Pure seasonal models

ARIMA Models in R

David Stoffer

Professor of Statistics at the University of Pittsburgh

Pure Seasonal Models

  • Often collect data with a known seasonal component
  • Air Passengers (1 cycle every S = 12 months)
  • Johnson & Johnson Earnings (1 cycle every S = 4 quarters)

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ARIMA Models in R

Pure Seasonal Models

Consider pure seasonal models such as an SAR$(P = 1)_{s = 12}$

$$X_t = \Phi X_{t-12} + W_t$$

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ARIMA Models in R

ACF and PACF of Pure Seasonal Models

$$SAR(P)_s$$ $$SMA(Q)_s$$ $$SARMA(P, Q)_s$$
ACF* Tails off Cuts off lag QS Tails off
PACF* Cuts off lag PS Tails off Tails off

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ARIMA Models in R

Let's practice!

ARIMA Models in R

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