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:
    t title is to be printed.
    l lines are to bracket the title.
    d a date and time is to be printed.
    v version number of program is to be printed.
    f file name being analyzed is to be printed.

    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