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Classical Time Series Models and Financial Series
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. 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 of crucial importance in finance.
In this chapter, we also present the main stylized facts (unpredictability of returns, volatility clustering and hence predictability of squared returns, leptokurticity of the marginal distributions, asymmetries, etc.) concerning financial series.
1.1 Stationary Processes
Stationarity plays a central part in time series analysis, because it replaces in a natural way the hypothesis of independent and identically distributed (iid) observations in standard statistics.
Consider a sequence of real random, variables (Xt)t
, defined on the same probability space. Such a sequence is called a time series, and is an example of a discrete-time stochastic process.
We begin by introducing two standard notions of stationarity.
Definition 1.1 (Strict stationarity) The process ( ...
