incrmaape

Compute the mean arctangent absolute percentage error (MAAPE) incrementally.

The mean arctangent absolute percentage error is defined as

upper M upper A upper A upper P upper E equals StartFraction 1 Over n EndFraction sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts arc tangent left-parenthesis StartAbsoluteValue StartFraction a Subscript i Baseline minus f Subscript i Baseline Over a Subscript i Baseline EndFraction EndAbsoluteValue right-parenthesis

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

Usage

var incrmaape = require( '@stdlib/stats/incr/maape' );

incrmaape()

Returns an accumulator function which incrementally computes the mean arctangent absolute percentage error.

var accumulator = incrmaape();

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 = incrmaape();

var m = accumulator( 2.0, 3.0 );
// returns ~0.3218

m = accumulator( 1.0, 4.0 );
// returns ~0.4826

m = accumulator( 3.0, 5.0 );
// returns ~0.4486

m = accumulator();
// returns ~0.4486

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 all 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.
  • 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 incrmaape = require( '@stdlib/stats/incr/maape' );

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

// Initialize an accumulator:
accumulator = incrmaape();

// For each simulated datum, update the 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.