Explanation:
D is correct. Seasonality is included in a model by multiplying the short-run lag polynomial by a seasonal lag polynomial. The specification of Seasonal ARMA models is denoted:
where and are the orders of the short-run lag polynomials, and are the orders of the seasonal lag polynomials, and is the seasonal horizon.
A and B are incorrect. Seasonality can be introduced to the AR component, the MA component, or both.
C is incorrect. As explained above, seasonality is included in a model by multiplying the short-run lag polynomial by a seasonal lag polynomial.
Learning Objective: Explain how seasonality is modeled in a covariance-stationary ARMA.
Reference: Global Association of Risk Professionals. Quantitative Analysis. New York, NY: Pearson, 2023, Chapter 10, Stationary Time Series [QA-10].
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Question 94 of 100
94. An equity research analyst specializing in the consumer goods sector is modeling retail sales data that exhibits seasonality using an autoregressive moving average (ARMA) process. The analyst notes that the ARMA process used in the model is covariance stationary. Which of the following correctly describes how seasonality is modeled in a covariance-stationary ARMA process?
A
Seasonality can be introduced to an ARMA process through the autoregressive (AR) component, but not through the moving average (MA) component.
B
Seasonality can be introduced to an ARMA process through the moving average (MA) component, but not through the autoregressive (AR) component.
C
Seasonality is included in an ARMA model by multiplying the number of full seasonal cycles by the lag lengths of the ARMA process.
D
Seasonality is included in an ARMA model by multiplying the short-run lag polynomial by a seasonal lag polynomial.
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