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?
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).
Nielsen and Whitby (2015) in A Joint Chow Test for Structural Instability, Econometrics 2015, 3, describe the test. They also say:
The pointwise one-step Chow test is essentially the “prediction interval” test described by Chow (1960), but computed recursively and over the sample (rather than at an a priori hypothesised change point). It first appears in PcGive Version 4.0 as part of a suite of model misspecification diagnostics; a similar diagnostic graphic, the “one-step forecast test”, is provided in EViews.
So you can look also at: Chow, G.C. Tests of equality between sets of coefficients in two linear regressions. Econometrica 1960, 28, 591–605.