coint_tsongetal

Purpose

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

new;
cls;
library tspdlib;

// Load dataset
data = loadd(getGAUSSHome() $+ "pkgs/tspdlib/examples/ts_coint.csv",
                          "Y1 + Y2 + Y3 + Y4 + date($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