Mean directional accuracy

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:

${\displaystyle {\frac {1}{N}}\sum _{t}\mathbf {1} _{\operatorname {sgn}(A_{t}-A_{t-1})=\operatorname {sgn}(F_{t}-A_{t-1})}}$

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 ${\displaystyle \operatorname {sgn}(\cdot )}$ is sign function and ${\displaystyle \mathbf {1} }$ is the indicator function.

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 and finance.[1][2]

MDA is used in economics 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.[3] Another example can be found in financial planning where the user wants to know if the demand has increasing direction or decreasing trend.[4]