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in a plot of my time series there is clearly visible that there is structural break, but I have to find the exact date. I want test this with the chow test. Although I understand how to perform this test if the date of the structural break is know, by simply using a linear regression with two dummy's one for the intercept and one for the slope,

$R_t$ = $\beta_0 $+ $\beta_0^* · D_i + \beta_1 R_{m,t} + \beta_1^* · D_t · R_{m,t} + ε_t,$

Than using the chow test.. But if I do not know the exact date, (in other words: I do not know when $D_i$ and $D_t$ should be 1) how can I find the exact date?

Thank you very much for reply

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  • $\begingroup$ You tagged the question as "cointegration", but do not mention it... are you asking for a "normal" relationship, or one where R and R_m might are potentially unit roots? $\endgroup$ – Matifou Jun 18 '14 at 16:06
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Your approach may work BUT lacks significant generality. You might want to review Change and anomaly detection as it raises issues about change point detection Your approach assumes a known date and a specific kind of change whereas the work of Tsay http://www.unc.edu/~jbhill/tsay.pdf and others actually can find the date of not only a change in the expected value but a change in the error variance. These methods and others such as detecting paramter changes in general and variance changes have been implemented fully in AUTOBOX and to a much lesser degree in SAS and SPSS. Automatic Forecasting Systems offers a complete 30 day free trial version so I suggest that you go to http://www.autobox.com/cms/ and avail yourself to this version. For transparency purposes you should know that I was involved in the design and implementation of change point methodologies for this software and am considered (by some) to be a thought leader in that field.. Some of my guidance came from http://www.osti.gov/scitech/biblio/161513

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