Markvov Switching regression model
res=ms_reg(endo,exo_com,exo_idio,MS_M,MS_M_V,MS_var_opt,arg1,...,argn)
* endo =
- either: (T x K) string matrix of endogenous variables
- or: a list containing all the endogenous variables in any of the following form:
. a time series
. a real matrix
. a string representing such objects
. the string 'const' (for the constant variable)
* exo_com =
- (T x K) string matrix of non switching exogenous variables
- or: a list containing all the non switching exogenous variables in any of the following form:
. a time series
. a real matrix
. a string representing such objects
. the string 'const' (for the constant variable)
. or: a list starting with the keyword 'diff' (as different) and containing thereafter as many elements as the number of endogenous variables; each element collects the names of the exogenous variables for the corresponding endogenous variable or their values
* exo_idio =
- (T x K) string matrix of switching exogenous variables
- or: a list containing all the switching exogenous variables in any of the following form:
. a time series
. a real matrix
. a string representing such objects
. the string 'const' (for the constant variable)
. or: a list starting with the keyword 'diff' (as different) and containing thereafter as many elements as the number of endogenous variables; each element collects the names of the exogenous variables for the corresponding endogenous variable or their values
* 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
- 'init_beta_id = xxx' where xxx is a vector of starting values for the switching exogenous variables
- 'init_beta_co = xxx' where xxx is a vector of starting values for the non switching exogenous variables
- 'init_prob' = xxx' where xxx is a matrix of starting values for the transition probabilities
- 'init_var' = xxx' where xxx is a matrix of starting values for the variances
- 'notstat' if the user does not want to calculate the Student statistics of the parameters
- 'optfunc=optim' if the user wants to use the optim optimisation function (default: optimg)
- 'opt_nelmead=crit,nitermax' with crit the value of the convergence criterion in the Nelder-Meade optimisation function and nitermax the maximum number of iterations (default = 'opt_nelmead=2*%eps,1000')
- 'opt_optim=opts' where opts are options for optim that can be entered after the starting value of the parameters (default = 'opt_optim=,''ar'',1e6,1e6'')
- 'opt_convg=val' where val is the threshold on gradient norm (default = 'opt_convg=1e-5')
* res = a results tlist with:
- res('meth') = 'ms regression'
- res('typmod') = model numbered type
- res('y') = a (T x K) matrix of original endogenous variables
- res('ymat') = (T*K x 1) matrix of stacked endogenous variables
- res('xmat') = (T*K x sum(n_x)) matrix of switching exogenous variables
- res('zmat') = (T*K x sum(n_z)) matrix of non switching exogenous variables
- res('switching V') = a scalar:
. 1 if the variance does not switch with the states
. M if the variance switches with the states
- res('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
- res('nobs') = the # if observations
- res('nendo') = the # of endogenous variables
- res('nb_states') = the # of states
- res('coeff') = the (np x 1) vector of parameters
- res('llike') = the log-likekihood
- res('grad') = the gradient at the solution
- res('yhat') = the adjusted y
- res('filtered resid') = the filtered residuals of the regression
- res('dll') = the degrees of freedom
- res('prob_st') = the (M x 1) vector of egodic state probabilities
- res('ptrans') = the (M x M) matrix of transition probabilities
- res('sigma') = the (M*M_V x M) variance-covariance matrix of the residuals
- res('beta_id') = the (1 x sum(n_x)*M) vector of switching parameters
- res('beta_co') = the (1 x sum(n_z)) vector of non switching parameters
- res('inv_sigma') = the (K x K) inverse of the variance matrix
- res('det_inv_sigma') = the determinant of the inverse of the variance matrix
- res('filtered probs') = the (T x M) vector of filtered probabilities
- res('smoothed probs') = the (T x M) vector of smoothed probabilities
- res('n_x') = the (K x 1) vector of the numbers of switching exogenous variables for each endogenous variable
- res('n_z') = the (K x 1) vector of the numbers of non switching exogenous variables for each endogenous variable
- res('stderr') = the (np x 1) vector of coefficients standard errors
- res('hes. delta') = the numerical increment for the calculation of the hessian matrix
- res('tstat') = the (np x 1) vector of associated t-stats
- res('pvalue') = the (np x 1) vector of associated p-values
- res('covbeta') = the (np x np) variance-covariance matrix of the parameters
- res('corbeta') = the (np x np) correlation matrix of the parameters
- res('ptrans_tstat') = the (M x 1) vector of t-stats for the transition probabilities
- res('beta_id_tstat') = the (1 x n_x*K*M) vector of t-stats for switching parameters
- res('beta_co_tstat') = the (1 x n_z*K) vector of t-stats for non switching parameters
- res('sigma_tstat') = the (M*M_V x M) matrix of t-stats for the variance-covariance matrix of the residuals
- res('ptrans_pvalue') = the (M x M) matrix of t-stats for transition probabilities
- res('beta_id_pvalue') = the (1 x n_x*K*M) vector of t-stats for switching parameters
- res('beta_co_pvalue') = the (1 x n_z*K) vector of t-stats for non switching parameters
- res('sigma_pvalue') = the (M*M_V x M) matrix of t-stats for the variance-covariance matrix of the residuals
- res('smoothed resid') = the smoothed residuals of the regression
- res('namey') = the (ny x 1) vector of names of the endogenous variables
- res('namex_id') = the (n_x x 1) vector of names of the swicthing exogenous variables
- res('namex_co') = the (n_x x 1) vector of names of the non swicthing exogenous variables
- res('apriori') = a scalar
. 0 if there is no a priori datation
. 1 if there is an a priori datation
- res('prests') = a boolean indicating whether there are ts in the regression
- res('prests') = a boolean indicating whether there are ts in the regression
- res('datation') = the a priori datation if any
- res('namedat') = the name of the series used for an a priori datation if any
- res('dropna') = boolean indicating if NAs have been dropped
- res('bounds') = if there is a timeseries in the forecast, the bounds of the regression
- res('nonna') = vector indicating position of non-NAs
load(GROCERDIR+'\data\us_revu.dat') bounds('1967m4','2004m2') nb_states=2 switch_var=2 var_opt=3 r=ms_reg('100*(log(us_revu)-lagts(2,log(us_revu)))',['100*(lagts(1,log(us_revu))-lagts(3,log(us_revu)))';... '100*(lagts(2,log(us_revu))-lagts(4,log(us_revu)))';'100*(lagts(3,log(us_revu))-lagts(5,log(us_revu)))'],'const',nb_states,switch_var,var_opt,'transf=stud',... 'prt=initial;final') // This example is taken from function ms_reg_d. // The endogenous variable is '100*(log(us_revu)-lagts(2,log(us_revu)))'. // The non switching exogenous variables are '100*(lagts(1,log(us_revu))-lagts(3,log(us_revu)))', // '100*(lagts(2,log(us_revu))-lagts(4,log(us_revu)))' and '100*(lagts(3,log(us_revu))-lagts(5,log(us_revu)))'. // The switching exogenous variables is here the constant. There are 2 states, the variances are switching (switch_var=2) and the var-cov matrix is unrestricted(var_opt=3). Two optional arguments have been given: 'transf= stud' which means that variables are studentuzed before estimation and 'prt=initial;final' which means that sarting values and final results are both printed. load(GROCERDIR+'\data\anas.dat') r=ms_reg(['delts(log(construc))';'delts(log(ipi))';'delts(log(helpwanted))';'delts(log(revu))'],... list('diff','lagts(delts(log(construc)))','lagts(delts(log(ipi)))','lagts(delts(log(helpwanted)))','lagts(delts(log(revu)))'),'const',2,2,1) // This example takes the 4 variables from the 'anas' database, // and estimates a MS model where all variables, once differentiated, follow an AR(1)+constant. // The non switching variables are the autoregressive parts of the AR. // Since they are obviously different for each endogenous variable, // 2nd argument is a list with first element the keyword 'diff', // For each regression, the constant is supposed to switch. // Since it is the same variable for each regression, 3rd argument in the function is simply 'const'. // The # of states is set to 2 (4th argument), the variances are supposed to swicth // (5th is set to 2, the number of states), the variance matrix is heteroskedstik. load(GROCERDIR+'\data\anas.dat') r=ms_reg(['delts(log(construc))';'delts(log(ipi))';'delts(log(helpwanted))';'delts(log(revu))'],... list('diff','lagts(delts(log(construc)))','lagts(delts(log(ipi)))',[],'lagts(delts(log(revu)))'),list('diff','const','const',['const';'lagts(delts(log(helpwanted)))'],'const'),2,2,1) // This example is the same as second one, except for the autoregressive coefficient // for variable 'delts(log(helpwanted))' which is now supposed to switch from one state to another: // this imposes to define the third argument as a list, starting with the keyword 'diff' // and with the exogenous variables for each regression entered as 2nd to 5th element of the list. | ![]() | ![]() |