﻿ Measures.ExponentialWeightedCovariance Method (Double[][], Double, Boolean)

Calculates the exponentially weighted covariance matrix.

Namespace:  Accord.Statistics
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0
Syntax
```public static double[,] ExponentialWeightedCovariance(
this double[][] matrix,
double alpha = 0,
bool unbiased = false
)```

#### Parameters

matrix
Type: SystemDouble
A matrix of observations whose EW covariance matrix will be calculated. It is assumed that the matrix is ordered with the most recent observations at the bottom of the matrix.
alpha (Optional)
Type: SystemDouble
The weighting to be applied to the calculation. A higher alpha discounts older observations faster. Alpha must be between 0 and 1 (inclusive).
unbiased (Optional)
Type: SystemBoolean
Use a standard estimation bias correction.

#### Return Value

Type: Double
Returns a vector containing the exponentially weighted average of the columns of the given matrix.

#### Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type . When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).
Examples

The following example shows how to compute the EW covariance matrix.

```/*
Suppose we have a time series of (possibly correlated) observations. Our
sample has 17 observations in 2 variables (x and y). We wish to compute
the covariance matrix for our series but would like to provide a heavier
weighting to the more recent observations. First, arrange the observations
in rows with the oldest data at the top and the newest data at the bottom. */
double[,] rawData =
{
{ 2, 2, 1, 3, 5, 6, 4, 2, 7, 8, 9, 2, 3, 4, 5, 6, 7 },
{ 1, 2, 5, 3, 8, 6, 4, 4, 3, 8, 9, 0, 9, 9, 1, 9, 2 }
};

// Transpose our raw data to get it into the required format.
double[][] timeSeries = rawData.ToJagged(transpose: true);

// The window size determines how many observations to include in the
// calculation. If no window is specified, the entire dataset is used.
int window = 15;

// We set alpha to 20% meaning each previous observation's contribution
// carries 20% less weight (relative to its immediate successor).
double alpha = 0.2;

// Now we calculate the covariance matrix. The result should be:
//
//  { 3.80, 0.55 }
//  { 0.55, 13.0 }
//
double[,] ewmCov = timeSeries.ExponentialWeightedCovariance(window, alpha);```