switchFit

Purpose

Estimates the parameters of the Markov switching regression model.

Format

swo = switchFit(y, [x, ]num_states, num_lags, swc)
swo = switchFit(dataset, formula, num_states, num_lags[, swc])
Parameters
  • y (Nx1 vector) – data.

  • x (Nxk vector) – independent data.

  • dataset (string) – name of data set or null string.

  • formula (string) – formula string of the model. E.g. "y ~ X1 + X2" ‘y’ is the name of dependent variable, ‘X1’ and ‘X2’ are names of independent variables; E.g. "y ~ ." , ‘.’ means including all variables except dependent variable ‘y’;

  • num_states (scalar) – number of states.

  • num_lags (scalar) – number of lagged values of the dependent variable.

  • swc (struct) –

    An instance of a switchFitControl structure. The following members of swc are referenced within this routine:

    swc.constVariance

    scalar, if nonzero, error variances are constant across states, otherwise if zero, not.

    swc.relevantStates

    scalar, if nonzero, lagged states are relevant for time series variable, otherwise if zero, only the current state is relevant.

    swc.aBayes

    scalar, if nonzero, “a” parameter controlling the Bayesian prior as described in James D. Hamilton, 1991, “A quasi-Bayesian approach to estimating parameters for mixtures of Normal distributions,” Journal of Business and Economic Statistics, 9:27-39.

    swc.bBayes

    scalar, if nonzero, “b” parameter controlling the Bayesian prior.

    swc.cBayes

    scalar, if nonzero, “c” parameter controlling the Bayesian prior.

    swc.userTransEqp

    scalar, pointer to user-provided function for setting equality constraints on transition probability matrix.

    swc.start

    instance of a PV structure containing start values.

    beta0

    1, num_states by 1 vector, constants.

    beta

    2, num_states by K, coefficients on K independent variables if any.

    phi

    3, num_lags by 1 vector, autoregression coefficients.

    sigma

    4, scalar or num_states by 1 vector, error variances. If swc.constVarianceis zero, it is a scalar, otherwise it is a vector.

    p

    5, num_states by num_states matrix, transition probabilities.

    For example:

    swc.start = pvPacki(swc.start, 3|3, "beta0", 1);
    swc.start = pvPacki(swc.start, .1|.01, "Phi", 3);
    swc.start = pvPacki(swc.start, 1, "Sigma", 4);
    swc.start = pvPacki(swc.start, (.8~.1)|(.2~.9), "P", 5);
    

    swc.control

    instance of an sqpsolvemtControl structure.

    swc.ctl.covType

    scalar, if 2, QML standard errors are computed, if 0, none; otherwise Wald-type.

    swc.ctl.printIters

    scalar, iteration information printed every swc.ctl.printIters-th iteration.

    See documentation for sqpsolvemtControl for further information regarding members of this structure.

    swc.header

    string, specifies the format for the output header. swc.header can contain zero or more of the following characters:

    Example:

    swc.header = "tld";
    

    If swc.header = "", no header is printed. Default = "tldvf".

    swc.output

    scalar, if nonzero, results are printed to screen. Default = 1 .

Returns

out (struct) –

Instance of a switchmtOut structure containing the following members:

out.par

instance of a PV structure containing the estimates:

beta0

1, num_states by 1 vector, constants.

beta

2, num_states by K, coefficients on K independent variables if any.

phi

3, num_lags by 1 vector, autoregression coefficients.

sigma

4, scalar or num_states by 1 vector, error variances. If swc. constVarianceis zero, it is a scalar, otherwise it is a vector.

p

5, num_states by num_states matrix, transition probabilities.

For example:

consts = pvUnpack(out.par, "beta0");

or

consts = pvUnpack(out.par, 1);

out.covPar

MxM matrix, covariance matrix of parameters.

out.logl

scalar, log-likelihood at maximum.

out.retcode

return code:

0

normal convergence.

1

forced exit.

2

maximum number of iterations exceeded.

3

function calculation failed.

4

gradient calculation failed.

5

Hessian calculation failed.

6

line search failed.

7

error with constraints.

8

function complex.

out.lagr

instance of sqpSolvemtLagrange structure

out.lagr.lineq

Mx1 vector, Lagrangeans of linear equality constraints.

out.lagr.nlineq

Nx1 vector, Lagrangeans of nonlinear equality constraints.

out.lagr.linineq

Px1 vector, Lagrangeans of linear inequality constraints.

out.lagr.nlinineq

Qx1 vector, Lagrangeans of nonlinear inequality constraints.

out.lagr.bounds

Kx2 matrix, Lagrangeans of bounds.

Whenever a constraint is active, its associated Lagrangean will be nonzero. For any constraint that is inactive throughout the iterations as well as at convergence, the corresponding Lagrangean matrix will be set to a scalar missing value.

Examples

This example reproduces the results for the French exchange rate in “Long Swings in the Exchange Rate: Are They in the Data and Do Markets Know It?” by Charles Engel and James D. Hamilton, American Economic Review, Sept. 1990.

y0 = loadd( getGAUSSHome() $+ "pkgs/tsmt/examples/exdata.dat");

y = y0[.,1];

//Estimation parameters

struct switchFitControl c0;
c0 = switchFitControlCreate();

c0.constVariance = 0;
c0.output = 1;
c0.aBayes = .2;
c0.bBayes = 1;
c0.cBayes = .1;

/*
** The log-likelihood is somewhat flat and thus
** the problem requires a good starting point.
*/

b0 = { 3.3, -2.7 };
sig = { 10, 37 };
p = { .8 .2, .2 .8 };

struct PV st0;
st0 = pvPacki(pvCreate(), b0, "beta0", 1);
st0 = pvPacki(st0, sig, "sigma", 4);
st0 = pvPacki(st0, p, "p", 5);

c0.start = st0;

struct switchmtOut out0;
out0 = switchFit(y, 2, 0, c0);

Library

tsmt

Source

switchmt.src