Respected Sir
I fitted that model... lnrpe= a+bt and conducted sup F test since
autocorelation is present in the data and AIC as you mentioned might
not .... Is it OK... Since I am not well versed with time series
econometrics can you please tell me if the
work is now correct or not
--
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Thanking you
Ayanendu Sanyal
PhD Scholar
Institute for Social and Economic Change (ISEC)
P.O- Nagarbhavi
Bangalore-72
State- Karnataka
Country- India
PIN- 560072
www.isec.ac.in/phd.html
http://ayanendusanyal.blogspot.com/
lnrpe
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6.147054773
R version 2.14.1 (2011-12-22)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
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> source("C:\\Documents and Settings\\ayaendu\\My Documents\\struc.R")
Loading required package: MASS
Loading required package: nnet
Loading required package: survival
Loading required package: splines
Loading required package: zoo
Attaching package: ‘zoo’
The following object(s) are masked from ‘package:base’:
as.Date, as.Date.numeric
Loading required package: sandwich
Warning message:
Overlapping confidence intervals
> ayan <- read.table("ayan.txt", header=T) ## Fetching files saved in My
> documents
> ayan = ts(ayan, start=1, frequency=1) ## Setting the data into time series
> data
> trend = time (ayan) ## defining the explanatory variable
> reg = lm(ayan~trend) ## regression lnrpe= a+bt
> summary (reg) ## regression results summary
Call:
lm(formula = ayan ~ trend)
Residuals:
Min 1Q Median 3Q Max
-0.35086 -0.11196 -0.01008 0.09193 0.38507
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.345373 0.049774 27.03 <2e-16 ***
trend 0.101771 0.001844 55.19 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.166 on 44 degrees of freedom
Multiple R-squared: 0.9858, Adjusted R-squared: 0.9854
F-statistic: 3046 on 1 and 44 DF, p-value: < 2.2e-16
> library (car) ## loading package to do dwtest
> library (strucchange) ## loading package to do structural break
> library (lmtest) ## loading package to do dwtest
> dwtest (reg) ## for testing serial auto correrelation
Durbin-Watson test
data: reg
DW = 0.4157, p-value = 1.405e-12
alternative hypothesis: true autocorrelation is greater than 0
> bp.ayan <- breakpoints(ayan ~ trend) ## searching for break points
> summary (bp.ayan) ## checking the breakpoints and minimum AIC level
Optimal (m+1)-segment partition:
Call:
breakpoints.formula(formula = ayan ~ trend)
Breakpoints at observation number:
m = 1 23
m = 2 23 33
m = 3 11 23 33
m = 4 11 23 33 40
m = 5 11 20 26 34 40
m = 6 8 14 20 26 34 40
Corresponding to breakdates:
m = 1 23
m = 2 23 33
m = 3 11 23 33
m = 4 11 23 33 40
m = 5 11 20 26 34 40
m = 6 8 14 20 26 34 40
Fit:
m 0 1 2 3 4 5
RSS 1.2131579 0.7466773 0.5243361 0.3570253 0.2712234 0.2589809
BIC -25.2008012 -36.0409283 -40.8160181 -47.0090984 -48.1669059 -38.8056613
m 6
RSS 0.2698858
BIC -25.4224766
> ci.ayan <- confint(bp.ayan)## confidence interval for the test
> breakdates (ci.ayan)
2.5 % breakpoints 97.5 %
1 10 11 15
2 22 23 24
3 32 33 34
4 25 40 41
Warning message:
Overlapping confidence intervals
> ci.ayan ## displays the confidence interval
Confidence intervals for breakpoints
of optimal 5-segment partition:
Call:
confint.breakpointsfull(object = bp.ayan)
Breakpoints at observation number:
2.5 % breakpoints 97.5 %
1 10 11 15
2 22 23 24
3 32 33 34
4 25 40 41
Corresponding to breakdates:
2.5 % breakpoints 97.5 %
1 10 11 15
2 22 23 24
3 32 33 34
4 25 40 41
Warning message:
Overlapping confidence intervals
> fs.ayan <- Fstats(ayan~trend, data = ayan, from = 0.1) ##sup F test h=0.1
> trimming parameter
> plot (fs.ayan)
> bp3 <- breakpoints(ayan ~ trend,breaks=3)## searching for break points with
> breakpoints assumed as three since AIC min can overestimate in presence of
> serial auto corelation
> summary (bp3)## checking the break points
Optimal (m+1)-segment partition:
Call:
breakpoints.formula(formula = ayan ~ trend, breaks = 3)
Breakpoints at observation number:
m = 1 23
m = 2 23 33
m = 3 11 23 33
Corresponding to breakdates:
m = 1 23
m = 2 23 33
m = 3 11 23 33
Fit:
m 0 1 2 3
RSS 1.2131579 0.7466773 0.5243361 0.3570253
BIC -25.2008012 -36.0409283 -40.8160181 -47.0090984
> ci.ayan1 <- confint(bp3)## confidence interval for the test when break points
> are 3
> breakdates (ci.ayan1) ## displays the confidence interval
2.5 % breakpoints 97.5 %
1 10 11 15
2 22 23 24
3 32 33 34
> ci.ayan1 ## displays the confidence interval for three breaks
Confidence intervals for breakpoints
of optimal 4-segment partition:
Call:
confint.breakpointsfull(object = bp3)
Breakpoints at observation number:
2.5 % breakpoints 97.5 %
1 10 11 15
2 22 23 24
3 32 33 34
Corresponding to breakdates:
2.5 % breakpoints 97.5 %
1 10 11 15
2 22 23 24
3 32 33 34
> plot (ayan) ## plots the series
> lines (ci.ayan1) ## shows the breaks and the CIs for three breaks
>
>
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