# incrmmpe

Compute a moving mean percentage error (MPE) incrementally.

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

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

## Usage

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).