1. Classical Time Series Models and Financial Series

  1. Christian Francq1 and
  2. Jean-Michel Zakoïan1,2

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch1

GARCH Models: Structure, Statistical Inference and Financial Applications

GARCH Models: Structure, Statistical Inference and Financial Applications

How to Cite

Francq, C. and Zakoïan, J.-M. (2010) Classical Time Series Models and Financial Series, in GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470670057.ch1

Author Information

  1. 1

    University Lille 3, Lille, France

  2. 2

    CREST, Paris, France

Publication History

  1. Published Online: 14 JUL 2010
  2. Published Print: 23 JUL 2010

ISBN Information

Print ISBN: 9780470683910

Online ISBN: 9780470670057

SEARCH

Keywords:

  • ARIMA Models;
  • autoregressive moving average (ARMA) models;
  • Box-Jenkins methodology;
  • financial time series;
  • random variance models;
  • standard time series analysis;
  • stationary processes

Summary

The standard time series analysis rests on important concepts such as stationarity, autocorrelation, white noise, innovation, and on a central family of models, the autoregressive moving average (ARMA) models. This chapter begins by recalling their main properties and how they can be used. As these concepts are insufficient for the analysis of financial time series, the chapter provides an introduction to the concept of volatility, which is of crucial importance in finance. The chapter also presents the main stylized facts (unpredictability of returns, volatility clustering and hence predictability of squared returns, leptokurticity of the marginal distributions, asymmetries) concerning financial series. For statistical convenience, ARMA (and ARIMA) models are generally used under stronger assumptions on the noise than that of weak white noise. The aim of the Box-Jenkins methodology is to find the most appropriate ARIMA (p, d, q) model and to use it for forecasting.

Controlled Vocabulary Terms

ARIMA model; ARMA model; Box-Jenkins model; stationary process