灰色预测模型是一种常用的时间序列预测模型，其思路十分简单，只要给定一个原始的时间序列串就可以预测出未来几期的结果，但这个比较适用于短期预测，不适用于中长期预测。原理我不想多讲了，大家自己去百度吧，直接代码，python3可以用，输入你的序列直接出结果，包括算法和检验所有内容。各位要是觉得有用，点个赞再走，哈哈。

import numpy as np
def cal_canshu(input_line):
    cumsum_input = np.cumsum(input_line)
#    print(cumsum_input)
    Y = input_line[1:]
    B = np.ones((len(input_line)-1,2))
    for i in range(np.shape(B)[0]):
        B[i,0] = -0.5 * (cumsum_input[i] + cumsum_input[i+1])
#    print(B)
    B = np.mat(B)
    Y = np.mat(Y)
    out_canshu = ((B.T*B).I)*B.T*Y.T
    return out_canshu


def forcast_hanshu(canshu,input_line,k):
    out_1 = (input_line[0] - canshu[1]/canshu[0]) * np.exp(-canshu[0] * (k-1)) + canshu[1]/canshu[0]
    return out_1


def forcast_out(canshu,input_line):
    n = len(input_line)
    out_1 = np.zeros(n)#默认按行排列
    for i in range(n):
        out_1[i] = forcast_hanshu(canshu,input_line,i+1)
    out_0 = np.zeros(n)
    out_0[0] = out_1[0]
    for i in range(1,n):
        out_0[i] = out_1[i] - out_1[i-1]
    return out_1.T,out_0.T
        

def model_test(input_line, forcast_line):
    sigma = np.abs(forcast_line - input_line)
    rela_sigma = np.average(sigma / input_line)
    print('相对误差为:',rela_sigma)
    yita = np.average((min(sigma) + 0.5 * max(sigma)) / (sigma + 0.5 * max(sigma)))
    print('关联度为:',yita)
    sq_input = np.square(input_line)
    sq_error = np.square(sigma)
    sq_ratio = np.average(sq_error)/np.average(sq_input)
    print('均方差比为:',sq_ratio)
    little_error = len(sigma[(sigma - np.average(sigma)) < 0.6745*np.average(sq_input)])/len(sigma)
    print('小误差概率为:',little_error)
    return rela_sigma, yita, sq_ratio, little_error

test = np.array([1,2,3,4,5,6])
a,b = forcast_out(cal_canshu(test), test)
model_test(test, b)