Accord.NET Framework

## MeasuresExponentialWeightedCovariance Method (Double, Double, Boolean) |

Calculates the exponentially weighted covariance matrix.

Syntax

public static double[,] ExponentialWeightedCovariance( this double[][] matrix, double alpha = 0, bool unbiased = false )

- 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.

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

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);

See Also