MovingAverage Routine

Summary

Single moving average.

Declaration

Function MovingAverage(Y: TVec; const N: Integer; M: TVec; out Index: Integer; Centered: boolean = true): TSample;

Parameter	Description
Y	Sample data.
N	Number of elements in period.
M	Smoothed data.
Index	Index of first value in smoothed data.
Centered	If true, a centered moving average is perfomed.

Result

MSE.

Description

Performs single moving average smoothing on data Y. General equation for moving average smoothing is:

where N indicates number of points in period and X.Length data sample size. When using single moving average smoothing, bear in mind that when used as forecasts for the next period, single moving average is not able to cope with a significant trend.

Example 1

Load sample time series, perform centered moving average smoothing with period 12 (yearly average) and finally plot the results using TChart.

  Uses MtxExpr, StatTimeSerAnalysis, Series, TeEngine;
  procedure Example(Series1,Series2: TLineSeries);
  var ts,Mv: Vector;
    FirstIndex: Integer;
  begin
    ts.LoadFromFile('testdata.vec');
    DrawValues(ts,Series1); // draw original time series
    MovingAverage(ts,12,Mv,FirstIndex,True);
    DrawValues(Mv,Series2,FirstIndex); // draw MA over original time series
  end;

  #include "MtxVecCpp.h"
  #include "Math387.hpp"
  #include "StatTimeSerAnalysis.hpp"
  void __fastcall Example(TLineSeries* Series1, TLineSeries* Series2);
  {
    Vector ts,Mv;
    int FirstIndex;
    ts->LoadFromFile("testdata.vec");
    DrawValues(ts,Series1,0.0,1.0); // draw original time series
    MovingAverage(ts,12,Mv,FirstIndex,true);
    DrawValues(Mv,Series2,FirstIndex,1.0); // draw MA over original time series
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  using Steema.TeeChart;
  namespace Dew.Examples
  {
    private void Example(Styles.Line line1, Styles.Line line2)
    {
      Vector ts = new Vector(0);
      Vector Mv = new Vector(0);
      int FirstIndex;
      ts.LoadFromFile("testdata.vec");
      MtxVecTee.DrawValues(ts,line1,0.0,1.0); // draw original time series
      StatTimeSerAnalysis.MovingAverage(ts,12,Mv,out FirstIndex,true);
      MtxVecTee.DrawValues(Mv,line2,FirstIndex,1.0); // draw MA over original time series
    }
  }