John C Frain frainj at gmail.com
Fri Aug 17 00:05:22 CEST 2007

```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)
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.

>
> 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
> 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
>
>        Augmented Dickey-Fuller Test
>
> data:  data[, 1]
> Dickey-Fuller = -1.1052, Lag order = 5, p-value = 0.9188
> alternative hypothesis: stationary
>
>
>        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
>
>        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 at yahoo.com>
> Sent by: r-help-bounces at stat.math.ethz.ch
> 08/16/2007 04:27 PM
>
> To
> r-help at stat.math.ethz.ch
> cc
>
> Subject
>
>
>
>
>
>
> 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 :
>
>          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]]
>
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--
John C Frain
Trinity College Dublin
Dublin 2
Ireland
www.tcd.ie/Economics/staff/frainj/home.html
mailto:frainj at tcd.ie
mailto:frainj at gmail.com

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