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 <[email protected]> To: [email protected] 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 -- View this message in context: http://r.789695.n4.nabble.com/Interpreting-cointegration-ur-df-and-ad-test-tp3416574p3416574.html Sent from the Rmetrics mailing list archive at Nabble.com. _______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go. _______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
