chafen.m

使用游程法对时间序列进行平稳性检验

function [ w ] = ChaFen( TimeSeries,dMax )
%UNTITLED1 Summary of this function goes here
%  Detailed explanation goes here
x=TimeSeries;
% 计算时间序列的长度
len=length(x);


%平稳性分析,确定差分次数d
%判断序列是否为平稳序列，是，则不变，不是则进行差分，直至差分后的序列是平稳的

d=0;  %初始化差分次数为0
%用w表示差分后的平稳时间序列
w=x;  %初始化

for i=1:dMax
   flag = stationary(w); % 判断是否平稳，平稳flag=1
	if  flag==0          %不平稳
        temp=zeros(1,len);
        for j=(i+1):len
            temp(j)=w(j)-w(j-1);
        end
        w=temp; 
		d=d+1;
    else                %平稳
        break;
    end
end

function flag = stationary(timeSeries)
%平稳性判断函数
%平稳序列满足均值方差与t无关，自相关函数与起始时间无关只与时间间隔有关
%根据游程法判断数据是否是平稳的,如果是平稳过程,flag=1;反之则flag=0;
%初始化
flag=0;
N1=0;
N2=0;
Num_ych=1;       %正符号数N1,负符号数N2,游程数Num_ych;
E_ych=0;
V_ych=0;
T_Z=0;

mean_timeSeries=mean(timeSeries);  %求平均值
flen=length(timeSeries);

for i=1:1:flen;
	if timeSeries(i)>=mean_timeSeries;
	    N1=N1+1;
    else
        N2=N2+1;
	end
	if i>1&&((timeSeries(i)>=mean_timeSeries&&timeSeries(i-1)<mean_timeSeries)||(timeSeries(i)<mean_timeSeries&&timeSeries(i-1)>=mean_timeSeries));
	    Num_ych= Num_ych+1;
	end
end

E_ych=1+2*N1*N2/(N1+N2);
V_ych=sqrt(2*N1*N2*(2*N1*N2-(N1+N2))/((N1+N2)*(N1+N2)*(N1+N2-1)));
T_Z=(Num_ych-E_ych)/(2*V_ych);

if abs(T_Z)<=1.96
   flag=1;            %平稳
else
    flag=0;          %不平稳
end