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

A researcher fits a log-linear trend model ln(y_t) = 4.00 + 0.02t + e_t to quarterly revenue, where revenue is measured in millions of dollars. Which statement correctly interprets the slope coefficient and gives the model's forecast for t = 10?

Revenue grows about 2% per quarter because the slope in a log-linear trend is the constant proportional growth rate. The forecast log revenue is 4.20 at t = 10, so revenue is e^4.20, about 66.7 million dollars, after exponentiating.

  1. ARevenue grows about 2% per quarter; the forecast is e^4.20, about 66.7 millionCorrect
  2. BRevenue grows about 2 million per quarter; the forecast is 4.20 million
  3. CRevenue grows about 2% per quarter; the forecast is 4.20 million
  4. DRevenue grows about 0.02% per quarter; the forecast is e^4.20, about 66.7 million

Explanation

In a log-linear model the slope is the approximate constant proportional growth rate, 0.02 or 2% per period. The forecast of ln(y) at t = 10 is 4.00 + 0.20 = 4.20, so y = e^4.20, about 66.7. The other options misread the slope as an absolute change or fail to exponentiate.

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