MDA - Mean Directional Accuracy

Calculates the mean directional accuracy function for the forecast and the eventual outcomes.


MDA (X, F)

is the eventual outcome time series sample data (a one-dimensional array of cells e.g., row or column).
is the forecast time series data (a one-dimensional array of cells e.g., row or column).


  1. The time series is homogeneous or equally spaced.
  2. The time series X and F must be of identical size.
  3. The time series X or F may include observations with missing values (e.g., #N/A or blank).
  4. Observations with missing values in Y or F are excluded from the MDA calculation.
  5. The MDA compares the forecast direction (upward or downward) to the actual realized direction
  6. The mean directional accuracy is given by: $$\mathrm{MDA} = \frac{1}{N}\sum_t \mathbf{1}_{sign(X_t - X_{t-1}) == sign(F_t - X_{t-1})}$$ Where:
    • $\{X_i\}$ is the actual observations time series.
    • $\{F_i\}$ is the estimated or forecast time series.
    • $N$ is the number of non-missing data points.
    • $sign(\cdot)$ is sign function.
    • $\mathbf{1}$ is the indicator function.
  7. In short, MDA provides the probability that the under-study forecasting method can detect the correct direction of the time series.
  8. MDA is a popular metric for forecasting performance in economics and finance.
  9. The MDA function is available starting with version 1.66 PARSON.

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