Mean directional accuracy (MDA), also known as mean direction accuracy, is a measure of prediction accuracy of a forecasting method in

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

. 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 a function that has the value , or according to whether the sign of a given real number is positive or negative, or the given number is itself zer ...

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 , then the indicator functio ...

. 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 a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...

and

finance Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Admin ...

. MDA is used in

applications where the economist is often interested only in directional movement of variable of interest. As an example in

macroeconomics Macroeconomics is a branch of economics that deals with the performance, structure, behavior, and decision-making of an economy as a whole. This includes regional, national, and global economies. Macroeconomists study topics such as output (econ ...

, 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 a u ...

, 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 considers 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