/**
 * Copyright (C) 2013-2017 Vasilis Vryniotis 
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package com.datumbox.framework.core.statistics.parametrics.onesample;

import com.datumbox.framework.common.dataobjects.FlatDataList;
import com.datumbox.framework.core.statistics.distributions.ContinuousDistributions;

/**
 * Durbin–Watson parametric test for detecting autocorrelation.
 *
 * @author Vasilis Vryniotis 
 */
public class DurbinWatson {

    /**
     * Test for Autocorrelation for k explanatory variables
     * 
     * @param errorList
     * @param k
     * @param is_twoTailed
     * @param aLevel
     * @return
     */
    public static boolean test(FlatDataList errorList, int k, boolean is_twoTailed, double aLevel) {
        int n= errorList.size();
        if(n<=0) {
            throw new IllegalArgumentException("The provided collection can't be empty.");
        }

        double DW=calculateScore(errorList);

        boolean rejectH0=checkCriticalValue(DW, n, k, is_twoTailed, aLevel);

        return rejectH0;
    }
    
    /**
     * Calculates DW score
     * 
     * @param errorList
     * @return 
     */
    public static double calculateScore(FlatDataList errorList) {
        double DWdeltasquare=0;
        double DWetsquare=0;

        int n = errorList.size();
        for(int i=0;i=1) {
                Double errorPrevious = errorList.getDouble(i-1);
                if(errorPrevious!=null) {
                    DWdeltasquare+=Math.pow(error - errorPrevious,2);        
                }
            }
            DWetsquare+=error*error;
        }
        double DW=DWdeltasquare/DWetsquare;

        return DW;
    }
    
    /**
     * Checks the Critical Value to determine if the Hypothesis should be rejected
     * 
     * @param score
     * @param n
     * @param k
     * @param is_twoTailed
     * @param aLevel
     * @return 
     */
    public static boolean checkCriticalValue(double score, int n, int k, boolean is_twoTailed, double aLevel) {
        /*
        if(n<=200 && k<=20) {
            //Calculate it from tables
            //http://www3.nd.edu/~wevans1/econ30331/Durbin_Watson_tables.pdf
        }
        */
        
        //Follows normal distribution for large samples
        //References: http://econometrics.com/guide/dwdist.htm
        double z=(score-2.0)/Math.sqrt(4.0/n);

        double probability=ContinuousDistributions.gaussCdf(z);

        boolean rejectH0=false;

        double a=aLevel;
        if(is_twoTailed) { //if to tailed test then split the statistical significance in half
            a=aLevel/2.0;
        }
        if(probability<=a || probability>=(1-a)) {
            rejectH0=true;
        }

        return rejectH0;
    }
}