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# incrmmaape

> Compute a moving [mean arctangent absolute percentage error][@kim:2016a] (MAAPE) incrementally.

<section class="intro">

For a window of size `W`, the [mean arctangent absolute percentage error][@kim:2016a] is defined as

<!-- <equation class="equation" label="eq:mean_arctangent_absolute_percentage_error" align="center" raw="\operatorname{MAAPE}  = \frac{1}{W} \sum_{i=0}^{W-1} \operatorname{arctan}\biggl( \biggl| \frac{a_i - f_i}{a_i} \biggr| \biggr)" alt="Equation for the mean arctangent absolute percentage error."> -->

<div class="equation" align="center" data-raw-text="\operatorname{MAAPE}  = \frac{1}{W} \sum_{i=0}^{W-1} \operatorname{arctan} \biggl( \biggl| \frac{a_i - f_i}{a_i} \biggr| \biggr)" data-equation="eq:mean_arctangent_absolute_percentage_error">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/677f6828831c61cabc84859897a5ee7e079d6ddf/lib/node_modules/@stdlib/stats/incr/mmaape/docs/img/equation_mean_arctangent_absolute_percentage_error.svg" alt="Equation for the mean arctangent absolute percentage error.">
    <br>
</div>

<!-- </equation> -->

where `f_i` is the forecast value and `a_i` is the actual value.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrmmaape = require( '@stdlib/stats/incr/mmaape' );
```

#### incrmmaape( window )

Returns an accumulator `function` which incrementally computes a moving [mean arctangent absolute percentage error][@kim:2016a]. The `window` parameter defines the number of values over which to compute the moving [mean arctangent absolute percentage error][@kim:2016a].

```javascript
var accumulator = incrmmaape( 3 );
```

#### accumulator( \[f, a] )

If provided input values `f` and `a`, the accumulator function returns an updated [mean arctangent absolute percentage error][@kim:2016a]. If not provided input values `f` and `a`, the accumulator function returns the current [mean arctangent absolute percentage error][@kim:2016a].

```javascript
var accumulator = incrmmaape( 3 );

var m = accumulator();
// returns null

// Fill the window...
m = accumulator( 2.0, 3.0 ); // [(2.0,3.0)]
// returns ~0.32

m = accumulator( 1.0, 4.0 ); // [(2.0,3.0), (1.0,4.0)]
// returns ~0.48

m = accumulator( 3.0, 9.0 ); // [(2.0,3.0), (1.0,4.0), (3.0,9.0)]
// returns ~0.52

// Window begins sliding...
m = accumulator( 7.0, 3.0 ); // [(1.0,4.0), (3.0,9.0), (7.0,3.0)]
// returns ~0.72

m = accumulator( 5.0, 3.0 ); // [(3.0,9.0), (7.0,3.0), (5.0,3.0)]
// returns ~0.70

m = accumulator();
// returns ~0.70
```

</section>

<!-- /.usage -->

<section class="notes">

## 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.
-   Note that, unlike the [mean absolute percentage error][@stdlib/stats/incr/mape] (MAPE), the [mean arctangent absolute percentage error][@kim:2016a] is expressed in radians on the interval \[0,π/2].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrmmaape = require( '@stdlib/stats/incr/mmaape' );

var accumulator;
var v1;
var v2;
var i;

// Initialize an accumulator:
accumulator = incrmmaape( 5 );

// For each simulated datum, update the moving mean arctangent absolute percentage error...
for ( i = 0; i < 100; i++ ) {
    v1 = ( randu()*100.0 ) + 50.0;
    v2 = ( randu()*100.0 ) + 50.0;
    accumulator( v1, v2 );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<section class="references">

## References

-   Kim, Sungil, and Heeyoung Kim. 2016. "A new metric of absolute percentage error for intermittent demand forecasts." _International Journal of Forecasting_ 32 (3): 669–79. doi:[10.1016/j.ijforecast.2015.12.003][@kim:2016a].

</section>

<!-- /.references -->

<section class="links">

[@kim:2016a]: https://www.sciencedirect.com/science/article/pii/S0169207016000121

[@stdlib/stats/incr/mape]: https://github.com/stdlib-js/stats/tree/main/incr/mape

</section>

<!-- /.links -->
