What are correlation coefficients
corrcoef for financial time series objects is based on the MATLAB ® corrcoef function. See corrcoef in the MATLAB documentation.
r=corrcoef(X) calculates a matrix r of correlation coefficients for an array X. in which each row is an observation and each column is a variable.
r=corrcoef(X,Y). where X and Y are column vectors, is the same as r=corrcoef([X Y]). corrcoef converts X and Y to column vectors if they are not; that is, r = corrcoef(X,Y) is equivalent to r=corrcoef([X(:) Y(:)]) in that case.
If c is the covariance matrix, c= cov(X). then corrcoef(X) is the matrix whose ( i,j ) 'th element is c i,j / sqrt ( c i,i * c ( j,j )).
[r,p]=corrcoef(. ) also returns p. a matrix of p -values for testing the hypothesis of no correlation. Each p -value is the probability of getting a correlation as large as the observed value by random chance, when the true correlation is zero. If p ( i,j ) is less than 0.05, then the correlation r ( i,j ) is significant.
[r,p,rlo,rup]=corrcoef(. ) also returns matrices rlo and rup. of the same size as r. containing lower and upper bounds for a 95% confidence interval for each coefficient.
[. ]=corrcoef(. 'PARAM1',VAL1,'PARAM2',VAL2. ) specifies additional parameters and their values. Valid parameters are:
'alpha' — A number between 0 and 1 to specify a confidence level of 100*(1-ALPHA)%. Default is 0.05 for 95% confidence intervals.
'rows' — Either 'all' (default) to use all rows, 'complete' to use rows with no NaN values, or 'pairwise' to compute r ( i,j ) using rows with no NaN values in column i or j .
The p -value is computed by transforming the correlation to create a t-statistic having N – 2 degrees of freedom, where N is the number of rows of X. The confidence bounds are based on an asymptotic normal distribution of 0.5*log((1 + r)/(1 – r)), with an approximate variance equal to 1/(N – 3). These bounds are accurate for large samples when X has a multivariate normal distribution. The 'pairwise' option can produce an r matrix that is not positive definite.Source: www.mathworks.com