Financial Toolbox™

nancov - Covariance ignoring NaNs

Syntax

c = nancov(X)
c = nancov(..., 'pairwise')

Arguments

Description

nancov for financial times series objects is based on the Statistics Toolbox™ function nancov. See nancov in the Statistics Toolbox documentation.

c = nancov(X), if X is a financial time series object with one series and returns the sample variance of the values in X, treating NaNs as missing values. For a financial time series object containing more than one series, where each row is an observation and each series a variable, nancov(X) is the covariance matrix computing using rows of X that do not contain any NaN values. nancov(X,Y), where X and Y are financial time series objects with the same number of elements, is equivalent to nancov([X(:) Y(:)]).

nancov(X) or nancov(X,Y) normalizes by (N-1) if N >1, where N is the number of observations after removing missing values. This makes nancov the best unbiased estimate of the covariance matrix if the observations are from a normal distribution. For N = 1, cov normalizes by N.

nancov(X,1) or nancov(X,Y,1) normalizes by N and produces the second moment matrix of the observations about their mean. nancov(X,Y,0) is the same as nancov(X,Y), and nancov(X,0) is the same as nancov(X).

c = nancov(..., 'pairwise') computes c(i,j) using rows with no NaN values in columns ior j. The result may not be a positive definite matrix. c = nancov(..., 'complete') is the default, and it omits rows with any NaN values, even if they are not in column i or j. The mean is removed from each column before calculating the result.

Examples

To generate random data having nonzero covariance between column 4 and the other columns:

x = randn(30, 4);                 % uncorrelated data
x(:, 4) = sum(x, 2);              % introduce correlation
x(2, 3) = NaN;                    % introduce one missing value
f = fints((today:today+29)', x);  % create a fints object using x
c = nancov(f)                     % compute sample covariance

See Also

cov, nanvar, var

mvnrstd

nanmax