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FRM Part I · FRM Exam Part I · Nonstationary Time Series

A risk analyst models monthly retail sales of a chain with a regression on an intercept and 11 monthly dummy variables (December is the omitted base month) plus a trend. The coefficient on the January dummy is -42.0 (in USD millions). What is the correct interpretation?

January sales are on average USD 42.0 million below December sales, controlling for trend. In a dummy-variable seasonal model, each coefficient is measured relative to the omitted base month, not relative to the annual average or the previous month.

  1. AJanuary sales are on average USD 42.0 million lower than December sales, after controlling for the trendCorrect
  2. BJanuary sales are on average USD 42.0 million lower than the annual average monthly sales
  3. CJanuary sales are 42.0% lower than December sales
  4. DJanuary sales are USD 42.0 million lower than those of the previous month

Explanation

With dummies for 11 months, each coefficient measures the seasonal difference relative to the omitted base month, here December. The -42.0 means January is USD 42.0 million below December holding the trend fixed. The comparison with the annual average would apply only to a model with seasonal effects constrained to sum to zero.

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