In measuring forecast errors, the MAD and the square root of the MSE will provide similar (but not identical) values, in that both provide a measure of the "typical" amount of error in forecasts.

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Quizplus · Accepted Answer

Both MAD (Mean Absolute Deviation) and the square root of MSE (Mean Squared Error) are measures of forecast accuracy that provide an average magnitude of errors, with MAD using absolute errors and the square root of MSE penalizing larger errors more due to squaring.

In Measuring Forecast Errors, the MAD and the Square Root