coint_tsongetal
==============================================

Purpose
----------------

Computes the test of the null of cointegration allowing for structural breaks of unknown form in deterministic trend by using the Fourier form.

Format
----------------
.. function:: { CIfols, FFols, CIfdols, FFdols, cv, Fols, Fdols } = coint_tsongetal(y, x, model[, bwl, kmax, varm, q])
    :noindexentry:

    :param y: Dependent variable.
    :type y: Nx1 matrix

    :param x: Independent variable.
    :type x: NxK matrix

    :param model: Model to be implemented.

        =========== ========================================
        1           Level shift model with Fourier
        2           Level & trend shift model with Fourier
        =========== ========================================

    :type model: Scalar

    :param bwl: Optional, bandwidth length for long-run variance computation. Default = round(4 * (T/100)^(2/9)).
    :type bwl:  Scalar

    :param kmax: Optional, maximum number of Fourier frequency. Default = 5.
    :type kmax: Scalar

    :param varm: Optional, long-run consistent variance estimation method. Default = 1.

        =========== ======================================================
        1           iid.
        2           Bartlett.
        3           Quadratic Spectral (QS).
        4           SPC with Bartlett (Sul, Phillips & Choi, 2005)
        5           SPC with QS
        6           Kurozumi with Bartlett
        7           Kurozumi with QS
        =========== ======================================================

    :type varm: Scalar

    :param q: Optional, number of leads and lags for DOLS estimation. Default = int(4 * (t/100)^(2/9)).
    :type q: Scalar

    :return CIols: CI test based on OLS estimation.
    :rtype CIols: Scalar

    :return FFols: Optimal Fourier frequency based on OLS estimation.
    :rtype FFols: Scalar

    :return CIDols: CI test based on DOLS estimation
    :rtype CIDols: Scalar

    :return FFdols: Optimal Fourier frequency based on DOLS estimation.
    :rtype FFdols: Scalar

    :return Fols: F-stat for Fourier terms significance based on OLS.
    :rtype Fols: Scalar

    :return Fdols: F-stat for Fourier terms significance based on DOLS.
    :rtype Fdols: Scalar

    :return cv: 1%, 5%, 10% critical values for the model chosen.
    :rtype cv: Scalar


Examples
--------

::

  library tspdlib;

  // Load dataset
  data = loadd(getGAUSSHome() $+ "pkgs/tspdlib/examples/ts_coint.csv",
                            ". + date($Date, '%b-%y')");

  // Define y and x matrix
  y = data[., 1];
  x = data[., 2:cols(data)];

  // Level shift
  model = 1;

  // Call test
  { CIfols, FFols, CIfdols, FFdols, cv_fourier, Fols, Fdols } = coint_tsongetal(y, x, model);

Source
------

coint_tsongetal.src