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.