Cross variance

Overview

The Cross variance analysis allows you to calculate the covariance matrix, the correlation matrix and a matrix displaying the slope of the regression line for a number of time series. This is a useful analysis if you want to quickly asses the pairwise behavior of several time series.

Settings

Estimation sample range

Specify the limits of the sample range for the calculation. If left blank, the calculation will be performed on the entire series.

Type of calculation

Covariance

This option will output the covariance matrix. The values on the principal diagonal of the matrix is the variance of one series. All off-diagonal elements represent the covariance between two series.

Correlation

Choose this option to get the correlation matrix.

Regression slope

Choosing this option, Macrobond will perform simple linear regression on all series included in the analysis. The rows in the matrix are the dependent time series and the columns represents the explanatory ones. The values in the matrix are the slope of the regression line or β in the relationship:

y=α+βx+ϵ

where y is the dependent time series, x is the explanatory series and the constants are found by minimizing the squared deviations (OLS)

Use only points in time with values in all series

When selected, the matrix will be calculated by only using points where values are present in all included series.

Example

Correlation and Regression slope Matrix

In this example we added the time series for the closing price of many large listed UK companies. Then, the Cross variance analysis is used to generate the correlation matrix and the regression slope for all pairs of companies.