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st: univariate time series intervention analysis
Hello, does anyone have some experience with time series and
intervention analysis? I have the following yearly time series:
This is for one country. (i have also data for other countries, also
between 0 and 1)
I want to find out whether significant changes have occured over time.
Especially the evolution since time index 22 (when using a time
variable, going from 1 to 30). I want to find whether the series has
increased linearly after this season. How do I do this? I thought I
start with Phillips Perron test for stationarity: there I find
stationarity (I just use the: 'statistics', 'time series', 'test', 'pp',
include trend+default lags. I get z(rho) and z(t) larger than the
critical values so stationarity. So no differences necessary I thought.
If I look at the autocorrelations (also via clicking) than the auto and
partial corr give four peaks but if I do same in SPSS, they fall between
the confidence intervals so I thought then no need of AR or MA. If I
do a PPplot to test normality in SPSS (I can not do so in STATA since
get remark, even with simple graph: system limit exceeded, and many
green notations but no graph) all are nicely close to the 45°line.
So I thought I just need to estimate:
xt = w/(1-B)It+Nt following the book of Mills. With xt my time series
from above, It a dummy with zero for t = 1-21 and 1 for t=22-30. Nt is
just the errorterm since no found ARMA. Now how do I this
practically??? I thought rewritten this model means xt(1-B)=wIt + Nt
(1-B), so diff xt= wIt + diff Nt. But do I this as follows:
'statistics', 'time series', 'ARIMA', choose d=1 and ma=1, dependent xt,
as independent the dummy and check box of suppress constant, I then get:
Wald chi2(2) = 13.24
Log likelihood = 43.61512 Prob > chi2 = 0.0013
Coef. Std. Err. z P>z [95% Conf.
D1. -.0707794 .060909 -1.16 0.245 -.1901589
L1. -.6275359 .2040303 -3.08 0.002 -1.027428
/sigma .0533161 .0078506 6.79 0.000 .0379293 .068703
Can I then conclude that there is evidence that the change in time
period 22 is significant? Because coeff of D1 falls between the
What if I need to look at two events but that I do not know the exact
date of the first intervention? (if look at graph of series on vertical
and time on horizontal seems that since timeperiod 13 or 14 also change)
Hope someone can help me soon. Thank you!
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