How can I make sure the residual signal, after subtracting the trend extracted
through some technique, is actually trend-free ?
I would greatly appreciate any suggestion about some Stationarity tests.
I'd like to make sure I have got the difference between ACF and PACF right.
In the following I am citing some definitions. I would appreciate your thoughts.
ACF(k) estimates the correlation between y(t) and y(t-k) like an ordinary
correlation coefficient.
ACF is the simple ( i.e. unconditional ) correlation between a time series and
it's lags thus
y(t)=a+b*y(t-k) gnerates the kth autocoreelation coefficient (b).
If we have form y(t)=a+b*y(t-1)+c*y(t-2) .. then (c) is the PARTIAL
AUTOCORRELATION COEFFFICIENT or in other words the
CONDITIONAL CORRELATION of lag 2 given lag1
PACF(k) estimates the correlation between y(t) and y(t-k) adjusted for the
effects of y(t-1), ..., y(t-k+1).
Model identification is achieved by looking at the pattern of the ACF and PACF.
- If the ACF dies off exponentially, but the PACF has p spikes, AR(p) is
indicated.
- If the ACF has q spikes and the PACF dies off exponentially, MA(q) is
indicated.
The ACF and the PACF for the resulting stationary series is used to determine
the best B/J model for the series according to the following rules:
a. If the ACF trails off and the PACF shows spikes, then an AR model with
order p = number of significant PACF spikes is the best
model.
b. If the PACF trails off and the ACF shows spikes, then an MA model with
order q= number of significant ACF spikes is the best model.
c. If both the ACF and the PACF trail off then a ARMA model is used with p=1
and q=1.
Thank you very much,
Maura
Thank you very much.
Best regards,
Maura Edelweiss
tutti i telefonini TIM!
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