cdTest
======

Purpose
-------
Runs cross-sectional dependence, CD, tests for panel data. The test
statistics constructed from the mean t-statistic has an asymptotic
standardized normal distribution and tests the null hypothesis that
all series are *I(1)* against the alternative that all series
are *I(0)*

Format
------
.. function:: cd = cdTest(res, model, grp_vector)

   :param res: residuals from panel data regression.
   :type res: Nx1 matrix

   :param model: indicates which test to run\: 1 for Pesaran's test, 2 for Friedman's test, 3 for Frees' test. Note\: the only model appropriate for unbalanced data is model 1. This model will run by default if unbalanced panel data is detected.
   :type model: scalar

   :param grp: group indicator variable.
   :type grp: Nx1 matrix

   :return cd: test statistic
   :rtype cd: matrix

Example
-------
::

   new;
   cls;
   library tsmt;

   /*************************************
   //Generate data
   **************************************/
   // Set panel size parameters
   N = 48;
   T = 17;

   // Simulate balanced group vector
   grp = vec(reshape(seqa(1, 1, N), 17, 48));

   // Simulate random stacked residuals
   rndseed 90782;
   y = rndn(T*N, 1);

   /*************************************
   /Run tests
   **************************************/
   // Run pesaran test [model = 1]
   z1 = cdTest(y, 1, grp);

   // Run Friedman test [model = 2]
   z2 = cdTest(y, 2, grp);

   // Run Frees test [model = 3]
   z3 = cdTest(y, 3, grp);

The results printed to screen are

::

 *** Pesaran's Test of Cross-Sectional Independence, Balanced Panels  ***

 Pesaran's CD Test Statistic =       0.77992932
 p_value =       0.21771624

 *** Friedman's Test of Cross-Sectional Independence, Balanced Panels  ***

 Friedman's Test Statistic =      21.77124183
 p_value =       0.15073260


 *** Frees' Test of Cross Sectional Independence for Balanced Panels  ***

 The Frees' Test Statistics =
  FRE =       0.08560793 	 Ave. of R^2 =       0.06428350

 Critical Values from Frees' Q-Distribution
 Alpha level =			    0.1	      0.05	 0.01
 Critical Values or Quantiles =   0.15205    0.19963    0.29284


 *** An Alternative Decision Rule ***
 The Null Hypothesis is Rejected when Ave. of R^2 > inv(T-1) + Qq/N	 =   0.06860
 Notes:
 Qq = quantile of the Q-Distribution
 N = number of groups

Library
-------
tsmt

Source
------
cdtestbalanced.src

.. seealso:: Functions :func:`cdTestUnbalanced`