Gabriel Perez-Quiros, Allan Timmermann(2000)

[fan]

Hi, Tom, Is there a RATS code to replicate the Perez-Quiros and Timmermann(2000),Firm Size and Cyclical Variations in Stock Returns? Many thanks. There are example codes for Matlab but I would prefer to run it in RATS. Thanks a lot.

[TomDoan]

Could you include the link to the Matlab codes (and I assume data).

[ejosmer]

Hi, Tom, I just wonder do you have the codes for replicating Perez-Quiros and Timmermann(2000),Firm Size and Cyclical Variations in Stock Returns? JF.

I completely stuck on creating Bi-variate Markov Model and Testing for the symmetry.

[TomDoan]

The previous poster said that there were Matlab codes, but I wasn't able to find them.

The likelihood for the bivariate model for regime St would be computed with exp(%logdensity(sigma(St),||u1(St),u2(St))). The asymmetry tests are done by pegging the slope coefficients to be equal to generate the LR test for changes in the variance and to set the variance coefficients to be equal to generate the LR test for changes in the regression.

[ejosmer]

Hi, Tom, thank you for the fast reply.
I find the following matlab code

Code: Select all

% Function for forecasting in t+1 an Markov Switching regression model
% estimated with MS_Regress_Fit.m
%
%   Input:  Spec_Output - Specification output from estimation (check MS_Regress_Fit.m)
%           newIndepData - New information that has arrived for t+1 and beyond (maybe lagged variables ?)
%           newpxData - New information that has arrived for t+1 and beyond for macro state variables
%
%   Output: meanFor - Forecast for the mean equation (column iterating over equations of system)
%           stdFor - Forecast for the standard deviation (columns iterating over
%           equations of system)
% 
%   Author: Marcelo Perlin
%   Email:  marceloperlin@gmail.com
%
%   Author: Marcelo Perlin (UFRGS/BR) for the constant transition probability version.  
%   Contact:  marceloperlin@gmail.com
%
%   Author: Zhuanxin Ding for the time varying transition probability version.
%
%   Modified by Zhuanxin Ding based on the original code by Marcelo Perlin to incorporate the 
%   time-varying transition probability matrix that depends on state variables, May 21,2012.
%   (see paper by Gabriel Perez-Quiros and Allan Timmermann, Journal of Finance, June 2000)
%

function [meanFor,stdFor]=MS_Regress_For_tvtp(Spec_Out,newIndepData,newpxData)

% Retrieving variables from Spec_Output
nEq=size(Spec_Out.condMean,2);
k=Spec_Out.k;
S=Spec_Out.S;
Coeff=Spec_Out.Coeff;

if ~iscell(newIndepData)
    temp=newIndepData;
    clear newIndepData;
    for iEq=1:nEq
        newIndepData{iEq}=temp;
    end
end

if ~iscell(newpxData)
    temp=newpxData;
    clear newpxData;
    for i=1:k-1
        for j=1:k
            newpxData{i,j}=temp;
        end
    end
end

% forecast horizon;
h=size(newIndepData{1},1);

for ik=1:k
    Std{ik}=sqrt(diag(Coeff.covMat{ik}));
end

distrib=Spec_Out.advOpt.distrib;

for iEq=1:nEq
    switch distrib
        case 'Normal'
            S_Std{iEq}=S{iEq}(end);
            n_dist_param=1; % Number of d
        case 't'
            S_Std{iEq}=S{iEq}(end-1);
            n_dist_param=2; % Number of distributional parameters
        case 'GED'
            S_Std{iEq}=S{iEq}(end-1);
            n_dist_param=2; % Number of distributional parameters
    end
end

indep_S=cell(nEq,1);
indep_nS=cell(nEq,1);
for iEq=1:nEq
    
    count_S=0;
    count_nS=0;
    
    for i=1:length(S{iEq})-n_dist_param
        if S{iEq}(i)==1
            count_S=count_S+1;
            indep_S{iEq}(:,count_S)=newIndepData{iEq}(:,i);
        else
            count_nS=count_nS+1;
            indep_nS{iEq}(:,count_nS)=newIndepData{iEq}(:,i);
        end
    end
    
    if count_nS==0
        indep_nS{iEq}=zeros(h,1);
    end
    
end

% Building Forecasts

% future time varying transition probability matrix;
pa=Spec_Out.Coeff.pa;
p=ones(k,k,h);
tvtp=ones(k,k,h);
for t=1:h
    for i=1:k-1
        for j=1:k
            tvtp(i,j,t)=normcdf(newpxData{i,j}(t,:)*pa{i,j});
            p(i+1,j,t)=p(i,j,t)*(1-tvtp(i,j,t));
        end
    end   
    p(:,:,t)=p(:,:,t).*tvtp(:,:,t);
end

% state probability;
firstProb=Spec_Out.filtProb;
for t=1:h
    if t==1
        E(t,:)=p(:,:,t)*firstProb(end,:)';      % Eq (9) of Hamilton's paper
    else
        E(t,:)=p(:,:,t)*E(t-1,:)';       % Eq (9) of Hamilton's paper or (22.4.6) of Hamilton's book
    end
end

for t=1:h
    for iEq=1:nEq

        for j=1:k
            meanFor_S{iEq}(t,j)=indep_nS{iEq}(t,:)*Coeff.nS_Param{iEq}+indep_S{iEq}(t,:)*Coeff.S_Param{iEq}(:,j); % mean forecast for each state
            stdFor_S{iEq}(t,j)=Std{j}(iEq); % sigma forecast for each state

        end
        
        meanFor{iEq}(1,t)=meanFor_S{iEq}(t,:)*E(t,:)'; % mean t+1 forecast
        stdFor{iEq}(1,t)=stdFor_S{iEq}(t,:)*E(t,:)';   % std t+1 forecast

    end
end

In addition, although I do not have the exact portfolios used in the paper, but I think Fama French Size Portfolios could be used as substitute. I have attached this as well.

Please let me know if there is any way to replicate this paper in RATS since this is my favorite software for research. Thank you.

Eric

[TomDoan]

That's actually for forecasting, not for fitting, though the site has the code for fitting the model instead. However, all that really does is reference the Perez-Quiros-Timmerman paper for the time-varying transition probabilities. The 2000 paper does two "non-standard" things: TVTP and the switching semi-structural variance process.

[ejosmer]

I know it is similar to Gray (1996), however, I am still having problem of setting up the bi variate estimation. Is there a sample code to set up bi variate MS switching ? Thank you.

[TomDoan]

That's what the MSSysRegression routines are for.