ewmCov(X, [com], [span], [halfLife], [alpha], [minPeriods=0], [adjust=true], [ignoreNA=false], [other], [bias=false])
Calculate exponentially weighted moving covariance of X and other.
Exactly one of the parameters com, span, halfLife and alpha must be specified.
X is a numeric vector.
com is a nonnegative floating number and specifies decay in terms of center of mass. alpha=1/(1+com) where alpha is the decay factor.
span is a positive floating number larger than 1 and specifies decay in terms of span. alpha=2/(span+1).
halfLife is a positive floating number and specifies decay in terms of half-life. alpha=1-exp(log(0.5)/halfLife).
alpha is a floating number between 0 and 1 and directly specifies decay.
minPeriods is an integer indicating the minimum number of observations in window required to have a value (otherwise result is NULL). The default value is 0.
adjust is a Boolean value. The default value is true.
If adjust=true, the weights are (1-alpha)^(n-1), (1-alpha)^(n-2), …, 1-alpha, 1 divided by their sum.
If adjust=false, the weights are (1-alpha)^(n-1), (1-alpha)^(n-2)*alpha, (1-alpha)^(n-3)*alpha^2,…, (1-alpha)*alpha, alpha.
ignoreNA is a Boolean value indicating whether to ignore missing values. The defaut value is false.
other is a numeric vector of the same length as X.
bias is a Boolean value indicating whether the result is biased. The default value is false, meaning the bias is corrected.
$ a=[0,1,2,int(),4] $ b=[2,4,3,6,5] $ ewmCov(X=a,other=b,com=0.5); [,1,-0.038462,-0.038462,2.112637] $ ewmCov(X=a,other=b,com=0.5,ignoreNA=true); [,1,-0.038462,-0.038462,1.969231]