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my_HARQ.m
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my_HARQ.m
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% Function to estimate the conditional volatility based on HARQ model of
% Bollerslev, T., Patton, A.J. and Quaedvlieg, R., 2016
% RQ= Realized Quarticity
% Script developed by Arman Hassanniakalager
% The script is based on some anonymous script found online.
% Created on 23 Jan. 2018
% Last modified 10 Jun. 2019 14:37 BST
%% Inputs:
% -date_ser: date series to help seperate weeks & months
% -rv : realized volatility series
% -mdl_type: model type HAR-RV (1) or HAR-log(RV) (2)
function [ht,oos_predict,b]=my_HARQ(date_ser,rv,RQ,mdl_type)
if nargin<2
error('Not enough input arguments')
elseif nargin==2
mdl_type=1;
end
YYYY = year(date_ser);
MM = month(date_ser);
DD = day(date_ser);
Date_NO = datenum(YYYY,MM,DD);
YYYYMM = 1000*YYYY + MM;
RV_Day = rv;
RQ_sq=RQ.^.5;
% empirical length of week
w_length=floor(numel(RV_Day)/52);
% empirical length of month
m_length=floor(numel(RV_Day)/12);
iter=0;
for s=m_length:numel(RV_Day)
iter=iter+1;
RV_w(iter)=mean(RV_Day(s-w_length+1:s));
RV_m(iter)=mean(RV_Day(s-m_length+1:s));
RQ_w(iter)=mean(RQ(s-w_length+1:s));
RQ_m(iter)=mean(RQ(s-m_length+1:s));
end
%% HAR regression
if mdl_type==1
X=[ones(numel(RV_w)-1,1),RV_Day(m_length:end-1),RV_Day(m_length:end-1).*(RQ(m_length:end-1).^.5),...
RV_w(1:end-1)',RV_w(1:end-1)'.*(RQ_w(1:end-1)'.^.5),RV_m(1:end-1)',RV_m(1:end-1)'.*(RQ_m(1:end-1)'.^.5)];
Y=RV_Day(m_length+1:end);
b = (X'*X)\(X'*Y);
Forecasted_Y = X*b;
oos_predict=[1,RV_Day(end),RV_Day(end)*RQ(end)^.5,RV_w(end),RV_w(end)*RQ_w(end)^.5,RV_m(end),RV_m(end)*RQ_m(end)^.5]*b;
ht=[nan(m_length,1);Forecasted_Y];
else
X=[ones(numel(RV_w)-1,1),log(RV_Day(m_length:end-1)),log(RV_Day(m_length:end-1).*(RQ(m_length:end-1).^.5)),...
log(RV_w(1:end-1)'),log(RV_w(1:end-1)'.*(RQ_w(1:end-1)'.^.5)),log(RV_m(1:end-1)'),log(RV_m(1:end-1)'.*(RQ_m(1:end-1)'.^.5))];
Y=log(RV_Day(m_length+1:end));
b = (X'*X)\(X'*Y);
Forecasted_logY = X*b;
Forecasted_Y=exp(Forecasted_logY);
logoos_predict=[1,log(RV_Day(end)),log(RV_Day(end)*RQ(end)^.5),log(RV_w(end)),log(RV_w(end)*RQ_w(end)^.5),log(RV_m(end)),log(RV_m(end)*RQ_m(end)^.5)]*b;
oos_predict=exp(logoos_predict);
ht=[nan(m_length,1);Forecasted_Y];
end
% % Plot the sequences
% plot(Date_NO(2:end),Y,'b-',Date_NO(2:end),Forecasted_Y,'r-')
% datetick('x','yyyymm','keeplimits')
% title('Observed and forecasted RV based on HAR model: HARRV')
% xlabel('Time')
% ylabel('Realized Volatility')
% legend('Observed RV','Forecasted RV')
end