A Course on Statistics for Finance

Chapter 8

Introduction to Time Series Analysis

8.1 Introduction

This chapter concerns various models for time series data. A time series will be denoted by notation such as

$\{Y_t,t=1,2,.\; .\; .,n\}\mathrm{.}$

This notation refers to a variable Y observed at time points t.

Such data, observed in time, are temporal data. The observations may be triggered by events, occurring at irregular intervals. Or the observation times may be planned, in which case they can be at regular intervals.

Tick-by-tick data (tick data) on the price of a stock are temporal data observed at irregular intervals. These are triggered by a purchase or sale. These data report the prices at each transaction of a specific stock. The subscript t refers to the t-th transaction.

Often ...