# Re: [R] [gently off topic] arima seasonal question

From: Rolf Turner <rolf_at_math.unb.ca>
Date: Fri 02 Jul 2004 - 23:46:36 EST

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.

===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===

``` > 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@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.
>