Name

ms_mean — Markov Switching mean-variance model

CALLING SEQUENCE

r=ms_mean(endo,MS_M,MS_M_V,MS_var_opt,arg1,…,argn)

PARAMETERS

Input

• endo =

    - (T x K) string matrix of endogenous variables

• or:

    - a list containing all the endogenous variables in an_y of the following form:

  * a time series

      * a real matrix

      * a string representing such objects

      * the string 'const' (for the constant variable)

• MS_M = a scalar equal the # of states

• MS_V = a scalar:

     - 1 if the variance of the residuals is the same for all states

   - MS_M if the variance of the residuals differs among the states

• MS_var_opt = a scalar:

  - 1 if the variance of residuals is heteroskedastic

  - 2 if the variance of residuals is homoskedastic

  - 3 if the variance of residuals is unconstrained

• arg1,… argn = optional arguments which can be:

  - 'datation=xx' where xx is the name of a series used as an a priori datation (default: no a priori datation)

  - 'transf=xx' where xx is either 'dem' if the user wants all series to be demeaned or 'stu' if the user wants all series to be studentized (default: no transformation)

  - 'gdelta=xx' where xx is a number used to calculate the numerical derivative of the log-likelihood (default 1e-4)

  - 'hdelta=xx' where xx is a number used to calculate the numerical hessian (default 1e-5)

  - 'prt=xx' where xx='nothing', 'final', 'all' or ['initial';'final'] if the user wants to print nothing, only the final results or the final and the initial results

  - 'noprint' if the user wants to print nothing (equivalent to 'prt=nothing')

 - the string 'dropna' if the user wants to remove the NA values from the data

Output

• r = a results tlist with:

  * r('meth') = 'ms mean'

  * r('typmod') = 1

  * r('y') = a (N x n_y) matrix of original endogenous variables

  * r('x') = the (N x n_x) matrix of exogenous switching regressors = ones(T,n_x)

  * r('z') = the [] matrix of exogenous non switching regressors

  * r('ymat') = the (N x M) matrix of -transformed- endogenous variables

  * r('xmat') = the (N x n_x) matrix of -transformed- exogenous switching regressors

  * r('zmat') = the [] matrix of -transformed- non switching regressors

  * r('switching V') = a scalar:

     . 1 if the variance does not switch with the states

     . M if the variance switches with the states

  * r('var_opt') = a scalar:

      . 1 if the variance of residuals is heteroskedastic

      . 2 if the variance of residuals is homoskedastic

      . 3 if the variance of residuals is unconstrained

  * r('nobs') = the # if observations

  * r('nendo') = the # of endogenous variables

  * r('nb_states') = the # of states

  * r('coeff') = the (np x 1) vector of parameters

  * r('llike') = the log-likekihood

  * r('grad') = the gradient at the solution

  * r('yhat') = the adjusted y

  * r('resid') = the residuals of the regression

  * r('dll') = the degrees of freedom

  * r('prob_st') = the (M x 1) vector of egodic state probabilities

  * r('ptrans') = the (M x M) matrix of transition probabilities

  * r('sigma') = the (M*M_V x M) variance-covariance matrix of the residuals

  * r('beta_id') = the (1 x K*M) vector of switching parameters

  * r('beta_co') = the [] vector of non switching parameters

  * r('inv_sigma') = the (K x K) inverse of the variance matrix

  * r('det_inv_sigma') = the determinant of the inverse of the variance matrix

  * r('smoothed probs') = the (T x M) vector of smoothed probabilities

  * r('stderr') = the (np x 1) vector of coefficients standard errors

  * r('tstat') = the (np x 1) vector of associated t-stats

  * r('pvalue') = the (np x 1) vector of associated p-values

  * r('covbeta') = the (np x np) variance-covariance matrix of the parameters

  * r('corbeta') = the (np x np) correlation matrix of the parameters

  * r('ptrans_tstat') = the (M x 1) vector of t-stats for the transition probabilities

  * r('beta_id_tstat') = the (1 x K*M) vector of t-stats for switching parameters

  * r('beta_co_tstat') = the [] vector of t-stats for non switching parameters

  * r('sigma_tstat') = the (M*M_V x M) matrix of t-stats for the variance-covariance matrix of the residuals

  * r('ptrans_pvalue') = the (M x M) matrix of t-stats for transition probabilities

  * r('beta_id_pvalue') = the (1 x n_x*K*M) vector of t-stats for switching parameters

  * r('beta_co_pvalue') = the [] vector of t-stats for non switching parameters

  * r('sigma_pvalue') = the (M*M_V x M) matrix of t-stats for the variance-covariance matrix of the residuals

  * r('namey') = the (n_y x 1) vector of names of the endogenous variables

  * r('namex_id') = the name of the swicthing exogenous variables = 'cte'

  * r('namex_co') = the [] vector of names of the non swicthing exogenous variables

  * r('apriori') = a scalar

     . 0 if there is no a priori datation

     . 1 if there is an a priori datation

  * r('prests') = a boolean indicating whether there is are ts in the regression

  * r('datation') = the a priori datation if any

  * r('namedat') = the name of the series used for an a priori datation if any

  * r('dropna') = boolean indicating if NAs have been dropped

  * r('bounds') = if there is a timeseries in the forecast, the bounds of the regression

  * r('nonna') = vector indicating position of non-NAs

DESCRIPTION

Estimates a Markvov Switching (MS) mean-variance model by the maximum likelihood method.

EXAMPLE

load('C:\SCI\macros\grocer\db\anas.dat')
bounds('1984m2','2003m1')
nb_states=3
switch_var=1
var_opt=1
r=ms_mean(['delts(log(construc))';'delts(log(ipi))';'delts(log(helpwanted))';'delts(log(revu))'],nb_states,switch_var,var_opt,'transf=stud','datation=datation_bb')
 
This example is taken from function ms_mean_d. The endogenous variables are 'delts(log(construc))', 'delts(log(ipi))', 'delts(log(helpwanted))' and 'delts(log(revu))'. There are 3 states, the variances are not switching (switch_var=1) and the var-cov matrix is heteroskedastic (var_opt=1). Two optional arguments have been given: 'transf= stud' which means that variables are studentuzed before estimation and 'datation=datation_bb' which means that the an priori datation (provided by Benoit Bellone) is given.

               

AUTHOR

Benoit Bellone/Eric Dubois 2006