The simple moving average model

Time Series Analysis in R

David S. Matteson

Associate Professor at Cornell University

The simple moving average model

The simple moving average (MA) model:

$ Today = Mean + Noise + Slope * (Yesterday's Noise)$

More formally:

where $ \epsilon_t$ is mean zero white noise (WN).

Three parameters:

  • The mean $\mu$
  • The slope $\theta$
  • The WN variance $\sigma^2$
Time Series Analysis in R

MA processes - I

$ Today = Mean + Noise + Slope * (Yesterday's Noise)$

$$Y_t = \mu + \epsilon_t + \theta\epsilon_{t-1}$$

  • If slope $\theta$ is zero then:

$Y_t = \mu + \epsilon_t$

And $Y_t$ is White Noise $(\mu, \sigma_{\epsilon}^2)$

Time Series Analysis in R

MA processes - II

$Today = Mean + Noise + Slope * (Yesterday's Noise)$

$$Y_t = \mu + \epsilon_t + \theta\epsilon_{t-1}$$

  • If slope $\theta$ is not zero then $Y_t$ depends on both $\epsilon_t$ and $\epsilon_{t-1}$

And the process ${Y_t}$ is autocorrelated

  • Large values of $\theta$ lead to greater autocorrelation

  • Negative values of $\theta$ result in oscillatory time series

Time Series Analysis in R

MA examples

Time Series Analysis in R

Autocorrelations

Only lag 1 autocorrelation non-zero for the MA model.

Time Series Analysis in R

Let's practice!

Time Series Analysis in R

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