incrmmape

Compute a moving mean absolute percentage error incrementally.

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

upper M upper A upper P upper E equals StartFraction 100 Over upper W EndFraction sigma-summation Underscript i equals 0 Overscript upper W minus 1 Endscripts StartAbsoluteValue StartFraction a Subscript i Baseline minus f Subscript i Baseline Over a Subscript i Baseline EndFraction EndAbsoluteValue

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

Usage

var incrmmape = require( '@stdlib/stats/incr/mmape' );

incrmmape( window )

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

var accumulator = incrmmape( 3 );

accumulator( [f, a] )

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

var accumulator = incrmmape( 3 );

var m = accumulator();
// returns null

// Fill the window...
m = accumulator( 2.0, 3.0 ); // [(2.0,3.0)]
// returns ~33.33

m = accumulator( 1.0, 4.0 ); // [(2.0,3.0), (1.0,4.0)]
// returns ~54.17

m = accumulator( 3.0, 9.0 ); // [(2.0,3.0), (1.0,4.0), (3.0,9.0)]
// returns ~58.33

// Window begins sliding...
m = accumulator( 7.0, 3.0 ); // [(1.0,4.0), (3.0,9.0), (7.0,3.0)]
// returns ~91.67

m = accumulator( 5.0, 3.0 ); // [(3.0,9.0), (7.0,3.0), (5.0,3.0)]
// returns ~88.89

m = accumulator();
// returns ~88.89

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.

  • Warning: the mean absolute percentage error has several shortcomings:

    • The measure is not suitable for intermittent demand patterns (i.e., when a_i is 0).
    • The mean absolute percentage error is not symmetrical, as the measure cannot exceed 100% for forecasts which are too "low" and has no limit for forecasts which are too "high".
    • When used to compare the accuracy of forecast models (e.g., predicting demand), the measure is biased toward forecasts which are too low.

Examples

var randu = require( '@stdlib/random/base/randu' );
var incrmmape = require( '@stdlib/stats/incr/mmape' );

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

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

// For each simulated datum, update the moving mean 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() );