[R-SIG-Finance] Interpreting cointegration - ur.df() and ad.test()
Paul Teetor
paulteetor at yahoo.com
Wed Mar 30 06:35:56 CEST 2011
algotr8der:
The adf.test function essentially detrends your data before performing the ADF
test. (That's what the help page means when it says, "The general regression
equation which incorporates a constant and a linear trend is used.") The data
plot may appear to be trending upward, but the function removes that trend
first. If you plot the detrended data, you'll see the data that the function is
testing. It should be going "sideways" compared to your original, trendy data.
The ur.df function performs a similar detrending when you specify type="trend".
(OK, more precisely: it detrends in conjunction with performing the ADF test.)
HTH,
Paul
Paul Teetor, Elgin, IL USA
http://quanttrader.info/public
----- Original Message ----
From: algotr8der <algotr8der at gmail.com>
To: r-sig-finance at stat.math.ethz.ch
Sent: Tue, March 29, 2011 6:39:48 PM
Subject: [R-SIG-Finance] Interpreting cointegration - ur.df() and ad.test()
Hello folks,
I have read several posts on here regarding cointegration and the various
tests that check for this.
Here is what I have done - where securityA and securityB are time series
price data.
series <- merge(securityA, securityB, all=FALSE)
series <- as.data.frame(series)
m <- lm(securityA ~ securityB+ 0, data=series)
beta1 <- coef(m)[1]
sprd = series$securityA - beta1*series$securityB
> adf.test(sprd, alternative="stationary",k=1)
Augmented Dickey-Fuller Test
data: sprd
Dickey-Fuller = -3.9226, Lag order = 1, p-value = 0.01281
alternative hypothesis: stationary
> summary(ur.df(sprd, type="trend", lag=1))
###############################################
# Augmented Dickey-Fuller Test Unit Root Test #
###############################################
Test regression trend
Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
Residuals:
Min 1Q Median 3Q Max
-0.91172 -0.02737 -0.00097 0.02553 0.98989
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.434e-02 6.790e-03 -3.584 0.000340 ***
z.lag.1 -5.309e-03 1.353e-03 -3.923 8.85e-05 ***
tt 8.143e-06 2.134e-06 3.816 0.000137 ***
z.diff.lag -5.345e-02 1.226e-02 -4.360 1.32e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.05266 on 6624 degrees of freedom
Multiple R-squared: 0.005505, Adjusted R-squared: 0.005055
F-statistic: 12.22 on 3 and 6624 DF, p-value: 5.676e-08
Value of test-statistic is: -3.9226 6.7405 7.7586
Critical values for test statistics:
1pct 5pct 10pct
tau3 -3.96 -3.41 -3.12
phi2 6.09 4.68 4.03
phi3 8.27 6.25 5.34
Both results indicate that the time series 'sprd' is cointegrated and thus
mean reverting. However looking at the plot one can clearly see that the
series is trending and is not mean reverting. Any thoughts would be greatly
appreciated.
>plot(sprd, type="l")
http://r.789695.n4.nabble.com/file/n3416574/Screen_shot_2011-03-29_at_7.37.39_PM.png
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