MULTIPLEBREAKS.RPF

MULTIPLEBREAKS.RPF is an example of the use of the @MULTIPLEBREAKS procedure for analyzing multiple (>1) break in a linear regression based upon a threshold value other than time. This uses the same algorithm as @BAIPERRON which is for analyzing multiple structural breaks (based upon time).

The example is based upon the example from Hansen(1996). It first uses the @TAR procedure to analyze a (one-break) threshold autoregression. Then uses the threshold series (lag two of the dependent variable) to examine up to three breaks on the same model (an autoregression with CONSTANT on lags 1, 2 and 5).

The output from @TAR is at the top. This has a much better established literature than the same with more than one break, and includes formal tests (three variants) of the single threshold effect. The break value is the same as the one-break value generated by @MULTIPLEBREAKS (it's just rounded to four decimals). The evidence in favor of even a single break in the TAR isn't particularly strong—only one of the three test variants is even slightly significant at the .05 level. So it isn't a surprise that no breaks is (slightly) favored over one break in the multiple break point analysis.

Full Program

open data gnp.asc

calendar(q) 1947

data(format=free,org=columns) 1947:01 1990:03 gnp dontknow

set ggrowth = log(gnp/gnp{1})*400.0

@tar(laglist=||1,2,5||,nreps=1000) ggrowth

set lagtwo = ggrowth{2}

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

# constant ggrowth{1 2 5}

Output

Threshold Autoregression

Threshold is GGROWTH{2}=0.0126

Tests for Threshold Effect use 1000 draws

SupLM 18.244777 P-value 0.046000

ExpLM 4.768378 P-value 0.088000

AveLM 4.564716 P-value 0.307000

Variable Full Sample <=Thresh >Thresh

Constant 1.992255 -3.212555 2.141862

( 0.478946) ( 1.672070) ( 0.638545)

GGROWTH{1} 0.317537 0.512781 0.300854

( 0.077048) ( 0.183042) ( 0.079967)

GGROWTH{2} 0.131979 -0.926923 0.184844

( 0.076781) ( 0.347333) ( 0.108861)

GGROWTH{5} -0.086963 0.384457 -0.158135

( 0.071641) ( 0.202972) ( 0.070146)

Observations 169 38 131

SEESQ 15.960496 23.533054 12.143010

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