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!


	[[alternative HTML version deleted]]


