# [R] KPSS test

markleeds at verizon.net markleeds at verizon.net
Thu Jul 6 21:39:29 CEST 2006

>From:  <markleeds at verizon.net>
>Date: Thu Jul 06 14:17:25 CDT 2006
>To: Sachin J <sachinj.2006 at yahoo.com>
>Subject: Re: [R] KPSS test

sachin : i think your interpretations are right given the data
but kpss is quite a different test than the usual tests
because it assumes that the null is stationarity while dickey fuller  ( DF )  and phillips perron ( PP ) ) assume that the null is a unit root. therefore, you should check whetheer
the conclusions you get from kpss are consistent with what you would get from DF or PP. the results often are not consistent.

also, DF depends on what terms ( trend, constant )
you used in your estimation of the model. i'm not sure if kpss
does also. people generally report Dickey fuller results but they
are a little biased towards acepting  unit root ( lower
power )  so maybe that's why
you are using KPSS ? Eric Zivot has a nice explanation
of a lot of the of the stationarity tests in his S+Finmetrics
book.

testing for cyclical variation is pretty complex because
that's basically the same as testing for seasonality.
check ord's or ender's book for relatively simple ways of doing that.

>
>>From: Sachin J <sachinj.2006 at yahoo.com>
>>Date: Thu Jul 06 14:17:25 CDT 2006
>>To: R-help at stat.math.ethz.ch
>>Subject: [R] KPSS test
>
>>Hi,
>>
>>  Am I interpreting the results properly? Are my conclusions correct?
>>
>>  > KPSS.test(df)
>>    ---- ----
>>  KPSS test
>>  ---- ----
>>    Null hypotheses: Level stationarity and stationarity around a linear trend.
>>  Alternative hypothesis: Unit root.
>>----
>>  Statistic for the null hypothesis of
>>   level stationarity: 1.089
>>      Critical values:
>>    0.10  0.05 0.025  0.01
>> 0.347 0.463 0.574 0.739
>>----
>>  Statistic for the null hypothesis of
>>   trend stationarity: 0.13
>>      Critical values:
>>    0.10  0.05 0.025  0.01
>> 0.119 0.146 0.176 0.216
>>----
>>  Lag truncation parameter: 1
>>
>>CONCLUSION: Reject Ho at 0.05 sig level - Level Stationary
>>     Fail to reject Ho at 0.05 sig level - Trend Stationary
>>
>>> kpss.test(df,null = c("Trend"))
>>          KPSS Test for Trend Stationarity
>>  data:  tsdata[, 6]
>>KPSS Trend = 0.1298, Truncation lag parameter = 1, p-value = 0.07999
>>
>>  CONCLUSION: Fail to reject Ho - Trend Stationary as p-value < sig. level (0.05)
>>
>>> kpss.test(df,null = c("Level"))
>>          KPSS Test for Level Stationarity
>>  data:  tsdata[, 6]
>>KPSS Level = 1.0891, Truncation lag parameter = 1, p-value = 0.01
>>  Warning message:
>>p-value smaller than printed p-value in: kpss.test(tsdata[, 6], null = c("Level"))
>>
>>  CONCLUSION: Reject Ho - Level Stationary as p-value > sig. level (0.05)
>>
>>  Following is my data set
>>
>>  structure(c(11.08, 7.08, 7.08, 6.08, 6.08, 6.08, 23.08, 32.08,
>>8.08, 11.08, 6.08, 13.08, 13.83, 16.83, 19.83, 8.83, 20.83, 17.83,
>>9.83, 20.83, 10.83, 12.83, 15.83, 11.83), .Tsp = c(2004, 2005.91666666667,
>>12), class = "ts")
>>
>>  Also how do I test this time series for cyclical varitions?
>>
>>
>>  Sachin
>>
>>
>>---------------------------------
>>
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>>
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