Mean directional accuracy (MDA), also known as mean direction accuracy, is a measure of prediction accuracy of a forecasting method in statistics. It compares the forecast direction (upward or downward) to the actual realized direction. It is defined by the following formula: :

\frac\sum_t \mathbf_

where ''A''_''t'' is the actual value at time ''t'' and ''F''_''t'' is the forecast value at time ''t''. Variable ''N'' represents number of forecasting points. The function

\sgn(\cdot)

sign function In mathematics, the sign function or signum function (from '' signum'', Latin for "sign") is an odd mathematical function that extracts the sign of a real number. In mathematical expressions the sign function is often represented as . To a ...

and

\mathbf

is the

indicator function In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if is a subset of some set , one has \mathbf_(x)=1 if x ...

. In simple words, MDA provides the probability that the under study forecasting method can detect the correct direction of the time series. MDA is a popular metric for forecasting performance in

economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analy ...

and finance. MDA is used in

applications where the economist is often interested only in directional movement of variable of interest. As an example in macroeconomics, a monetary authority who wants to know the direction of the inflation, to raise or decrease interest rates if inflation is predicted to rise or drop respectively. Another example can be found in financial planning where the user wants to know if the demand has increasing direction or decreasing trend.

Comparison to other forecasting metrics

Many techniques, such as

mean absolute percentage error The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics. It usually expresses the accuracy as a ratio defined by the formula: : ...

median absolute deviation In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated by the MAD calculated from a sample. For ...

, evaluate forecasting and provided information about the accuracy and value of the forecasts. While accuracy, as measured by quantitative errors, is important, it may be more crucial to accurately forecast the direction of change. Directional accuracy is similar to a binary evaluation. The metric only consider the upward or downward direction in the time series and is independent of quantitive value of increase or decrease. For example, will prices rise or fall? How much it will increase or decrease can be detected by other forecasting metrics.Sinclair, T. M., Stekler, H. O., & Kitzinger, L. (2010). Directional forecasts of GDP and inflation: a joint evaluation with an application to Federal Reserve predictions. Applied Economics, 42(18), 2289-2297.

References

{{Machine learning evaluation metrics Statistical forecasting