How to use ARIMA in GARCH model

问题

I have financial data and my goal is to be able to forecast. I ran an arima model and found that the best fit was arima(1,1,1) w/ drift. I want to use GARCH on the data set because it is the better model to use due to volatility and when I squared my residuals it did have the arch effect. But I know that GARCH takes in a 2 parameter arima and I am not sure how that translates from the 3 parameter arima I currently have.

library(dplyr)
library(tidyr)
library(lubridate)
library(ggplot2)
library(TSA)
library(forecast)
spnew<-read.csv(file="~/Desktop/SPNEW.csv", header=T, 
sep=",",check.names=FALSE)
sfts1=ts(sp$`Adj Close`, 
freq=260,start=decimal_date(ymd("2009-01-02")))
arsf1=auto.arima(sfts1, trace=T)

I have the code to run for GARCH but am not sure what to input for the arima portion.

model1 <-  ugarchspec(variance.model = list(model="sGARCH",         
                                                 garchOrder=c(_,_)), 
                           mean.model = list(armaOrder=c(_,_)), 
                           distribution.model = "norm")        
mod2 <- ugarchfit(spec=model1, 
                          data=sfts1)

I left blanks for what I would need to input. I will play with the garch order once I know how to put in arima. If a better way to code the GARCH model is known please let me know.

回答1:

Below, I refer to the model that you call 2 parameter arima as ARMA.
rugarch::ugarchspec() can treat ARMA(p, q) or ARFIMA(p, d, q) model as mean.model.
(NOTE: when d is integer, ARFIMA(p, d, q) is equivalent to ARIMA(p, d, q))

Here is my example;

p <- 1
q <- 1
# d <- 1    # if you want to fix d

model1 <-  ugarchspec(variance.model = list(model="sGARCH",         
                                            garchOrder=c(_, _)), 
                      mean.model = list(armaOrder=c(p, q),
                                        arfima = T),    # using arfima model
                      # fixed.pars=list(arfima = d),    # If you want to fix d
                      distribution.model = "norm"))

回答2:

Seasonality can be incorporated by including external.regressors = in your mean.model = in ugarchspec(). The fourier()-function from the forecast package can help you find appropriate fourier terms that can be used as external regressors to represent seasonality.

来源：https://stackoverflow.com/questions/61242237/how-to-use-arima-in-garch-model

标签

data-modeling

finance

arima

forecast