The option alternative in adf.test() takes the value 'stationary' or 'explosive'. The value 'explosive' is used to test if the series is stationary about a linear time trend. This means that a constant and trend are to be included in the DF or ADF test regression. In the case here the series is trended. The question is if the trend is stochastic or deterministic. Have a look at the following analysis
t=1:length(x) plot(t,x) trend = lm(x~t) abline(lm(x~t)) summary(trend) library(urca) x = ts(x, start=1, end = length(x), frequency=1) x.ct = ur.df(x,lags=0,type='trend') plot(x.ct) library(tseries) adf.test(x,alternative = "explosive" , k=0) summary(ur.df(x,lags=0,type='trend') which analyses your data using two different libraries. (x is your data and both procs. produce the same DF test). I should remark that your data are rounded and this possibly acts against a full analysis. Some knowledge of the data generating process might suggest a more appropriate way of testing for stationarity. On 16/08/07, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote: > > Hi Megh > > i hope you have confused with 'what is my NULL hypothesis' ? > i suggest you to take any ideal dataset about which you know that whether > it is stationary or not ? apply the test to know what is the NULL > hypothesis > used in any software :) > usually in many softwares the NULL hypothesis is in negative sense. Please > everybody comment on this :) > > hoping that you series is return series and not price series :). Thus > applying adf test for your series :) > my test show that your series is not stationary at all as my correlalogram > comes as follows. > 1 > 0.998283718 > 0.997582959 > 0.99703921 > 0.99665648 > 0.996548006 > 0.99647617 > 0.995925698 > 0.995317271 > 0.994746317 > 0.994727781 > 0.99508777 > 0.99501576 > 0.99437404 > 0.993338292 > 0.992684933 > 0.992310313 > > @@@ HHHHmmmmmmmmm > Although if i assume that your series is a price series and defining > return = 100*ln(pt/pt-1). Returns become as follows > 0 > -0.201816416 > 0.201816416 > 0 > 0.201409937 > 0 > 0 > 0 > 0 > 0.201005093 > 0 > 0 > 0 > 0 > 0.200601873 > 0 > 0.200200267 > 0.199800266 > 0 > -0.199800266 > 0.199800266 > 0 > 0 > 0 > 0.199401861 > -0.199401861 > 0.199401861 > 0 > 0.199005041 > 0 > 0 > 0 > 0 > 0.198609797 > 0 > 0 > 0 > 0 > 0 > 0.19821612 > 0 > 0.197824001 > 0 > 0 > 0.19743343 > 0 > 0 > 0 > 0.197044399 > -0.197044399 > 0.197044399 > 0 > 0.196656897 > 0.196270917 > 0 > -0.196270917 > 0.196270917 > 0 > 0 > 0 > 0 > 0 > 0 > 0 > 0.195886449 > 0 > 0 > 0 > 0 > 0 > 0 > 0.195503484 > 0 > 0 > 0 > 0.195122013 > 0.194742028 > 0 > 0 > 0 > 0 > 0.194363521 > 0 > 0 > 0 > -0.194363521 > 0.194363521 > 0 > 0 > 0.193986482 > 0 > 0 > 0 > 0 > 0 > 0 > 0 > 0 > 0 > 0 > 0.193610903 > 0 > 0 > 0 > 0 > 0.193236775 > 0 > 0 > 0 > 0 > 0.192864091 > 0 > 0.192492841 > 0 > 0 > 0 > 0 > 0.192123018 > 0 > 0 > 0 > 0 > 0 > 0.191754613 > 0 > 0.191387618 > 0 > 0 > 0 > 0.191022026 > 0 > 0 > 0.190657827 > -0.190657827 > 0 > 0.190657827 > 0.190295015 > 0 > 0 > 0 > 0 > 0 > 0 > 0.18993358 > 0 > -0.18993358 > 0.18993358 > 0 > 0.189573516 > 0.189214815 > 0 > 0 > 0 > 0.188857469 > 0 > 0 > 0.18850147 > 0 > 0 > 0.18814681 > 0 > 0.187793482 > 0 > then the value of autocorrelations i.e. correlalogram comes as approx > 1 > 0.089252308 > 0.058227292 > 0.017934984 > 0.025264591 > -0.014925678 > -0.004668544 > 0.014890995 > 0.001625333 > 0.010669589 > -0.010587179 > -0.03000206 > -0.011863654 > 0.00772247 > 0.024272208 > -0.019521244 > -0.035998575 > -0.061608877 > -0.048401231 > -0.008594859 > > which show that the values are quite likely to make series stationary :) > > > data[1:10,] > V1 V2 > 1 4.96 0.0000000 > 2 4.95 -0.2018164 > 3 4.96 0.2018164 > 4 4.96 0.0000000 > 5 4.97 0.2014099 > 6 4.97 0.0000000 > 7 4.97 0.0000000 > 8 4.97 0.0000000 > 9 4.97 0.0000000 > 10 4.98 0.2010051 > > adf.test(data[,1]) > > Augmented Dickey-Fuller Test > > data: data[, 1] > Dickey-Fuller = -1.1052, Lag order = 5, p-value = 0.9188 > alternative hypothesis: stationary > > > adf.test(data[,2]) > > Augmented Dickey-Fuller Test > > data: data[, 2] > Dickey-Fuller = -6.2265, Lag order = 5, p-value = 0.01 > alternative hypothesis: stationary > > Warning message: > p-value smaller than printed p-value in: adf.test(data[, 2]) > > > > this explains everything clearly :) > your NULL hypothesis is "Series is not stationary" - hence hypothesis in > negative sense > > prooved by taking ideal data > > > data1<-rnorm(10000) #normal data > > adf.test(data1) > > Augmented Dickey-Fuller Test > > data: data1 > Dickey-Fuller = -21.2118, Lag order = 21, p-value = 0.01 > alternative hypothesis: stationary > > Warning message: > p-value smaller than printed p-value in: adf.test(data1) > > > > HTH > > > > > Megh Dal <[EMAIL PROTECTED]> > Sent by: [EMAIL PROTECTED] > 08/16/2007 04:27 PM > > To > r-help@stat.math.ethz.ch > cc > > Subject > [R] ADF test > > > > > > > Hi all, > > Hope you people do not feel irritated for repeatedly sending mail on > Time series. > > Here I got another problem on the same, and hope I would get some answer > from you. > > I have following dataset: > > data[,1] > [1] 4.96 4.95 4.96 4.96 4.97 4.97 4.97 4.97 4.97 4.98 4.98 4.98 4.98 > 4.98 4.99 4.99 5.00 5.01 > [19] 5.01 5.00 5.01 5.01 5.01 5.01 5.02 5.01 5.02 5.02 5.03 5.03 5.03 > 5.03 5.03 5.04 5.04 5.04 > [37] 5.04 5.04 5.04 5.05 5.05 5.06 5.06 5.06 5.07 5.07 5.07 5.07 5.08 > 5.07 5.08 5.08 5.09 5.10 > [55] 5.10 5.09 5.10 5.10 5.10 5.10 5.10 5.10 5.10 5.10 5.11 5.11 5.11 > 5.11 5.11 5.11 5.11 5.12 > [73] 5.12 5.12 5.12 5.13 5.14 5.14 5.14 5.14 5.14 5.15 5.15 5.15 5.15 > 5.14 5.15 5.15 5.15 5.16 > [91] 5.16 5.16 5.16 5.16 5.16 5.16 5.16 5.16 5.16 5.16 5.17 5.17 5.17 > 5.17 5.17 5.18 5.18 5.18 > [109] 5.18 5.18 5.19 5.19 5.20 5.20 5.20 5.20 5.20 5.21 5.21 5.21 5.21 > 5.21 5.21 5.22 5.22 5.23 > [127] 5.23 5.23 5.23 5.24 5.24 5.24 5.25 5.24 5.24 5.25 5.26 5.26 5.26 > 5.26 5.26 5.26 5.26 5.27 > [145] 5.27 5.26 5.27 5.27 5.28 5.29 5.29 5.29 5.29 5.30 5.30 5.30 5.31 > 5.31 5.31 5.32 5.32 5.33 > [163] 5.33 > > > Now I want to conduct a test for stationarity using ADF test : > > > adf.test((data[,1]), "stationary", 0) > Augmented Dickey-Fuller Test > data: (data[, 1]) > Dickey-Fuller = -3.7351, Lag order = 0, p-value = 0.02394 > alternative hypothesis: stationary > > But surprisingly it leads towards rejestion of NULL [p-value is less > than 0.05], i.e. indicates a possible stationary series. However ploting a > graph of actual data set it doesn't seem so. > > Am I making any mistakes ? Can anyone give me any suggestion? > > Regards, > Megh > > > --------------------------------- > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > > > ============================================================================================ > DISCLAIMER AND CONFIDENTIALITY CAUTION:\ \ This message and ...{{dropped}} > > ______________________________________________ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > -- John C Frain Trinity College Dublin Dublin 2 Ireland www.tcd.ie/Economics/staff/frainj/home.html mailto:[EMAIL PROTECTED] mailto:[EMAIL PROTECTED] ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
