Estimating Seasonal ARIMA-GARCH Models for Electricity Prices

# Is there any way to easily estimate and forecast seasonal ARIMA-GARCH model in any software?


# Is there any way to easily estimate and forecast seasonal ARIMA-GARCH model in any software?












I use R to estimate a seasonal ARIMA(8,0,0)(5,0,1)[7] model for the seasonal differences of logs of daily electricity prices:

```
daily.fit <- arima(sd_l_daily_adj$Price,
                   order=c(8,0,0),
                   seasonal=list(order=c(5,0,1), period=7),
                   xreg = sd_l_daily_adj$Holiday,
                   include.mean=FALSE)
```

Problem is that from all the packages I've tried, only the R's base arima function allows for the seasonal specification. Packages with GARCH estimation functions such as fGarch and rugarch only allow for ordinary ARMA(p, q) specification for the mean equation.

Any suggestions for any kind of software are welcome,

Thanks

## Answer by Quantopik (score 4, accepted)

https://quant.stackexchange.com/a/15929

You can use Matlab too, that, in my humble opinion, is simpler than R from a syntax point of view.

The model you need for is run by the Matlab function `arima` that can be used with `seasonality` option to do what you have to do.

Here you can find an example and a brief explanation of the model.

Type ctrl + F and search for:

"Specify a seasonal ARIMA model"

You will find how to do that explained in the example.

If you want to combine ARIMA with GARCH you can also do that, as described in the MATLAB help.

## Answer by stofer (score 2)

https://quant.stackexchange.com/a/15946

The mean equation specification for ARIMAX(8,0,0)(5,0,1)[7] (as in the R code above): $$ (1 - \phi_1L^1 - \ldots - \phi_8L^8)(1-\Phi_1L^7 - \Phi_2L^{14} - \ldots - \Phi_5L^{35})y_t = \beta x_t + (1 + \Theta_1L^7)\varepsilon_t $$ where $x_t$ is the holiday dummy variable.

Equivalent ARIMA fit in Matlab (+ GARCH and forecasting):

```
% specify seasonal ARIMA(8,0,0)(5,0,1)[7]-GARCH(1,1) model
Md2 = arima('Constant', 0, 'D', 0, 'ARLags', [1,2,3,4,5,6,8],'SARLags', [7,14,21,28,35], 'SMALags', 7, 'Variance', garch(1,1))

% estimate (use Holiday as exogenous variable)
[fitT_garch,~,LogLT_garch] = estimate(Md2, Price(44:end), 'X', Holiday, 'Y0', Price(1:43))

% forecast 30 periods ahead
V = forecast(fitT_garch, 30, 'Y0', Price, 'X0', Holiday, 'XF', zeros(30, 1))
```

Matlab will need the first 43 observations as a presample response data.

## Answer by Kian (score 0)

https://quant.stackexchange.com/a/15975

Use the R package fgarch. Hope this is helpful to you.

## Answer by Manuel (score 0)

https://quant.stackexchange.com/a/17134

You can try:

```
daily.fit=ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1, 1)),
mean.model = list(armaOrder = c(35, 7), include.mean = T, arfima=F),
fixed.pars=list(ar9=0,ar10=0,...,ar13=0,ar15=0,...,ar20=0,ar22=0,...,ar27=0,ar29=0,...,ar34=0,ma1=0,...,ma6=0))
```

from rugarch package.