R Programming for Actuarial Science

30 Time Series Modelling in R

Dr Alfred Kume

library(fGarch)
library(forecast)
library(tseries)
library(latex2exp)

30.1 Introduction

Time series data are generally considered as a set of observations ordered in time, typically at equally spaced intervals such as days, hours, minutes, and months. The main aim of the time series analysis is to understand the driving dynamics of the data generating process and use this for forecasting future values.

The key departure from the standard statistical theory is that the data do not satisfy the independent and identically distributed (i.i.d.) assumption. This generates some technical challenges in the modelling process that are found difficult by some students. Based on our experience by teaching this material, once some of these difficulties are overcome, the modelling is then considerably simplified to the level of a regression modelling. In this chapter, we will go through some of these challenging points while covering the basic theory and the relevant computations in R/Rstudio. This joint approach will provide further insight into some potential issues of working with real time series data.

We normally fit to the real (time series) data some specific stochastic processes, defined as a collection of infinitely many random variables , indexed by the discrete time points . The time series observations are then considered as a finite ...