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Chapter

9

Autoregressive Moving Average Models

a

fter reading this chapter you will understand:

■ (^) The concept of autoregression and autoregressive models.
■ (^) How to identify autoregressive models.
■ (^) The concept of moving average process and moving average models.
■ (^) How to identify moving average models.
■ (^) How to model autoregressive moving average (ARMA) models.
■ (^) How to use information criteria for ARMA model selection.
■ (^) How to apply ARMA in modeling stock returns.
■ (^) How to use autoregressive models, moving average models, and ARMA
models to forecast stock returns and how to evaluate the forecasting
performance of these models.
■ (^) The concept of vector autoregression.
In Chapter 5 we introduced time series analysis where variables change
over time. As discussed in that chapter, the foundation of time series models
is based on the assumption that the disturbance term is a white noise pro-
cess. The implication of this assumption is that the last period’s disturbance
term cannot be used to predict the current disturbance term and that the
disturbance term has constant variance. In other words, the implication of
this assumption is the absence of serial correlation (or predictability) and
homoscedasticity (or conditional constant variance).
However, in empirical applications the white noise assumption is often
violated. That is, successive observations show serial dependence. Under
these circumstances, forecasting tools such as exponential smoothing^1 may
(^1) See, for example, Svetlozar T. Rachev, Stefan Mittnik, Frank J. Fabozzi, Sergio M.
Focardi, and Teo Jasic, Financial Econometrics (Hoboken, NJ: John Wiley & Sons,
2007).