Log-linear trend

A trend model of the log of a series, ln y = b0 + b1 × t, implying growth at a constant rate. Forecasts are converted back to the original units by raising e to the fitted value.

Where you will meet it

Log-linear trend appears in 2 learning outcomes on the CFA syllabus. A few of them:

• Work out a trend forecast for a time series, whether fitted as a linear or a log-linear trend, from given trend coefficients, and judge the result
  CFA Level II · Quantitative Methods

  “A log-linear trend regresses the natural log of the series on t instead, so the series grows at a constant rate and the forecast, converted back from logs, is y = e^(b0 + b1 × t).”

• Explain what decides the choice between a linear and a log-linear trend for a given series, and assess where trend models fall short
  CFA Level II · Quantitative Methods

  “If it compounds at a roughly constant rate, its plot curves upward, and a linear trend leaves residuals that are positive at both ends and negative in the middle, so a log-linear trend is better.”

Practise it

• Today's practice question One question, with every wrong option explained.
• Free Level I diagnostic test Twelve questions that show which topics to start with.
• Free finance calculators Check your arithmetic on the exam's core formulas.

All terms beginning with L · Glossary