Explain what decides the choice between a linear and a log-linear trend for a given series, and assess where trend models fall short
The idea
Choose the trend model by the pattern of growth. If a series rises by roughly the same amount each period, a linear trend fits. 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. Both models share limits: they assume the past pattern continues indefinitely, and their residuals are often serially correlated, which a Durbin–Watson test detects. Serial correlation makes the trend model's inference unreliable and suggests an autoregressive model instead. A high R² does not settle the choice between the two.
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