advanced-algorithmic-trading

Chapter 10
Autoregressive Moving Average
Models
In the last chapter we looked at random walks and white noise as basic time series models for
certain financial instruments, such as daily equity and equity index prices. We found that in
some cases a random walk model was insufficient to capture the full autocorrelation behaviour
of the instrument, which motivates more sophisticated models.
In this chapter we are going to discuss three types of model, namely the Autoregressive
(AR) model of order p, the Moving Average (MA) model of order q and the mixed Autogressive
Moving Average (ARMA) model of order p, q. These models will help us attempt
to capture or "explain" more of the serial correlation present within an instrument. Ultimately
they will provide us with a means of forecasting the future prices.
However, it is well known that financial time series possess a property known as volatility
clustering. That is, the volatility of the instrument is not constant in time. The technical term
for this behaviour is conditional heteroskedasticity. Since the AR, MA and ARMA models
are not conditionally heteroskedastic, that is, they don’t take into account volatility clustering,
we will ultimately need a more sophisticated model for our predictions.
Such models include the Autogressive Conditional Heteroskedastic (ARCH) model,
the Generalised Autogressive Conditional Heteroskedastic (GARCH) model and the
many variants thereof. GARCH is particularly well known in quant finance and is primarily used
for financial time series simulations as a means of estimating risk.
However, we will be building up to these models from simpler versions in order to see how
each new variant changes our predictive ability. Despite the fact that AR, MA and ARMA are
relatively simple time series models, they are the basis of more complicated models such as the
Autoregressive Integrated Moving Average (ARIMA) and the GARCH family. Hence it
is important that we study them.
One of our trading strategies later in the book will be to combine ARIMA and GARCH
in order to predict prices n periods in advance. However, we will have to wait until we have
discussed both ARIMA and GARCH separately before we apply them to this strategy.
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