example_ms_ar_simul_and_fit_4_states.m

Autoregressive Markov Switching Model函数用于评估、仿真及预测自回归的马尔可夫转换模型。可以选择用于模型估计的分布函数。用于研究时间序列结构性变化

% Example Script for MS_AR_Simul.m and MS_AR_Fit.m (run it in the same directory - just press f5)

% This script will first simulate a 4 states MS model with some pre defined parameters
% using MS_AR_Sim.m and then fit the model with MS_AR_Fit.m.

% You can change the coefficients for your own flavor

% You'll see that fmincon() is doing a pretty good job estimating the MS
% model (cheers for it!)

addpath('m_Files');

clear; 

nr=1000;                    % Number of observations in simulation
advOpt.distrib='Normal';    % Distribution to use ('Normal' or 't' - default = 'Normal')
advOpt.std_method=1;        % Method for standard error calculation ('white' or 'newey_west' - default = 'white')

Coeff.p=[.97 .01 .01 .1; ...   % Transition matrix (this also defines the value of k)
         .01 .97 .01 .1; ...   % Each collum of it should sum to 1
         .01 .01 .97 .1; ...   % Notes that the transition matrix output for fitting may 
         .01 .01 .01 .7];      % not be exactly equal to this one since the
                               % the fit function doesn't know which states is
                               % 1 2 3 or 4, it just tries to find them and
                               % separate. This means that the pii (prob os staying at state i) can be
                               % deslocated through the collums, but it
                               % should respect the structure at Coeff.p


Coeff.C(1,1)= .1;   % Setting up the mean constant at State 1
Coeff.C(1,2)=-.2;   % Setting up the mean constant at State 2
Coeff.C(1,3)=0.05;  % Setting up the mean constant at State 3
Coeff.C(1,4)=-.4;   % Setting up the mean constant at State 4

Coeff.AR(:,1)=[ .5   .1  .2];   % Setting up the AR param at State 1 (you can increase/decrease it as wanted)
Coeff.AR(:,2)=[-.15 -.1  .1];   % Setting up the AR param at State 2 (you can increase/decrease it as wanted)   
Coeff.AR(:,3)=[ .15 -.2 -.1];   % Setting up the AR param at State 3 (you can increase/decrease it as wanted)   
Coeff.AR(:,4)=[-.5   .1 -.2];   % Setting up the AR param at State 4 (you can increase/decrease it as wanted)   

Coeff.Std(1,1)=.2;  % Setting up the standard deviavion at State 1
Coeff.Std(1,2)=.1;  % Setting up the standard deviavion at State 2
Coeff.Std(1,3)=.05; % Setting up the standard deviavion at State 3
Coeff.Std(1,4)=.05; % Setting up the standard deviavion at State 4

k=length(Coeff.p);      % Number of states simulated (according to Coeff.p)
ar=size(Coeff.AR,1);    % Number of lags in autoregressive component

[Simul_Out]=MS_AR_Sim(nr,Coeff,k,advOpt.distrib); % Simulating the series

x=Simul_Out.Sim_x;      % Passing the vector from simulations to x

figure(2);  % Making sure matlab plots both figures
[Spec_Output]=MS_AR_Fit(x,ar,k,advOpt);    % Fitting to get parameters

rmpath('m_Files');