
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 <megh700004@yahoo.com> 
Sent by: r-help-bounces@stat.math.ethz.ch
08/16/2007 04:27 PM

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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

 
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