBM faculty award Prague 11 05 1 Illustrative Example 6 4 2 0 2 4 6 How many segments do you see 0 Prague 11 05 1 51 100 200 2 151 300 time 3 251 400 2 Illustrative Example Auto PARM Auto Piecewise AutoRegressive Modeling 6 4 2 0 2 4 6 4 pieces 2 58 seconds 0 Prague 11 05 1 51 100 200 2 157 300 time 3 259 400 3 Example Monthly Deaths Serious Injuries UK 1600 1200 1400 Counts 1800 2000 2200 Data yt number of monthly deaths and serious injuries in UK Jan 75 Dec 84 t 1 120 Remark Seat belt legislation introduced in Feb 83 t 99 1976 1978 1980 1982 1984 Year Prague 11 05 4 Example Monthly Deaths Serious Injuries UK cont Data xt number of monthly deaths and serious injuries in UK differenced at lag 12 Jan 75 Dec 84 t 13 120 Remark Seat belt legislation introduced in Feb 83 t 99 200 0 bf tt W Wt YYtt aa bf t 0 if if 11 tt 98 98 0 f t f t 1 if 98 t 120 1 if 98 t 120 XXtt YYtt YYtt 1212 bg tt N Ntt bg 600 400 Differenced Counts 200 Traditional regression analysis 1976 1978 1980 1982 1984 99 tt 110 110 11 ifif 99 g t g t 0 otherwise otherwise 0 Year Model b 373 4 Nt AR 13 Prague 11 05 5 Introduction yExamples AR GARCH Stochastic volatility State space models Model selection using Minimum Description Length MDL y General principles y Application to AR models with breaks Optimization using a Genetic Algorithm y Basics y Implementation for structural break estimation Simulation results Applications Simulation results for GARCH and SSM Prague 11 05 6 Introduction The Premise in a general framework Base model P family or probability models for a stationary time series Observations y1 yn Segmented model there exist an integer m 0 and locations 0 1 1 m 1 m n 1 such that Yt X t j if j 1 t j where Xt j is a stationary time series with probability distr P j and j j 1 Objective



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