Has anyone heard of 1-step Chow test? I've searched the keyword "1-step chow test" in Google but can not find any hits. What's the formula of this test?
Solved – How to do 1-step Chow test
chow-test
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Your question is most interesting to me and it's solution has been my primary research for a number of years.
There are a number of ways that "a structural break" may occur.
If there is a change in the Intercept or a change in Trend in "the latter portion of the time series" then one would be better suited to perform Intervention Detection (N.B. this is the empirical identification of the significant impact of an unspecified Deterministic Variable such as a Level Shift or a Change in Trend or the onset of a Seasonal Pulse ). Intervention Detection then is a pre-cursor to Intervention Modelling where a suggested variable is included in the model. You can find information on the web by googling "AUTOMATIC INTERVENTION DETECTION" . Some authors use the term "OUTLIER DETECTION" but like a lot of statistical language this can be confusing/imprecise . Detected Interventions can be any of the following (detecting a significant change in the mean of the residuals );
- a 1 period change in Level ( i.e. a Pulse )
- a multi-period contiguous change in Level ( i.e. a change in Intercept )
- a systematic Pulse ( i.e. a Seasonal Pulse )
- a trend change (i.e. 1,2,3,4,5,7,9,11,13,15 ..... )
These procedures are easily programmed IN R/SAS/Matlab and routinely available in a number of commercially available time series packages however there are many pitfalls that you need to be wary of such as whether to detect the stochastic structure first or do Intervention detection on the original series. This is like the chicken and egg problem. Early work in this area was limited to type 1's and as such will probably be insufficient for your needs .
If no such phenomenon is detected then one might consider the CHOW TEST which normally requires the user to pre-specify the point of hypothesized change. I have been researching and implementing procedures to DETECT the point of change by evaluating alternative hypothetical points in time to determine the most likely break point.
In closing one might also be sensitive to the possibility that there might have been a structural change in the error variance thus that might mask the CHOW TEST leading to a false acceptance of the null hypothesis of no significant break points in parameters.
The strucchange package contains Chow and F tests for structural changes in regression models. The package comes with a vignette which shows how to use the package.
Best Answer
A Chow test is a test to verify if your time series have a structural break. To do so, you fit a model on the entire range of your time series. Afterwards you fit the same model on a number of subsets of your time series, and compare the sum of error squares. Formulas are given on wikipedia: http://en.wikipedia.org/wiki/Chow_test
And I believe that a 1-step Chow test checks if you have one structural break in your data, you can also check for multiple structural breaks (becoming a 2-step, or n-step Chow test).