% Time Series. Econ232C. Spring 2006. Homework 1 clear all; %close all; clc; %define parameters N=100; %cross-section size (50,100,500) T=500; %time horizon ro=0.7; %AR(1) parameter L=10; %Lag number sigmax=10; %error variance %construct data Xjt=sigmax*randn(N,T); %generate X err=randn(1,T); Zt=zeros(1,T); for i=2:T %generate Z as AR(1) Zt(i)=ro*Zt(i-1)+err(i); end Yjt=Xjt+Kron(Zt,ones(N,1)); %construct Y %compute ACF h=Yjt(1,:); gamma0=(h*h')/T; for j=1:L gamma(j)=( h(1,(j+1):T) * (h(1,1:(T-j)))')/(T-j); ster(j)=2/sqrt(T); end ACF=gamma/gamma0; figure(1); subplot(1,2,1); stem_hadles=stem(1:L,ACF,'fill'); hold on; plot_hadles=plot(1:L,ster,'r',1:L,-ster,'r'); title('ACF') hold off; %compute PACF h=Yjt(1,:); for j=1:L Y=h(1,(j+1):T)'; X=zeros((T-j),j); for k=1:j X(:,k)=h(1,(j+1-k):(T-k))'; end beta=inv(X'*X)*(X'*Y); alpha(j)=beta(j); ster(j)=2/sqrt(T); end PACF=alpha; subplot(1,2,2); stem_hadles=stem(1:L,PACF,'fill'); hold on; plot_hadles=plot(1:L,ster,'r',1:L,-ster,'r'); title('PACF') hold off; SY=ones(1,N)*Yjt; %compute ACF h=SY; gamma0=(h*h')/T; for j=1:L gamma(j)=( h(1,(j+1):T) * (h(1,1:(T-j)))')/(T-j); ster(j)=2/sqrt(T); end ACF=gamma/gamma0; figure(2); subplot(1,2,1); stem_hadles=stem(1:L,ACF,'fill'); hold on; plot_hadles=plot(1:L,ster,'r',1:L,-ster,'r'); title('ACF') hold off; %compute PACF h=SY(1,:); for j=1:L Y=h(1,(j+1):T)'; X=zeros((T-j),j); for k=1:j X(:,k)=h(1,(j+1-k):(T-k))'; end beta=inv(X'*X)*(X'*Y); alpha(j)=beta(j); ster(j)=2/sqrt(T); end PACF=alpha; subplot(1,2,2); stem_hadles=stem(1:L,PACF,'fill'); hold on; plot_hadles=plot(1:L,ster,'r',1:L,-ster,'r'); title('PACF') hold off;