clear;
%--------------------------------油價序列零均值化后的數據如下----------------------------------------%：
P=[?19.5900?14.9100?15.7400?15.4000?13.0600?19.0700?15.2800?15.8200?12.7700?12.0500...???
??11.6900?13.8500?13.8500?10.0700?9.1700?10.7900?13.4400?21.1700?18.6400?13.2100...???
??15.5400?21.9400?23.1100?18.6400?14.9400?16.9000?15.4600?11.1500?13.1300?12.4800...???
??12.9500?12.5900?10.5800?10.5800?12.3900?15.5300?13.0600?10.2200?16.3300?19.7200...
??21.3100?18.8400?24.8400?15.6700?15.5700?12.7300?13.5600?15.5400?17.2200?12.1400...
??11.0700?12.0200?11.5500?6.9200?10.3300?8.3800?12.1100?11.4600?12.7500?13.3200...
??13.0000?11.9000?11.7900?12.5500?11.8400?11.2500?11.1500?10.9900?11.7000?14.0100...
??17.5100?17.2700?16.9000?15.7900?15.4500?6.2400?16.7100?16.7700?16.6400?17.8000...
??16.8700?16.1300?15.7600?15.6600?15.5400?15.3000?15.0500?14.6900?14.3900?14.1800...
??13.70?13.66?13.27?13.56?13.14?14.19?];
F=[?19.5900?14.9100?15.7400?15.4000?13.0600?19.0700?15.2800?15.8200?12.7700?12.0500...???
??11.6900?13.8500?13.8500?10.0700?9.1700?10.7900?13.4400?21.1700?18.6400?13.2100...
??15.5400?21.9400?23.1100?18.6400?14.9400?16.9000?15.4600?11.1500?13.1300?12.4800...
??12.9500?12.5900?10.5800?10.5800?12.3900?15.5300?13.0600?10.2200?16.3300?19.7200...
??21.3100?18.8400?24.8400?15.6700?15.5700?12.7300?13.5600?15.5400?17.2200?12.1400...
??11.0700?12.0200?11.5500?6.9200?10.3300?8.3800?12.1100?11.4600?12.7500?13.3200...
??13.0000?11.9000?11.7900?12.5500?11.8400?11.2500?11.1500?10.9900?11.7000?14.0100...
??17.5100?17.2700?16.9000?15.7900?15.4500?6.2400?16.7100?16.7700?16.6400?17.8000...
??16.8700?16.1300?15.7600?15.6600?15.5400?15.3000?15.0500?14.6900?14.3900?14.180];

%----------------------由于時間序列有不平穩趨勢，進行兩次差分運算，消除趨勢性----------------------%
for?i=2:96
??Yt（i）=P（i）-P（i-1）;
end
for?i=3:96
??L（i）=Yt（i）-Yt（i-1）;
end
figure;
L=L（3:96）;
Y=L（1:88）;
plot（P）;
title（‘原數據序列圖‘）;
hold?on;??
plot（Y‘r‘）;
title（‘兩次差分后的序列圖和原數對比圖‘）;??
%--------------------------------------對數據標準化處理----------------------------------------------%
Ux=sum（Y）/88?%?求序列均值
yt=Y-Ux;
b=0;
for?i=1:88
??b=yt（i）^2/88+b;
end
v=sqrt（b）?%?求序列方差
Y=（Y-Ux）/v;?%?標準化處理公式
f=F（1:88）;
t=1:88;
figure;
plot（tftY‘r‘）
title（‘原始數據和標準化處理后對比圖‘）;
xlabel（‘時間t‘）ylabel（‘油價y‘）;
legend（‘原始數據?F?‘‘標準化后數據Y?‘）;???
%--------------------------------------對數據標準化處理----------------------------------------------%


%------------------------檢驗預處理后的數據是否符合AR建模要求，計算自相關和偏相關系數---------------%
??%---------------------------------------計算自相關系數-----------------------------------%
R0=0;
for?i=1:88??
??R0=Y（i）^2/88+R0;
end
R0
for?k=1:20
??R（k）=0;
??for?i=k+1:88
??R（k）=Y（i）*Y（i-k）/88+R（k）;
??end
??R?%自協方差函數R???
end
x=R/R0?%自相關系數x
figure;
plot（x）
title（‘自相關系數分析圖‘）;??
%-----------------------------------計算自相關系數-------------------------------------%
%-----------------------解Y-W方程，其系數矩陣是Toeplit矩陣。求得偏相關函數X-----------------------%
X1=x（1）;
X11=x（1）/1;
B=[x（1）?x（2）]‘;
x2=[1?x（1）];