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Chow test for structural change

Chow tests assess the stability of coefficients *β* in
a multiple linear regression model of the form *y* = *X**β* + *ε*.
Data are split at specified break points. Coefficients are estimated
in initial subsamples, then tested for compatibility with data in
complementary subsamples.

`h = chowtest(X,y,bp)`

`h = chowtest(Tbl,bp)`

`h = chowtest(___,Name,Value)`

```
[h,pValue,stat,cValue]
= chowtest(___)
```

returns
test decisions (`h`

= chowtest(`X`

,`y`

,`bp`

)`h`

) from conducting Chow tests on the multiple
linear regression model `y`

= `X`

*β* + *ε* at the break points in `bp`

.

uses
any of the input arguments in the previous syntaxes and additional
options specified by one or more `h`

= chowtest(___,`Name,Value`

)`Name,Value`

pair
arguments. For example, you can specify which type of Chow test to
conduct or specify whether to include an intercept in the multiple
regression model.

Chow tests assume continuity of the innovations variance across structural changes. Heteroscedasticity can distort the size and power of the test. You should verify the innovations-variance-continuity assumption holds before using the test results for inference.

If both subsamples contain more than

`numCoeffs`

observations, then you can conduct a forecast test instead of a break point test. However, the forecast test might have lower power relative to the break point test [1]. Nevertheless, Wilson (1978) suggests conducting the forecast test in the presence of unknown specification errors .You can apply the forecast test to cases where both subsamples have size greater than

`numCoeffs`

, where you would typically apply a breakpoint test. In such cases, the forecast test might have significantly reduced power relative to a break point test [1]. Nevertheless, Wilson (1978) suggests use of the forecast test in the presence of unknown specification errors [4].The forecast test is based on the unbiased predictions, with zero mean error, which result from stable coefficients. However, zero mean forecast error does not, in general, guarantee coefficient stability. Thus, forecast tests are most effective in checking for structural breaks, rather than model continuity [3].

To obtain diagnostic statistics for each subsample, such as regression coefficient estimates, their standard errors, error sums of squares, and so on, pass the appropriate data to

`fitlm`

. For details on working with`LinearModel`

model objects, see Multiple Linear Regression (Statistics and Machine Learning Toolbox).

[1] Chow, G. C. “Tests of Equality Between
Sets of Coefficients in Two Linear Regressions.” *Econometrica*.
Vol. 28, 1960, pp. 591–605.

[2] Fisher, F. M. “Tests of Equality Between Sets
of Coefficients in Two Linear Regressions: An Expository Note.” *Econometrica*.
Vol. 38, 1970, pp. 361–66.

[3] Rea, J. D. “Indeterminacy of the
Chow Test When the Number of Observations is Insufficient.” *Econometrica*.
Vol. 46, 1978, p. 229.

[4] Wilson, A. L. “When is the Chow Test
UMP?” *The American Statistician*. Vol.
32, 1978, pp. 66–68.

`LinearModel`

| `cusumtest`

| `fitlm`

| `recreg`

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