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  1. Classical Time Series Models and Financial Series
    1. Stationary Processes
    2. ARMA and ARIMA Models
    3. Financial Series
    4. Random Variance Models
    5. Bibliographical Notes
    6. Exercises

Christian Francq and Jean-Michel Zakoļan

Keywords: ARMA and ARIMA models, autocorrelation, autocovariance, Bartlett's formula, conditional heteroscedasticity, ergodicity, leptokurticity, leverage effect, linearly regular processes, purely non deterministic processes, stochastic volatility, strict and second-order stationarity, strong and weak white noise, volatility, volatility clustering, Wold's decomposition.

Description: The standard time series analysis rests on important concepts such as stationarity, autocorrelation, white noise, innovation, and on a central family of models, the ARMA (AutoRegressive Moving Average). We start by recalling their main properties and how they can be used. As we shall see, these concepts are insufficient for the analysis of financial time series. In particular, we shall introduce the concept of volatility, which is crucial in Finance. In this chapter, we also present the main stylized facts (unpredictability of the returns, volatility clustering and hence predictability of the squared returns, leptokurticity of the marginal distributions, asymmetries, ...) of financial series.

R code R used for Figures 1-5

CAC 40 Index from 01/03/1990 to 15/10/2008 : data used for Figures 1-5 (obtained via yahoo).