(This version: 12/31/2017)

The MATLAB program LRCOV.M computes confidence intervals for long-run covariability parameters using the methods discussed in:

Long-Run Covariability
Ulrich Mueller and Mark Watson
December 2017

To use the program you should look at and them execute the program:

example_lrcov.m

which reads in a bivariate dataset (the GDP-Consumption or Interest rates data sets used as running examples in the paper Mueller-Watson paper), calls LRCOV.M, and then prints out results.

You can modify example_lrcov.m to read in your data for analysis.


A few notes:

(1) The directory lrcov_parms_dir contains matlab files that are necessary for LRCOV.  These are the various "Sigma" and "Omega" covariance matrices, the values of the (A,B,c,d) parameters, the approximate least favorable distribution weights, and so forth. The location for this directory is an input to LRCOV and is given as "parmdir" near the top of example_lrcov.m. In the distribution files, the files for q=2 through q=12 are in this directory.  You can also download additional files for q=13 through q=26.  These files are large (particularly for large values of q), so we suggest that you download them only as necessary. 

(2) The program example_lrcov.m prints the output for the confidence sets (and Bayes sets), but doesn't print the long-run projection coefficients (cosine transforms) or the long-run projections (both shown in Figure 1 of the paper for the yc_example dataset). However, these are computed in LRCOV.M and you can find them in the array "misc" that is returned from LRCOV.  (See the internal documentation in LRCOV for details.) 

Addendum (9/11/2018): The 12/31/2017 versions of the program did not impose symmetry in the correlation calculations; that is, results using (x,y) were not numerically equal to results using (y,x). These updated programs impose this symmetry. (We thank Kurt Lunsford and Ken West for alerting us to the lack of symmetry in our original analysis.)