Marina Balboa, Paulo M. M. Rodrigues, Antonio Rubia, and A. M. Robert
Taylor, "Multivariate Fractional Integration Tests allowing for
Conditional Heteroskedasticity with an Application to Return
Volatility and Trading Volume", Journal of Applied Econometrics,
Vol. 36, No. 5, 2021, pp. 544-565.

All files are zipped in the file brrt-files.zip. The xlsx files are
binary. The other files are ASCII text files in DOS format.

The program Program_JAE.m shows an example of the procedure implemented
in the paper. The procedure imports the Excel data, a measure of daily
volatility and volume, and implements the LM test for fractional
integration. The necessary main steps are made by the auxiliary
function BRRTtest.

To run the program, edit lines 25 and 28, setting the input paths (the
path to the folder where the Excel file AAPL_Data.xlsx is) and output
path (the path to the folder you want to store results in). You can
change other settings, such as the specification of the deterministics
in the auxiliary regression (lines 8,9), the augmentation order (line
7) and the grid in which the the long-memory coefficients are
evaluated (lines 14-22).

The program Program_JAE.m and the data provided will replicate the
values in the first line of Table 5 in the paper corresponding to the
Log Range.  

The program will store summarising results in an Excel file named
ResultsLongMemoryTesting_AAPL.xlsx and show them on screen, such as,

  Columns 1 through 5

    {'Stock'}    {'dhat_logRangeGK'}    {'lower95CI_logRa…'}
    {'upper95CI_logRa…'}    {'dhat_logVLM'} {'AAPL' }    {[         0.6000]}
    {[           0.5200]}    {[           0.6700]}    {[     0.6500]}

  Columns 6 through 10

    {'lower95CI_logVLM'}    {'upper95CI_logVLM'}    {'lower95common'}
    {'upper95common'}    {'Correlation'}    {[          0.5600]}
    {[          0.7300]}    {[       0.5600]}    {[       0.6700]}
    {[     0.6259]}

  Columns 11 through 12

    {'K-order augment.'}    {'Observations'}
    {[               9]}    {[        3019]}

Note: augmentation based on Schwert Rule with nlags= 4*(T/100)^0.25=9.

dhat shows point estimates of d given by the d values in the grid that
minimize the LM test statistic.

Lower and upper 95 are the lower and upper bounds of the projection of
the 95% confidence ellipsoids on the axes.

Lower and upper common show the values of a common d contained in the
95% confidence ellipsoid (if not empty).

Correlation is the endogeneous correlation of estimated innovations.

Note that no data, besides the example series, are provided, as these
are proprietary data obtained from CRSP databases. The data tickers
are reported in the paper (please see Table 5).

If you use the code, please cite the paper.

If you find errors, please get in touch with us.

We cannot be held responsible for any use and mis-use of our code.