[R] [gently off topic] arima seasonal question
Rolf Turner
rolf at math.unb.ca
Fri Jul 2 15:46:36 CEST 2004
The seasonal aspect of arima models allows, essentially, for a
special realtionship between X_t and X_{t+s} where s is the
``seasonality'' of the model. It (``the model'') couldn't care less
what the time ***units*** are --- they could be weeks, quarters,
days, hours, microseconds, 1.14135*microseconds, .... What matters
is: Do you have reason to believe that there is a special
relationship between X_t and X_{t+s}??? If so, go for it. If not,
don't.
Such relationships are ***most likely*** to arise in quarterly and
monthly data --- with s = 4 in the quarterly data, s = 12 in the
monthly data. You could conceiveably get seasonality with s = 7 in
daily data; at a stretch with s = 30 (pretending all months are 30
days long ... a bit dubious). You might (ah, well, sort of ....)
also have s = 365 seasonality in daily data, but such a large s is
unlikely to ``work'' very well. You might get seasonality with s =
52 in weekly data. (Dubious.) You might get seasonality with s = 24
in hourly data. U.s.w.
It might clarify your thinking to note that a seasonal ARIMA model is
just an ``ordinary'' ARIMA model with some coefficients constrained
to be 0 in an efficient way. E.g. a seasonal AR(1) s = 4 model is
the same as an ordinary (nonseasonal) AR(4) model with coefficients
theta_1, theta_2, and theta_3 constrained to be 0. You can get the
same answer as from a seasonal model by using the ``fixed'' argument
to arima. E.g.:
===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===
> set.seed(42)
> x <- arima.sim(list(ar=c(0,0,0,0.5)),300)
> f1 <- arima(x,seasonal=list(order=c(1,0,0),period=4))
> f2 <- arima(x,order=c(4,0,0),fixed=c(0,0,0,NA,NA),transform.pars=FALSE)
> f1
.
Coefficients:
sar1 intercept
0.4987 -0.0775
s.e. 0.0499 0.1051
sigma^2 estimated as 0.8536: log likelihood = -402.51, aic = 811.02
> f2
.
Coefficients:
ar1 ar2 ar3 ar4 intercept
0 0 0 0.4987 -0.0774
s.e. 0 0 0 0.0499 0.1051
sigma^2 estimated as 0.8536: log likelihood = -402.51, aic = 811.02
===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===
Hope this is a bit enlightening.
cheers,
Rolf Turner
rolf at math.unb.ca
> Hello R People:
>
> When using the arima function with the seasonal option, are the
> seasonal options only good for monthly and quarterly data, please?
>
> Also, I believe that weekly and daily data are not appropriate for
> seasonal parm estimation via arima.
>
> Is that correct, please?
>
> Thanks,
> Sincerely,
> Laura Holt
> mailto: lauraholt_983 at hotmail.com
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