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function [Z] = ARFIMA_SIM(N,F,O,d,stdx,er)
%The code performs the simulation of time series with autoregressive
%fractionally integrated moving average (ARFIMA) models that generalize
%ARIMA (autoregressive integrated moving average) and ARMA autoregressive
%moving average models. ARFIMA models allow non-integer values of the
%differencing parameter and are useful in modeling time series with long memory.
%The model is generally represented as ARFIMA(p,d,q) model where d is the differencing parameter
%and p and q are the order of the autoregressive and moving average parts of the model respectively.
%%% INPUTS
%%%->N = # % Length of the time series we would like to generate
%%%->F = [ F1 F2 F3 .... ] % Parameters of the AR model, length(F) is the order p. Default p = 0
%%%->O = [ O1 O2 O3 .... ] % Parameters of the MA model, length(O) is the order q. Default q = 0
%%%->d = # ; % Fractionally differencing parameter, default d = 0
%%%->stdx = % Optional input: parameter to force the standard deviation of the
%output time series. Impose std(Z)==stdx
%%%-->er = % Optional input: predefined time ser
%%%%%%%%% THE ARFIMA PROCESS IS DEFINED AS:
%%%% F(B)[(1-B)^d]Z=O(B)er
%%%% F(B)Z=[(1-B)^-d]O(B)er
%%%%%%% where B is the backshift operator,
%%%% F(B)= 1+ B F1 + B^2 F2 ... + B^p Fp --> AR PART
%%%% O(B)= 1+ B O1 + B^2 O2 ... + B^q Oq --> MA PART
%%%% er = white noise, it can be specified as an input
%%% Note that F(B) and O(B) are both defined with plus sign as in the "armax" function of matlab
%and in Box et al., (1994).
%%% OUTPUTS
%-->Z = Time series simulated with the ARFIMA mo
%%%%%%%%%% EXAMPLES
%%% White noise
%[Z] = ARFIMA_SIM(N);
%%% AR(1) model
%[Z] = ARFIMA_SIM(N,[F1]);
%%% MA(1) model
%[Z] = ARFIMA_SIM(N,[],[O1])
%%% ARMA(2,2) model
%[Z] = ARFIMA_SIM(N,[F1,F2],[O1,O2])
%%% ARFIMA(0,d,0)
%[Z] = ARFIMA_SIM(N,[],[],d)
%%% ARFIMA(1,d,1)
%[Z] = ARFIMA_SIM(N,[F1],[O1],d)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Simone Fatichi -- simonef@dicea.unifi.it
% Copyright 2009
% $Date: 2009/10/19 $
%%%inizialization
X=zeros(1,N); Y=zeros(1,N); Z=zeros(1,N);
%%%% FI(B)[(1-B)^d]Z=O(B)e
%%%% FI(B)Z=[(1-B)^-d]O(B)e
%%%% FI(B)= 1+ B F1 + B^2 F2 ...
%%%% O(B) = 1+ B O1 + B^2 O2 ...
switch nargin
case 1
d=0;
F=[];
O=[];
t=0;
stdx=NaN;
case 2
d = 0;
O =[];
t = 0;
stdx=NaN;
case 3
d = 0;
t=0;
stdx=NaN;
case 4
t=0;
stdx=NaN;
case 5
t=0;
case 6
t=1;
otherwise
msgbox('ERROR: Not enough or too much input arguments')
Z=[];
return
end
e=normrnd(0,1,N,1);
if t==1
e=er;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if isempty(O) && isempty(F) && (d==0)
Z=e;
return
end
%%%%% N =length
MA_ord=length(O);
AR_ord=length(F);
%%%%%%%%%%%% Computing part: MA(q)
t=0;
if MA_ord >= 1
for t=1:N
j=0;map=0;
for j=1:MA_ord
if t > j
map = map + O(j)*e(t-j);
end
end
X(t)= e(t)+ map;
end
else
X=e;
end
t=0;
%%%%%%%%%%% Computing part: d
if d == 0
Y=X;
else
infi =100; s=0;
for s=0:infi
%b(s+1)=((-1)^s)*gamma(-d+1)./(gamma(s+1)*gamma(-d-s+1));
b(s+1)=gamma(s+d)/(gamma(s+1)*gamma(d));
end
for t=1:N
Y(t)=0;
for s=0:infi
if t > s
Y(t)= Y(t)+ b(s+1)*X(t-s);
end
end
end
end
%%%%%%%%%%%%% Computing part: AR(p)
t = 0;
if AR_ord >= 1
for t=1:N
j=0; arp=0;
for j=1:AR_ord
if t > j
arp = arp - F(j)*Z(t-j);
end
end
Z(t)= Y(t)+ arp;
end
else
Z=Y;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Z=Z';
if not(isnan(stdx))
Z=Z*stdx/std(Z);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end
下载地址：http://www.mathworks.com/matlabcentral/fileexchange/?search_submit=fileexchange&query=ARFIMA&term=ARFIMA 第一个就是。
已经有122个RV数据 想做lnRV－ARFIMA模型，但是不知道怎么用这个模型。
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