# MDA - Mean Directional Accuracy

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

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.

## Examples

Example 1:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
A B C
Date Data Forecast
2008-01-01 -2.9 -2.95
2008-02-01 -2.83 -2.7
2008-03-01 -0.95 -1.00
2008-04-01 -0.88 -0.68
2008-05-01 1.21 1.50
2008-06-01 -1.67 -1.00
2008-07-01 0.83 0.90
2008-08-01 -0.27 -0.37
2008-09-01 1.36 1.26
2008-10-01 -0.34 -0.54
2008-11-01 0.48 0.58
2008-12-01 -2.83 -2.13
2009-01-01 -0.95 -0.75
2009-02-01 -0.88 -0.89
2009-03-01 1.21 1.25
2009-04-01 -1.67 -1.65
2009-05-01 -2.99 -3.20
2009-06-01 1.24 1.29
2009-07-01 0.64 0.60

Formula Description (Result)
=MDA($B$3:$B$21,$C$3:$C$21) MDA (94.44%)