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

{ CIfols, FFols, CIfdols, FFdols, cv, Fols, Fdols } = coint_tsongetal(y, x, model[, bwl, kmax, varm, q])

Parameters:

• y (Nx1 matrix) – Dependent variable.

• x (NxK matrix) – Independent variable.

• model (Scalar) –

  Model to be implemented.

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

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

• kmax (Scalar) – Optional, maximum number of Fourier frequency. Default = 5.

• varm (Scalar) –

  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

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

Returns:

• CIols (Scalar) – CI test based on OLS estimation.

• FFols (Scalar) – Optimal Fourier frequency based on OLS estimation.

• CIDols (Scalar) – CI test based on DOLS estimation

• FFdols (Scalar) – Optimal Fourier frequency based on DOLS estimation.

• Fols (Scalar) – F-stat for Fourier terms significance based on OLS.

• Fdols (Scalar) – F-stat for Fourier terms significance based on DOLS.

• cv (Scalar) – 1%, 5%, 10% critical values for the model chosen.

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