MULTIPLEBREAKS Procedure

@MultipleBreaks does multiple structural change analysis as described in Bai and Perron(2003), but using a threshold variable other than time. The related procedure which does the breaks based upon time from the Bai-Perron paper is @BaiPerron.

@MULTIPLEBREAKS( options ) depvar start end

# list of regressors (in regression format)

Parameters

depvar	dependent variable
start, end	range for regression. By default, the maximum range permitted by all variables involved in the regression.

Options

MINSPAN=shortest distance between two breaks [number of regressors]

MAXBREAKS=maximum breaks allowed [2]

THRESH=threshold series

If omitted, time is used. If you're using a lagged value, you need to create the lag as a separate series.

Example

This is from MULTIPLEBREAKS.RPF. The regression being run is an autoregression of GGROWTH (GDP growth) on its own lags 1, 2 and 5, using the second own lag as the threshold variable. This has to be created as its own series (thus the SET LAGTWO instruction). This allows for three breaks (thus four branches).

set lagtwo = ggrowth{2}

@multiplebreaks(thresh=lagtwo,max=3) ggrowth

# constant ggrowth{1 2 5}

The output includes the original regression, and then a table with change point analysis. This shows the residual sum of squares (so when #Breaks is 0 it will match the regression output), the Bayesian Information Criterion and the list of break values. The minimum BIC value is starred—here it's with no breaks.

Note that even though here the break values are "nested" (the one break value is one of the two and three break values, the other two break value is also a three break value), that isn't a requirement of the algorithm. In fact, if there are, for instance, two fairly clear breaks (so a one break model is inadequate), the one break value may be between the two two break values.

Output

Linear Regression - Estimation by Least Squares

Dependent Variable GGROWTH

Quarterly Data From 1948:03 To 1990:03

Usable Observations 169

Degrees of Freedom 165

Centered R^2 0.1628153

R-Bar^2 0.1475938

Uncentered R^2 0.4528378

Mean of Dependent Variable 3.1410076234

Std Error of Dependent Variable 4.3271293927

Standard Error of Estimate 3.9950589009

Sum of Squared Residuals 2633.4817776

Regression F(3,165) 10.6964

Significance Level of F 0.0000018

Log Likelihood -471.8514

Durbin-Watson Statistic 1.9623

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant 1.992254876 0.478945795 4.15967 0.00005115

2. GGROWTH{1} 0.317536956 0.077047985 4.12129 0.00005952

3. GGROWTH{2} 0.131978784 0.076780857 1.71890 0.08750766

4. GGROWTH{5} -0.086962975 0.071640801 -1.21387 0.22653010

Multiple Change Point Analysis

Dependent Variable GGROWTH

Threshold Variable LAGTWO

# Breaks RSS BIC Break Values

0 2633.4817776 2.86758113*

1 2342.2860873 2.87181942 0.012572093

2 2113.4355876 2.89042459 -1.859113332 0.012572093

3 1934.9685629 2.92361853 -1.859113332 0.012572093 2.337910891