phpOMS/Math/Finance/Forecasting/ARIMA.php

<?php

class ARIMA {
	public function __construct(array $data, int $order = 12) {
		if($order !== 12 && $order !== 4) {
			throw new \Exceptions('ARIMA only supports quarterly and monthly decomposition');
		}
	}

	public function getDecomposition() : array {
		$iteration1 = $this->getIteration($this->data);
		$iteration2 = $this->getIteration($iteration1);
		$iteration3 = $this->getIteration($iteration2);

		return $iteration3;
	}

	private function getIteration(array $data) : array {
		$multiplicativeDecomposition = new ClassicalDecomposition($data, $this->order, ClassicalDecomposition::MULTIPLICATIVE);
		$tempDecomposition = $multiplicativeDecomposition->getDecomposition();

		// 1
		$trendCycleComponent = ClassicalDecomposition::computeTrendCycle($data, $this->order);
		$centeredRatios = ClassicalDecomposition::computeDetrendedSeries($this->data, $trendCycleComponent, ClassicalDecomposition::MULTIPLICATIVE);
		$prelimSeasonalComponent = Average::totalMovingAverage(Average::totalMovingAverage($centeredRatios, 3, null, true), 3, null, true);
		$prelimRemainder = $this->getPrelimRemainder($centeredRatios, $prelimSeasonalComponent);
		$modifiedRemainder = $this->removeOutliers($prelimRemainder, 0.5);
		$modifiedCenteredRatios = $this->getModifiedCenteredRatios($prelimSeasonalComponent, $modifiedRemainder); 
		$revisedSeasonalComponent = Average::totalMovingAverage(Average::totalMovingAverage($modifiedCenteredRatios, 3, null, true), 3, null, true);
		$prelimSeasonalAdjustedSeries = $this->getPrelimSeasonalAdjustedSeries($revisedSeasonalComponent);
		$trendCycleComponent = $this->getTrendCycleEstimation($prelimSeasonalAdjustedSeries);

		// 2
		$centeredRatios = ClassicalDecomposition::computeDetrendedSeries($this->data, $trendCycleComponent, ClassicalDecomposition::MULTIPLICATIVE);
		$prelimSeasonalComponent = Average::totalMovingAverage(Average::totalMovingAverage($centeredRatios, 5, null, true), 3, null, true);
		$prelimRemainder = $this->getPrelimRemainder($centeredRatios, $prelimSeasonalComponent);
		$modifiedRemainder = $this->removeOutliers($prelimRemainder, 0.5);
		$modifiedCenteredRatios = $this->getModifiedCenteredRatios($prelimSeasonalComponent, $modifiedRemainder);
		$revisedSeasonalComponent = Average::totalMovingAverage(Average::totalMovingAverage($modifiedCenteredRatios, 5, null, true), 3, null, true);
		$seasonalAdjustedSeries = $this->getSeasonalAdjustedSeries($revisedSeasonalComponent);

		$remainder = $this->getRemainder($seasonalAdjustedSeries, $trendCycleComponent);
		$modifiedRemainder = $this->removeOutliers($remainder, 0.5);
		$modifiedData = $this->getModifiedData($trendCycleComponent, $seasonalAdjustedSeries, $modifiedRemainder);

		return $modifiedData;
	}

	private function getPrelimRemainder(array $centeredRatios, array $prelimSeasonalComponent) : array {
		$remainder = [];
		$count = count($prelimSeasonalComponent);

		for($i = 0; $i < $count; $i++) {
			// +1 since 3x3 MA
			$remainder[] = $centeredRatios[$i+1] / $prelimSeasonalComponent[$i];
		}

		return $remainder;
	}

	private function removeOutliers(array $data, float $deviation = 0.5) : array {
		$avg = AVerage::arithmeticMean($data);

		foreach($data as $key => $value) {
			if($value / $avg - 1 > $deviation) {
				$data[$key] = $avg;
			}
		}

		return $data;
	}

	private function getModifiedCenteredRatios(array $seasonal, array $remainder) : array {
		$centeredRatio = [];
		$count = count($seasonal);

		for($i = 0; $i < $count; $i++) {
			// +1 since 3x3 MA
			$centeredRatio[] = $remainder[$i+1] * $seasonal[$i];
		}

		return $centeredRatio;
	}

	private function getSeasonalAdjustedSeries(array $seasonal) : array {
		$adjusted = [];
		$count = count($seasonal);
		$start = ClassicalDecomposition::getStartOfDecomposition(count($this->data), $count);

		for($i = 0; $i < $count; $i++) {
			$adjusted[] = $this->data[$start + $i] / $seasonal[$i];
		}

		return $adjusted;
	}

	private function getTrendCycleEstimation(array $seasonal) : array {
		$count = count($seasonal);

		if($count >= 12) {
			$weight = Average::MAH23;
		} elseif($count >= 6) {
			$weight = Average::MAH13;
		} else {
			$weight = Average::MAH9;
		}

		// todo: implement

		return $seasonal;
	}

	private function getRemainder(array $seasonal, array $trendCycle) {
		$remainder = [];
		foreach($seasonal as $key => $e) {
			$remainder = $e / $trendCycle[$key];
		}

		return $remainder;
	}

	private function getModifiedData(array $trendCycleComponent, array $seasonalAdjustedSeries, array $remainder) : array {
		$data = [];
		$count = count($trendCycleComponent);

		for($i = 0; $i < $count; $i++) {
			$data[] = $trendCycleComponent[$i] * $seasonalAdjustedSeries[$i] * $remainder[$i];
		}

		return $data;
	}
}