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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

$$\mathop{\mathrm{MAAPE}} = \frac{1}{W} \sum_{i=0}^{W-1} \mathop{\mathrm{arctan}}\biggl( \biggl| \frac{a_i - f_i}{a_i} \biggr| \biggr)$$

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

Installation

npm install @stdlib/stats-incr-mmaape

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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.

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See Also

• @stdlib/stats-incr/maape: compute the mean arctangent absolute percentage error (MAAPE) incrementally.
• @stdlib/stats-incr/mmape: compute a moving mean absolute percentage error (MAPE) incrementally.
• @stdlib/stats-incr/mmpe: compute a moving mean percentage error (MPE) incrementally.
• @stdlib/stats-incr/mmean: compute a moving arithmetic mean incrementally.

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Notice

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.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.