incrmme

Compute a moving mean error (ME) incrementally.

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

upper M upper E equals StartFraction 1 Over upper W EndFraction sigma-summation Underscript i equals 0 Overscript upper W minus 1 Endscripts left-parenthesis y Subscript i Baseline minus x Subscript i Baseline right-parenthesis

Usage

var incrmme = require( '@stdlib/stats/incr/mme' );

incrmme( window )

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

var accumulator = incrmme( 3 );

accumulator( [x, y] )

If provided input values x and y, the accumulator function returns an updated mean error. If not provided input values x and y, the accumulator function returns the current mean error.

var accumulator = incrmme( 3 );

var m = accumulator();
// returns null

// Fill the window...
m = accumulator( 2.0, 3.0 ); // [(2.0,3.0)]
// returns 1.0

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

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

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

m = accumulator( -5.0, -3.0 ); // [(3.0,9.0), (-7.0,3.0), (-5.0,-3.0)]
// returns 6.0

m = accumulator();
// returns 6.0

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 (x,y) 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 error as errors can cancel. This stated, that errors can cancel makes the mean error suitable for measuring the bias in forecasts.
  • Warning: the mean error is scale-dependent and, thus, the measure should not be used to make comparisons between datasets having different scales.

Examples

var randu = require( '@stdlib/random/base/randu' );
var incrmme = require( '@stdlib/stats/incr/mme' );

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

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

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