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Compute a moving mean percentage error (MPE) incrementally.

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

Equation for the mean percentage error.

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


npm install @stdlib/stats-incr-mmpe


var incrmmpe = require( '@stdlib/stats-incr-mmpe' );

incrmmpe( window )

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

var accumulator = incrmmpe( 3 );

accumulator( [f, a] )

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

var accumulator = incrmmpe( 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 ~2.78

m = accumulator( 5.0, 3.0 ); // [(3.0,9.0), (7.0,3.0), (5.0,3.0)]
// returns ~-44.44

m = accumulator();
// returns ~-44.44


  • 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.
  • Be careful when interpreting the mean percentage error as errors can cancel. This stated, that errors can cancel makes the mean percentage error suitable for measuring the bias in forecasts.
  • Warning: the mean percentage error is not suitable for intermittent demand patterns (i.e., when a_i is 0). Interpretation is most straightforward when actual and forecast values are positive valued (e.g., number of widgets sold).


var randu = require( '@stdlib/random-base-randu' );
var incrmmpe = require( '@stdlib/stats-incr-mmpe' );

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

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

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

See Also


This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.






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