MD

166. MD

166.1. MD (Mean Deviation / Bias)

Average of the signed forecast errors $𝑒_{𝑡} = 𝑥_{𝑡} - {\hat{𝑥}}_{𝑡}$ . Captures bias — whether the forecast systematically over- or under-shoots.

MD = \frac{1}{𝑛} \sum_{𝑡 = 1}^{𝑛} 𝑒_{𝑡} = \frac{1}{𝑛} \sum_{𝑡 = 1}^{𝑛} (𝑥_{𝑡} - {\hat{𝑥}}_{𝑡})

$MD \approx 0$ : forecast is unbiased on average
$MD > 0$ : forecast under-predicts (actuals exceed forecast)
$MD < 0$ : forecast over-predicts

Caveat. Positive and negative errors cancel out, so MD says nothing about accuracy — a forecast that alternates wildly between $+ 100$ and $- 100$ has MD $= 0$ . Pair MD with MAE / RMSE to separate bias from accuracy.