advanced-algorithmic-trading

Chapter 11
Autoregressive Integrated Moving
Average and Conditional
Heteroskedastic Models
In the previous chapter we went into significant detail about the AR(p), MA(q) and ARMA(p,q)
linear time series models. We used these models to generate simulated data sets, fitted models
to recover parameters and then applied these models to financial equities data.
In this chapter we are going to discuss an extension of the ARMA model, namely the Autoregressive
Integrated Moving Average model, or ARIMA(p,d,q) model as well as models that
incorporate conditional heteroskedasticity, such as ARCH and GARCH.
We will see that it is necessary to consider the ARIMA model when we have non-stationary
series. Such series occur in the presence of stochastic trends.
11.1 Quick Recap
We have steadily built up our understanding of time series with concepts such as serial correlation,
stationarity, linearity, residuals, correlograms, simulation, model fitting, seasonality, conditional
heteroscedasticity and hypothesis testing.
As of yet we have not carried out any prediction or forecasting from our models and so have
not had any mechanism for producing a trading system or equity curve.
Once we have studied ARIMA we will be in a position to build a basic long-term trading
strategy based on prediction of stock market index returns.
Despite the fact that I have gone into a lot of detail about models which we know will
ultimately not have great performance (AR, MA, ARMA), we are now well-versed in the process
of time series modeling.
This means that when we come to study more recent models (including those currently in
the research literature) we will have a significant knowledge base on which to draw. This will
allow effective evaluation of these models rather than treating them as a "turn key" prescription
or "black box".
More importantly it will provide us with the confidence to extend and modify them on our
own and understand what we are doing when we do it.
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