8 ARMA Models

Learning Goals

• Understand the notation for an ARMA(p,q) and the general mathematical approaches for deriving variance and covariance.
• Explain and implement partial autocorrelation function estimation by assuming stationarity (PACF).
• Explain the common patterns in ACF and PACF for MA(q) and AR(p) models.
• Fit ARMA models to stationary detrended data (also seasonality removed).

Slides from today are available here.

Name that Model

You’ve been selected to participate in our game show called, NAME that MODEL!

For each data set, guess AR, MA, or Not Stationary! Then for each, make sure to specify the order of the model.

It may be useful to describe the general patterns you might expect in the estimated ACF for data generated from an AR, MA, or Not Stationary model.

Data set 1

Data set 2

Data set 3

Data set 4

Data set 5

Data set 6