incrmmda

Compute a moving mean directional accuracy (MDA) incrementally.

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

upper M upper D upper A equals StartLayout Enlarged left-brace 1st Row 1st Column 1 2nd Column if upper W equals 1 2nd Row 1st Column StartFraction 1 Over upper W EndFraction sigma-summation Underscript i equals 1 Overscript upper W Endscripts delta Subscript s g n left-parenthesis normal upper Delta f Sub Subscript i comma i minus 1 Subscript right-parenthesis comma s g n left-parenthesis normal upper Delta a Sub Subscript i comma i minus 1 Subscript right-parenthesis Baseline 2nd Column if upper W greater-than 1 EndLayout

where f_i is the forecast value, a_i is the actual value, sgn(x) is the signum function, and δ is the Kronecker delta.

Usage

var incrmmda = require( '@stdlib/stats/incr/mmda' );

incrmmda( window )

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

var accumulator = incrmmda( 3 );

accumulator( [f, a] )

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

var accumulator = incrmmda( 3 );

var m = accumulator();
// returns null

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

m = accumulator( 1.0, 4.0 ); // [(+,+), (-,+)]
// returns 0.5

m = accumulator( 3.0, 9.0 ); // [(+,+), (-,+), (+,+)]
// returns ~0.67

// Window begins sliding...
m = accumulator( 7.0, 3.0 ); // [(-,+), (+,+), (+,-)]
// returns ~0.33

m = accumulator( 5.0, 3.0 ); // [(+,+), (+,-), (-,0)]
// returns ~0.33

m = accumulator();
// returns ~0.33

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.

Examples

var randu = require( '@stdlib/random/base/randu' );
var incrmmda = require( '@stdlib/stats/incr/mmda' );

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

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

// For each simulated datum, update the moving mean directional accuracy...
for ( i = 0; i < 100; i++ ) {
    v1 = ( randu()*100.0 ) - 50.0;
    v2 = ( randu()*100.0 ) - 50.0;
    accumulator( v1, v2 );
}
console.log( accumulator() );