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

## Syntax

**MDA **(**X**, **F**)

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

## Remarks

- The time series is homogeneous or equally spaced.
- The time series X and F must be of identical size.
- The time series X or F may include observations with missing values (e.g., #N/A or blank).
- Observations with missing values in Y or F are excluded from the MDA calculation.
- The MDA compares the forecast direction (upward or downward) to the actual realized direction
- 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.

- In short, 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.
- The MDA function is available starting with version 1.66 PARSON.

## Files Examples

## Related Links

## References

- R.J. Hyndman, A.B. Koehler, "Another look at measures of forecast accuracy", International Journal of Forecasting, 22 (2006), pp. 679-688.
- James Douglas Hamilton; Time Series Analysis; Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896.
- Tsay, Ruey S.; Analysis of Financial Time Series; John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740.
- D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906.

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