Hi S helpers,
To check how two time series (I(1), non-stationary,
show seasonal variation), are related/correlated with each-other I started
looking beside correlation coefficients at 'cointegration' possibilities.
How can the strength of coïntegration be assessed? I’m
using the book Modelling Fin. Time series with S-plus book but get stuck each example.
Is coïntegration appropriate in this case and is there a good method to assess
the strength of it?
The B2 coefficient is different from 1 so the DOLS
estimator of B2 has to be used. How can this be done is this case (12.4 p435)?
a)
deseasonalise the data by diff? is
than the real coïntegration assessed?
b)
DOLS(…)? Regression equation
estimation? How can the following be solved (correct) towards cointegration
vector estimation?
attach(Timeserie)
serie1 <- rts(Timeserie[,1],start=
c(1998,10), frequency=36)
serie2 <- rts(Timeserie[,2],start=
c(1998,10), frequency=36)
detach(Timeserie)
#(regular spaced time series, non calendar
based
ts.ser1 <-ts.update(serie1)
ts.ser2 <-ts.update(serie2)
> ts.ser1d <- diff(ts.ser1)
# signalSeries
> colIds(ts.ser1d ) <- c(
"D.serie1")
Warning messages:
Cannot set a column ID for a vector in: colIds(.A0,
.A1)
> ts.ser1.dlag <- tslag(ts.ser1d
,-3:3,trim=T)
> merge.DOLS <- seriesMerge(ts.ser2,ts.ser1,ts.ser1.dlag)
Problem in object@positions: Class
"matrix" has no "positions"
slot
Use traceback() to see the call stack
>
=> S-plus 6.1, module financial metrics
1.0, Win XP station
Thanks a lot in advance,
Ph.D. student,
Jan
______________________________________________________________________
Jan Verbesselt
Research Associate
Lab of Geomatics and Forest Engineering K.U. Leuven
Vital Decosterstraat 102. B-3000 Leuven Belgium
Tel:+32-16-329750 Fax: +32-16-329760
http://gloveg.kuleuven.ac.be/
_______________________________________________________________________
Results:
The estimated regression function between the two time
series! (OLS)
Call:
OLS(formula = ser2 ~ ser1, data = "">
Residuals:
Min 1Q Median 3Q Max
-212.8883 -63.4366 9.4245 68.1576 315.3256
Coefficients:
Value Std. Error t value Pr(>|t|)
(Intercept) -483.1393 8.8140 -54.8148 0.0000
ser1 1519.7852 56.7010 26.8035 0.0000
Regression Diagnostics:
R-Squared 0.8023
Adjusted R-Squared 0.8012
Durbin-Watson Stat 0.8990
Residual Diagnostics:
Stat P-Value
Jarque-Bera 1.4695 0.4796
Ljung-Box 104.6771 0.0000
Residual standard error: 91.12 on 177 degrees of
freedom
F-statistic: 718.4 on 1 and 177 degrees of freedom, the
p-value
is 0
(strong autocorrelation indicated by the DW test and ljung-box)
> us <- serie1 - serie2
> unitroot(us,trend="c",method="adf",lags=11)
Test for Unit Root: Augmented DF Test
Null Hypothesis: there is a unit root
Type of Test: t-test
Test Statistic: -4.831
P-value: 7.871e-5
Coefficients:
lag1 lag2 lag3 lag4 lag5 lag6
-0.1917 0.2523 0.0920 0.1753 0.0883 0.0728
lag7 lag8 lag9 lag10 lag11 constant
0.0147 0.1847 0.0730 0.0991 0.1218 62.4556
Degrees of freedom: 168 total; 156 residual
Residual standard error: 71.94 _