# incrmmda
> Compute a moving [mean directional accuracy][mean-directional-accuracy] (MDA) incrementally.
For a window of size `W`, the [mean directional accuracy][mean-directional-accuracy] is defined as
where `f_i` is the forecast value, `a_i` is the actual value, `sgn(x)` is the [signum][@stdlib/math/base/special/signum] function, and `δ` is the [Kronecker delta][@stdlib/math/base/special/kronecker-delta].
## Usage
```javascript
var incrmmda = require( '@stdlib/stats/incr/mmda' );
```
#### incrmmda( window )
Returns an accumulator `function` which incrementally computes a moving [mean directional accuracy][mean-directional-accuracy]. The `window` parameter defines the number of values over which to compute the moving [mean directional accuracy][mean-directional-accuracy].
```javascript
var accumulator = incrmmda( 3 );
```
#### accumulator( \[f, a] )
If provided input values `f` and `a`, the accumulator function returns an updated [mean directional accuracy][mean-directional-accuracy]. If not provided input values `f` and `a`, the accumulator function returns the current [mean directional accuracy][mean-directional-accuracy].
```javascript
var accumulator = incrmmda( 3 );
var m = accumulator();
// returns null
// Fill the window...
m = accumulator( 2.0, 3.0 ); // [(+,+)]
// returns 1.0
m = accumulator( 1.0, 4.0 ); // [(+,+), (-,+)]
// returns 0.5
m = accumulator( 3.0, 9.0 ); // [(+,+), (-,+), (+,+)]
// returns ~0.67
// Window begins sliding...
m = accumulator( 7.0, 3.0 ); // [(-,+), (+,+), (+,-)]
// returns ~0.33
m = accumulator( 5.0, 3.0 ); // [(+,+), (+,-), (-,0)]
// returns ~0.33
m = accumulator();
// returns ~0.33
```
## Notes
- Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for **at least** `W-1` future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
- As `W` (f,a) pairs are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrmmda = require( '@stdlib/stats/incr/mmda' );
var accumulator;
var v1;
var v2;
var i;
// Initialize an accumulator:
accumulator = incrmmda( 5 );
// For each simulated datum, update the moving mean directional accuracy...
for ( i = 0; i < 100; i++ ) {
v1 = ( randu()*100.0 ) - 50.0;
v2 = ( randu()*100.0 ) - 50.0;
accumulator( v1, v2 );
}
console.log( accumulator() );
```
[mean-directional-accuracy]: https://en.wikipedia.org/wiki/Mean_Directional_Accuracy_%28MDA%29
[@stdlib/math/base/special/signum]: https://www.npmjs.com/package/@stdlib/math-base-special-signum
[@stdlib/math/base/special/kronecker-delta]: https://www.npmjs.com/package/@stdlib/math-base-special-kronecker-delta
