Can MDA be high while MAE is poor?

Yes. Large errors can still point in the correct direction.

Must unchanged values count as correct?

Only when the declared rule treats no change as a category and both actual and predicted directions match that category.

AI Glossary / Statistics and probability / Intermediate

Mean directional accuracy

Definition

Mean directional accuracy, or MDA, is the proportion of evaluated forecasts that correctly predict the direction of a specified change. For a common one-step definition, it compares the sign of the actual change from the previous observation with the sign of the forecast change from that same previous observation. It measures direction, not the size of the prediction error.

What it means

A forecast can correctly predict an increase while badly underestimating how large the increase will be. Conversely, a very small numerical error can receive no directional credit if it lies on the wrong side of the comparison value.
MDA is useful when up-versus-down behavior matters, but it needs a clear reference point. Comparing a forecast with the last actual value is not the same as comparing it with the preceding forecast.

How it works

Define the forecast origin, horizon, and reference value. For a one-step forecast made after observing y[t-1], the actual change is y[t]-y[t-1], and the predicted change is y-hat[t|t-1]-y[t-1]. Both use information aligned with the same forecast task.
Convert changes into directions using a stated rule. A three-way sign convention gives -1 for a decrease, 0 for no change, and +1 for an increase. Other applications group zero with one direction, exclude zero changes, or define a practically meaningful no-change band.
For each eligible case, record one if the predicted and actual directions match and zero otherwise. The ordinary MDA is the average of those indicators. Multiply by 100 to express it as a percentage.
Document the denominator. Missing actuals, missing forecasts, an unavailable initial reference, or excluded no-change cases can reduce the number of scored comparisons.
For multi-step forecasts, decide whether direction means change from the forecast origin or change between successive future periods. These definitions differ, particularly when an entire forecast path is issued at one time. Do not use later observed information to construct a reference that was unavailable for the intended decision.
Compare with suitable baselines. If the series rises most of the time, an always-up rule can achieve a high score without learning useful conditional information. Fifty percent is not a universal no-skill benchmark, especially with unequal direction frequencies or a third no-change category.
Keep magnitude-based errors alongside direction. MDA gives the same directional credit to a slightly correct movement and a wildly exaggerated movement. It can therefore rank models differently from MAE or RMSE without either calculation being wrong.
A weighted reward or penalty scheme may be more relevant when some correct directions matter more than others. Such a score is a different quantity from the ordinary fraction correct and should not be labeled as an unqualified accuracy percentage.
Use a time-respecting evaluation design. Repeated tuning on the evaluation period, overlapping forecast horizons, and serial dependence affect how much evidence a directional score provides. A simple independent-binomial significance calculation may be inappropriate.
If formal evidence of predictive direction is required, use a test whose null model and assumptions match the task. The MDA point estimate itself is not a p-value, and a high hit rate does not establish operational benefit or causal understanding.

Three practical examples

An operations team checks whether a demand model correctly predicts increases and decreases before reviewing the size of its forecast errors.
A capacity planner compares directional performance with an always-increase baseline in a growing service.
An AI forecasting evaluation reports MDA separately for different horizons and states how unchanged outcomes are scored.

Think of it this way

Think of asking whether a signpost points uphill, downhill, or along level ground. MDA checks that directional choice. It does not tell you how steep the route is or how far you will travel, so it cannot replace a distance-based assessment.

Worked example

An original example begins with an observed value of 100. The next four actual values are 105, 103, 103, and 108. The corresponding one-step forecasts, each compared with its immediately preceding actual value, are 104, 106, 103, and 102.
Actual changes are +5, -2, 0, and +5. Predicted changes relative to the same four reference values are +4, +1, 0, and -1. Under a three-way sign rule, the first and third directions match, while the second and fourth do not.
MDA is therefore 2/4 = 50%. The absolute forecast errors are 1, 3, 0, and 6, so MAE is 10/4 = 2.5 units. These summarize different aspects of the same predictions.
If actual no-change cases are excluded under a different declared protocol, only three comparisons remain and one is correct, giving 1/3, approximately 33.33%. An always-up rule scores 2/4 under the original three-way protocol.
The example shows why the reference point, zero rule, denominator, and baseline must accompany the reported directional accuracy.

Illustrative case study

In a fictional case, Hawthorn Demand introduces MDA into a forecasting dashboard. The score appears strong during a sustained growth period, but an always-up baseline performs similarly.
Analysts retain the directional score, add a baseline comparison, and examine declining and unchanged periods separately. They also inspect forecast magnitudes before using predictions to allocate resources. The case illustrates the limits of a headline hit rate; it does not claim a real forecast improvement or suggest that directional correctness alone justifies an operational action.

Common misconceptions and mistakes

Do not calculate predicted direction from consecutive forecasts when the stated definition uses the last actual observation. Do not assume 50% is always the relevant baseline or that a high MDA implies small errors.
Do not change the handling of ties after seeing which rule improves a preferred model. MDA is also different from mean directional value, which incorporates a value or magnitude weighting.

Business use

MDA can supplement forecasting evaluation when the direction of change has operational relevance. It is most useful with an explicit decision horizon, meaningful baseline, and magnitude-sensitive measures. A team planning capacity still needs to know whether the expected increase is small or large, even when the directional forecast is correct.

Check your understanding

Why does excluding the unchanged case reduce the example's score?

Answer: That case was one of the two correct directions. Removing it changes both the numerator and denominator, from 2/4 to 1/3.

Related terms

Forecast horizon
Mean Absolute Error
Sign test
Directional forecast
Forecast origin
Baseline forecast
Pesaran-Timmermann test

Learn next

Next, define direction for multi-step forecasts and compare baseline hit rates. Then study uncertainty methods that account for dependence and the particular direction categories used.

Sources

Fabletools, Directional accuracy measures: https://search.r-project.org/CRAN/refmans/fabletools/html/directional_accuracy_measures.html Fabletools, accuracy implementation: https://raw.githubusercontent.com/tidyverts/fabletools/master/R/accuracy.R Statsmodels, Pesaran-Timmermann directional predictive accuracy test: https://www.statsmodels.org/stable/generated/statsmodels.stats.diagnostic.pesaran_timmermann.html

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