# Forecasting Air Passenger Volatility Using GARCH Modelling

## Modelling generalised autoregressive conditional heteroscedasticity using R

When attempting to forecast a time series, consideration is given as to both the trend and seasonality patterns in the series.

That said, we can often come across a time series where the volatility in the series is not constant over time. This is known as **autoregressive conditional heteroscedasticity.**

In this regard, a GARCH model can be used to forecast the volatility in a time series. The purpose of this article is to illustrate how to test for the presence of autoregressive conditional heteroscedasticity using air passenger data sourced from DataSF Open Data and then build a GARCH model to forecast volatility for this time series.

## Time series with no ARCH present

To illustrate this better, let us consider a series of normally distributed random numbers in R — formatted as a yearly time series.

`df<-rnorm(100)`

tsrnorm <- ts(df, start = c(2015,3), frequency = 12)

plot(tsrnorm,type="l",ylab="Values")

title("Values")

Plotting this time series yields the following: