# incrmmaape

Compute a moving mean arctangent absolute percentage error (MAAPE) incrementally.

For a window of size W, the mean arctangent absolute percentage error is defined as

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

## Usage

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


#### incrmmaape( window )

Returns an accumulator function which incrementally computes a moving mean arctangent absolute percentage error. The window parameter defines the number of values over which to compute the moving mean arctangent absolute percentage error.

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. If not provided input values f and a, the accumulator function returns the current mean arctangent absolute percentage error.

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


## 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 (MAPE), the mean arctangent absolute percentage error is expressed in radians on the interval [0,π/2].

## Examples

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() );


## 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.