Applied Econometrics Seminar 2 Introduction to Time Series (Stationarity and Unit Root Testing) Please note that for interactive manipulation you need Mathematica 6 version of this .pdf. Mathematica 6 will be available soon at all Lab's Computers at IES http://staff.utia.cas.cz/barunik Jozef Barunik ( barunik @ utia. cas . cz ) |
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Seminar 2 - Welcome to UTIAstaff.utia.cas.cz/barunik/files/appliedecono/Seminar2.pdf · Seminar2.nb 11. Unit Root Tests in JMulti - ADF ADF test - Dy t =fy t-1 +u H 0:f=0 versus H
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Applied Econometrics
Seminar 2Introduction to Time Series
(Stationarity and Unit Root Testing)
Please note that for interactive manipulation you need Mathematica 6 version of this .pdf. Mathematica 6 will be available soon at all Lab's Computers at IES
http://staff.utia.cas.cz/barunikJozef Barunik ( barunik @ utia. cas . cz )
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A brief revision
To warm you up, please tell me what are the main ideas and why we use these concepts(from lecture):
StationarityAR processMA processAutocorrelation function (ACF)
there is interactive study material on ARIMA at my web pagehttp://staff.utia.cas.cz/barunik
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2 Seminar2.nb
Stationarity
A time series 8rt< is said to be weakly stationary if both mean of rtand covariancebetween rt and rt-l are time-invariant - EHrtL = m and CovHrt , r-l L = gl .
In other words, stationarity requires distribution of time series to be constant under timeshift, weak stationarity, which is assumed more often requires only fluctuation with con-stant variation around constant level.
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Seminar2.nb 3
Why do we need to care about stationarity ?
]:[ nonstationary series can strongly influence its behavior and properties (persistence ofshocks might be infinite) ]:[ spurious regressions - 2 trending variables over time which are totally unrelated willhave high R2
]:[ assumptions for assymptotic analysis is not valid for nonstationary series (we can nottest hypotheses validly)
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4 Seminar2.nb
Tests of Stationarity - Visually
Simple Plot of series is always first stepWhich series is stationary?
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Seminar2.nb 5
Tests of Stationarity - Visually
Let us load the data from previous pictures
CZK/EUR 2007-2008
Run JMulti
load file CZK_EUR_2008.txt
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6 Seminar2.nb
Tests of Stationarity - Visually: CZK/EUR
Can we see constant mean and variance at exchange rate?
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Seminar2.nb 7
Tests of Stationarity - Visually: CZK/EUR cont.
What about ACF/PACF - for stationary series, it should decay exponentially, or be non-significant if there is no pattern
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8 Seminar2.nb
Tests of Stationarity - Visually: CZK/EUR cont.
What we can do is to difference the exchange rate, so we plot "returns", as rt =Pt
Pt-1- 1 or
continuously rt = lnI PtPt-1
M
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Seminar2.nb 9
Tests of Stationarity - Visually: CZK/EUR cont.
Let's look at ACF/PACF of differenced series
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10 Seminar2.nb
Tests of Stationarity - Formally (Unit Root Tests)
Exact tests can be found in the lecture, or in textbooks
H0: unit rootHA: no unit root (stationarity)
Thus we need to reject the null hypothesis to be sure we have stationary time series. Ifseries has unit root, it is not stationary
H0 : f = 0 versus H1 : f < 0(or process yt has unit root and is nonstationary, against alternative that it is stationary
Options: constant (intercept in regression), time trend (trend stationarity), seasonal dum-mies (mondays...)
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12 Seminar2.nb
What does ADF tells us about our CZK/EUR series?
let's run on levels and differences, try using constant (consistency), residuals should bewhite noise, also significant autocorrelation should not be present among remaining lags.
for exchange rate (level):statistics is -1.6090 (10% level critical value is -1.62 )we can not reject the null of unit root even at 10% - series are not stationary !!!
for differenced exchange rate:statistics is -9.5549 (1% level critical value is -2.56)we can strongly reject the null of unit root - series are stationary !!!
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Seminar2.nb 13
Unit Root Tests in JMulti - KPSS
We test
H0 : yt~IH0L againstH1 : yt~IH1L
thus null hypothesis is, that series are stationary ! (different from ADF, take care), againsta unit root