strucchange

Structural Change Tests in Linear Regression Models

Description

Performs tests for structural change in linear regression models.

Usage

## S3 method for class 'formula'
sctest(formula, type = , h = 0.15,
    alt.boundary = FALSE, functional = c("max", "range",
    "maxL2", "meanL2"), from = 0.15, to = NULL, point = 0.5,
    asymptotic = FALSE, data, ...)

Arguments

formula a formula describing the model to be tested.

type a character string specifying the structural change test that is to be performed, the default is “Rec-CUSUM”. Besides the test types described in efp and sctest.Fstats the Chow test and the Nyblom-Hansen test can be performed by setting type to “Chow” or “Nyblom-Hansen”, respectively.

h numeric from interval (0,1) specifying the bandwidth. Determines the size of the data window relative to the sample size (for MOSUM and ME tests only).

alt.boundary logical. If set to TRUE alternative boundaries (instead of the standard linear boundaries) will be used (for CUSUM processes only).

functional indicates which functional should be used to aggregate the empirical fluctuation processes to a test statistic.

from, to numeric. If from is smaller than 1 they are interpreted as percentages of data and by default to is taken to be the 1 - from. F statistics will be calculated for the observations (nfrom):(nto), when n is the number of observations in the model. If from is greater than 1 it is interpreted to be the index and to defaults to n - from. (for F tests only)

point parameter of the Chow test for the potential change point. Interpreted analogous to the from parameter. By default taken to be floor(n*0.5) if n is the number of observations in the model.

asymptotic logical. If TRUE the asymptotic (chi-square) distribution instead of the exact (F) distribution will be used to compute the p value (for Chow test only).

data an optional data frame containing the variables in the model. By default the variables are taken from the environment which sctest is called from.

… further arguments passed to efp or Fstats.

Details

sctest.formula is a convenience interface for performing structural change tests in linear regression models based on efp and Fstats. It is mainly a wrapper for sctest.efp and sctest.Fstats as it fits an empirical fluctuation process first or computes the F statistics respectively and subsequently performs the corresponding test. The Chow test and the Nyblom-Hansen test are available explicitly here.

An alternative convenience interface for performing structural change tests in general parametric models (based on gefp) is available in sctest.default.

Value

An object of class “htest” containing:

statistic the test statistic,

p.value the corresponding p value,

method a character string with the method used,

data.name a character string with the data name.

Examples

library("strucchange")

## Example 7.4 from Greene (1993), "Econometric Analysis"
## Chow test on Longley data
data("longley")
sctest(Employed ~ Year + GNP.deflator + GNP + Armed.Forces, data = longley,
  type = "Chow", point = 7)


    Chow test

data:  Employed ~ Year + GNP.deflator + GNP + Armed.Forces
F = 3.9268, p-value = 0.06307

## which is equivalent to segmenting the regression via
fac <- factor(c(rep(1, 7), rep(2, 9)))
fm0 <- lm(Employed ~ Year + GNP.deflator + GNP + Armed.Forces, data = longley)
fm1 <- lm(Employed ~ fac/(Year + GNP.deflator + GNP + Armed.Forces), data = longley)
anova(fm0, fm1)

Analysis of Variance Table

Model 1: Employed ~ Year + GNP.deflator + GNP + Armed.Forces
Model 2: Employed ~ fac/(Year + GNP.deflator + GNP + Armed.Forces)
  Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
1     11 4.8987                              
2      6 1.1466  5    3.7521 3.9268 0.06307 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## estimates from Table 7.5 in Greene (1993)
summary(fm0)


Call:
lm(formula = Employed ~ Year + GNP.deflator + GNP + Armed.Forces, 
    data = longley)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.9058 -0.3427 -0.1076  0.2168  1.4377 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)   
(Intercept)   1.169e+03  8.359e+02   1.399  0.18949   
Year         -5.765e-01  4.335e-01  -1.330  0.21049   
GNP.deflator -1.977e-02  1.389e-01  -0.142  0.88940   
GNP           6.439e-02  1.995e-02   3.227  0.00805 **
Armed.Forces -1.015e-04  3.086e-03  -0.033  0.97436   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.6673 on 11 degrees of freedom
Multiple R-squared:  0.9735,    Adjusted R-squared:  0.9639 
F-statistic: 101.1 on 4 and 11 DF,  p-value: 1.346e-08

summary(fm1)


Call:
lm(formula = Employed ~ fac/(Year + GNP.deflator + GNP + Armed.Forces), 
    data = longley)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.47717 -0.18950  0.02089  0.14836  0.56493 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)   
(Intercept)        1.678e+03  9.390e+02   1.787  0.12413   
fac2               2.098e+03  1.786e+03   1.174  0.28473   
fac1:Year         -8.352e-01  4.847e-01  -1.723  0.13563   
fac2:Year         -1.914e+00  7.913e-01  -2.419  0.05194 . 
fac1:GNP.deflator -1.633e-01  1.762e-01  -0.927  0.38974   
fac2:GNP.deflator -4.247e-02  2.238e-01  -0.190  0.85576   
fac1:GNP           9.481e-02  3.815e-02   2.485  0.04747 * 
fac2:GNP           1.123e-01  2.269e-02   4.951  0.00258 **
fac1:Armed.Forces -2.467e-03  6.965e-03  -0.354  0.73532   
fac2:Armed.Forces -2.579e-02  1.259e-02  -2.049  0.08635 . 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4372 on 6 degrees of freedom
Multiple R-squared:  0.9938,    Adjusted R-squared:  0.9845 
F-statistic: 106.9 on 9 and 6 DF,  p-value: 6.28e-06