stationarity tests
The following searches for help pages in contributed packages
including terms "stationarity" or "unit root":
library(RSiteSearch)
st <- RSiteSearch.function('stationarity')
ur <- RSiteSearch.function('unit root')
ur. <- st|ur
nrow(st) # 68
nrow(ur) # 122
nrow(ur.)# 180
HTML(st&ur) # Shows the 10 with both terms
summary(ur.) # A summary by package
HTML(ur.) # Shows all 180 sorted by package then score for the help page.
You may also be interested in the Box-Ljung test. For this, try
the following:
bl <- RSiteSearch.function('Ljung')
HTML(bl)
"The partial autocorrelations may be estimated by fitting
successively autregressive processes of orders 1, 2, 3, ... by least
squares ... and picking out the estimated phi.hat[1,1], phi.hat[2,2],
phi.hat[3,3], ... of the last coefficient fitted at each stage." (Box
and Jenkins, 1975, Time Series Analysis, Forecasting and Control,
Holden-Day, sec. 3.2.6; see also
"www.itl.nist.gov/div898/handbook/pmc/section4/pmc4463.htm")
Your rules for reading ACF and PACF sound right to me.
Hope this helps.
Spencer Graves
mauede at alice.it wrote:
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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