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Ahrens Moving Average PHP Example

//========================================================================
// Ahrens Moving Average						//
//									//
// The Ahrens Moving Average is an IIR (Infinite Impulse Response),	//
// front-weighted moving average which can be used to filter time	//
// series data using a window as short as 2 periods. It provides	//
// superior smoothing and is less likely to be perturbed by transient	//
// spikes than either a simple moving average or a exponential moving	//
// average with the same smoothing period.				//
//									//
// This program is free software: you can redistribute it and/or modify	//
// it under the terms of the GNU General Public License as published by	//
// the Free Software Foundation, either version 3 of the License, or	//
// (at your option) any later version.					//
//									//
// This program is distributed in the hope that it will be useful,	//
// but WITHOUT ANY WARRANTY; without even the implied warranty of	//
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the	//
// GNU General Public License for more details.				//
//									//
// You should have received a copy of the GNU General Public License	//
// along with this program.  If not, see 	//
//========================================================================

<?php

function ahrens_moving_average($input_data,	// data to be smoothed
                               $period,		// smoothing window
                               $x_end) {	// end of input data

    //--------------------------------------------------------------
    // create the output array

    $avg = array();

    //--------------------------------------------------------------
    // the AMA may be used to smooth raw data or the output of
    // other calculations. since other calculations may introduce
    // significant phase lag so there is no guarantee that the
    // input data will actually start at the beginning of the
    // array passed to this function. this loop searches for the
    // first actual datapoint in the input series.

    $x_start = 1;
    for ($a = $x_start; $a <= $x_end; $a++) {
        if (isset($input_data[$a]) && is_numeric($input_data[$a])) {
            $x_start = $a;
            break;
        }
    }

    //--------------------------------------------------------------
    // the first raw data point in a series may be (significantly)
    // divergent from the data that follows. this loop creates a
    // reasonably representative set of initial values to seed the
    // average.  it uses an "expanding period" simple moving average
    // over the first N samples (where N equals the period of the
    // average)

    $count = 0;
    $total = 0;
    for ($a = $x_start; $a < $x_start + $period && $a <= $x_end; $a++) {
        $count++;
        $total += $input_data[$a];
        $avg[$a] = $total / $count;
    }

    //--------------------------------------------------------------
    // once the seed values have been calculated, shift gears and
    // calculate the AMA for $x_start + $period through $x_end

    for ($a = $x_start + $period; $a <= $x_end; $a++) {
        $numerator = $input_data[$a] - ($avg[$a-1] + $avg[$a-$period]) / 2;
        $avg[$a]   = $avg[$a-1] + $numerator / $period;
    }

    return $avg;
}
?>





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