My interest is to check for structural changes in a time series. I know the time point which I wish to check for structural break. This point happens to be near the end of the series. Also I am doing a univariate modeling on the series (so no other regressors other that it's own lags).

Following is what I understood after browsing through the net:

  1. There are many tests to check for Structural breaks: Chow test, sup-Wald test, sup-LM test, sup-LR (Andrews test), etc.

  2. The classical chow test can handle near the end problem but requires linearity of the model, exogenous regressors and normality of errors. Since auto.arima in R gives a (1,0,0)(1,0,0) model, two of these three requirements are not met.

  3. Some websites suggest to use Andrews test as this test can handle non-linearity and own-lagged regressors (Q1: would be great if someone can confirm this). Further, this test allows for automatic detection of break points. Q2: Can it detect only one breakpoint or many?

  4. Then I discovered that this test may not be good as it assumes large number of observations before and after the breakpoint.

  5. Latest information that I have is that Andrews developed another test in 2003, which can handle all these problems.

Q3: Is there a R package which has this latest test?

Q4: Can either of sup-Wald test or sup-LM test work for me?

Q5: Can someone give a brief idea of the tests above, particularly their assumptions, applicability and possibly a source to study theory behind them?


1 Answer 1


"I know the time point which I wish to check for structural break."

A structural break can be due to

1) an observation that is significantly different from the expected thus a pulse indicator would be approriate ....to identify this pulse follow http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html

2) a sequence of recent errant observations can be suggested by the need for a level/step shift using the above reference .

3) a sequence of recent errant observations can be suggested by a change in the model form testable by the 1960 CHOW test https://de.wikipedia.org/wiki/Chow-Test for constant PARAMETERS across groups. This is different from the "typically available Chow test for a level shift in the expected value" which is dealt with 2)

4) a sequence of errant observations can be suggested by detecting deterministic change points in the model error variance using the same reference

Precisely which structural break are you after ?

Finally you say you know the break point thus this is de jure . Often time there is a de facto break point which can differ from the presumed one requiring it to be found via analytics from the aforementioned reference.

  • $\begingroup$ I didn't say I know the breakpoint. I am saying there's a time point that I want to check for structural break. What you are referring to seems similar to AO and LS type outlier detection . But I think structural change covers more possibilities that what outliers cover. My interest as mentioned is know more about the tests. Chow test shouldn't be applicable as I said it requires linear models with exogenous regressors only. $\endgroup$
    – Dayne
    Commented Sep 7, 2019 at 7:45
  • $\begingroup$ When you specify the breakpoint that is implicitly assuming knowledge or a "possible truth". We agree on that. The search for AO and LS is conducting one kind of "structural break" while the tests for constant parameters and constant error process are also conducting "structural break tests". These two tests do not require an ARIMA component to be nul but are fully applicable to a general SARMAX model autobox.com/pdfs/SARMAX.pdf $\endgroup$
    – IrishStat
    Commented Sep 7, 2019 at 9:48
  • $\begingroup$ By "these two tests" are you referring to AO and LS tests? I am aware about outlier detection in time series. In fact I did use the algorithm from Chen and Liu (1993) to detect an LS type outlier. My interest here, as also mentioned above, is to know about structural break tests near the for time series. $\endgroup$
    – Dayne
    Commented Sep 11, 2019 at 11:37
  • $\begingroup$ The two tests are 1) do the parameters (collectively) duffer from one one region to another ... and 2) does the model error variance change from one region to another $\endgroup$
    – IrishStat
    Commented Sep 11, 2019 at 11:53
  • $\begingroup$ Right. Can you give the names of these tests and confirm whether these tests would work for breaks near the end of sample? Please refer to [this] (onlinelibrary.wiley.com/doi/abs/10.1111/1468-0262.00466) for details. $\endgroup$
    – Dayne
    Commented Sep 11, 2019 at 11:57

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