Time Series Analysis for Financial Data III— Moving Average Models

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In the second post in this series, we talked about Auto-Regressive Models — models which only depend on past data of the system. We saw that these models only partially explained the log-returns of stock prices.

We turn to another model, the Moving Average model to see if they perform better on our data.

Moving Average Models

MA(q) models are very similar to AR(p) models. MA(q) model is a linear combination of past error terms as opposed to a linear combination of past observations like the AR(p) model. The motivation for the MA model is that we can explain “shocks” in the error process directly by fitting a model to the error terms. The first order model, MA(1) is:

x(t) = b*e(t-1) + e(t)

where b is the coefficient and e is the error term.