滑动t检验

Function 
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'''
滑动t检验
输入：
inputdata：输入数据，一维序列
step：滑动步长
输出：t1：t统计量
注：自由度v =2*n-2
'''
def slide_t(inputdata,step):
    inputdata = np.array(inputdata)
    n = inputdata.shape[0]
    t = np.zeros(n)
    t1 = np.empty(n)
    n1 = step    #n1, n2为滑动步长，需调整
    n2 = step
    n11 = 1 / n1
    n22 = 1 / n2
    m = np.sqrt(n11 + n22)
    for i in range (step, n-step+1):
        x1_mean = np.mean(inputdata[i-step : i])   
        x2_mean = np.mean(inputdata[i : i+step])
        s1 = np.var(inputdata[i-step : i])          
        s2 = np.var(inputdata[i : i+step])
        s = np.sqrt((n1 * s1 + n2 * s2) / (n1 + n2 - 2))
        t[i-step] = (x2_mean - x1_mean) / (s * m)
        t1 = np.roll(t , step-1)
        t1[:step]=np.nan  
        t1[n-step+1:]=np.nan             
    return  t1
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from scipy import signal
import numpy as np

y = np.array([15.4,14.6,15.8,14.8,15.0,15.1,15.1,15.0,15.2,15.4,
              14.8,15.0,15.1,14.7,16.0,15.7,15.4,14.5,15.1,15.3,
              15.5,15.1,15.6,15.1,15.1,14.9,15.5,15.3,15.3,15.4,
              15.7,15.2,15.5,15.5,15.6,15.1,15.1,16.0,16.0,16.8,
              16.2,16.2,16.0,15.6,15.9,16.2,16.7,15.8,16.2,15.9,
              15.8,15.5,15.9,16.8,15.5,15.8,15.0,14.9,15.3,16.0,
              16.1,16.5,15.5,15.6,16.1,15.6,16.0,15.4,15.5,15.2,
              15.4,15.6,15.1,15.8,15.5,16.0,15.2,15.8,16.2,16.2,
              15.2,15.7,16.0,16.0,15.7,15.9,15.7,16.7,15.3,16.1])

t = slide_t(y,10)

fig = plt.figure(figsize=(15,15))
f_ax1 = fig.add_axes([0.1, 0.1, 0.4, 0.3])
f_ax1.plot(np.arange(1900,1990,1),y,'k')

f_ax2 = fig.add_axes([0.6, 0.1, 0.4, 0.3])
f_ax2.plot(np.arange(1900,1990,1),t,'k')
f_ax2.set_xlim(1900,1990)
f_ax2.set_ylim(-4,7)
# 0.01显著性检验
f_ax2.axhline(2.9)
f_ax2.axhline(-2.9)
plt.show()

image-20200521090717453