advanced-algorithmic-trading

Chapter 9
Random Walks and White Noise
Models
In the previous chapter we discussed the importance of serial correlation and why it is extremely
useful in the context of quantitative trading.
In this chapter we will make full use of serial correlation by discussing our first time series
models, including some elementary linear stochastic models. In particular we are going to discuss
the White Noise and Random Walk models.
9.1 Time Series Modelling Process
What is a time series model? Essentially, it is a mathematical model that attempts to "explain"
the serial correlation present in a time series.
When we say "explain" what we really mean is once we have "fitted" a model to a time series
it should account for some or all of the serial correlation present in the correlogram. That is,
by fitting the model to a historical time series, we are reducing the serial correlation and thus
"explaining it away".
Our process, as quantitative researchers, is to consider a wide variety of models including
their assumptions and their complexity, and then choose a model such that it is the "simplest"
that will explain the serial correlation. Once we have such a model we can use it to predict
future values, or future behaviour in general. This prediction is obviously extremely useful in
quantitative trading.
If we can predict the direction of an asset movement then we have the basis of a trading
strategy. If we can predict volatility of an asset then we have the basis of another trading
strategy, or a risk-management approach. This is why we are interested in so-called second
order properties of a time series, since they give us the means to generate forecasts.
How do we know when we have a good fit for a model? What criteria do we use to judge
which model is best? We will be considering these questions in this part of the book.
Let us summarise the general process we will be following throughout the time series section:
• Outline a hypotheis about a particular time series and its behaviour
• Obtain the correlogram of the time series using R and assess its serial correlation
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