python构建指数平滑预测模型示例

#year time_id number
1994 1 10
1995 2 3
1996 3 27
1997 4 13
1998 5 12
1999 6 13
2000 7 14
2001 8 23
2002 9 32
2003 10 30
2004 11 36
2005 12 40
2006 13 58
2007 14 51
2008 15 73
2009 16 80
2010 17 106
2011 18 127
2012 19 135
2013 20 161
2014 21 149
2015 22 142

# -*- coding: utf-8 -*-
# @Date  : 2017-04-11 21:27:00
# @Author : Alan Lau (rlalan@outlook.com)
# @Language : Python3.5

import numpy as np
from matplotlib import pyplot as plt

#指数平滑公式
def exponential_smoothing(alpha, s):
 s2 = np.zeros(s.shape)
 s2[0] = s[0]
 for i in range(1, len(s2)):
  s2[i] = alpha*s[i]+(1-alpha)*s2[i-1]
 return s2

#绘制预测曲线
def show_data(new_year, pre_year, data, s_pre_double, s_pre_triple):
 year, time_id, number = data.T

 plt.figure(figsize=(14, 6), dpi=80)#设置绘图区域的大小和像素
 plt.plot(year, number, color='blue', label="actual value")#将实际值的折线设置为蓝色
 plt.plot(new_year[1:], s_pre_double[2:],color='red', label="double predicted value")#将二次指数平滑法计算的预测值的折线设置为红色
 plt.plot(new_year[1:], s_pre_triple[2:],color='green', label="triple predicted value")#将三次指数平滑法计算的预测值的折线设置为绿色
 plt.legend(loc='lower right')#显示图例的位置，这里为右下方
 plt.title('Projects')
 plt.xlabel('year')#x轴标签
 plt.ylabel('number')#y轴标签
 plt.xticks(new_year)#设置x轴的刻度线为new_year
 plt.show()


def main():
 alpha = .70#设置alphe，即平滑系数
 pre_year = np.array([2016, 2017])#将需要预测的两年存入numpy的array对象里
 data_path = r'data1.txt'#设置数据路径
 data = np.loadtxt(data_path)#用numpy读取数据
 year, time_id, number = data.T#将数据分别赋值给year, time_id, number
 initial_line = np.array([0, 0, number[0]])#初始化，由于平滑指数是根据上一期的数值进行预测的，原始数据中的最早数据为1995，没有1994年的数据，这里定义1994年的数据和1995年数据相同
 initial_data = np.insert(data, 0, values=initial_line, axis=0)#插入初始化数据
 initial_year, initial_time_id, initial_number = initial_data.T#插入初始化年

 s_single = exponential_smoothing(alpha, initial_number)#计算一次指数平滑
 s_double = exponential_smoothing(alpha, s_single)#计算二次平滑字数，二次平滑指数是在一次指数平滑的基础上进行的，三次指数平滑以此类推

 a_double = 2*s_single-s_double#计算二次指数平滑的a
 b_double = (alpha/(1-alpha))*(s_single-s_double)#计算二次指数平滑的b
 s_pre_double = np.zeros(s_double.shape)#建立预测轴
 for i in range(1, len(initial_time_id)):
  s_pre_double[i] = a_double[i-1]+b_double[i-1]#循环计算每一年的二次指数平滑法的预测值，下面三次指数平滑法原理相同
 pre_next_year = a_double[-1]+b_double[-1]*1#预测下一年
 pre_next_two_year = a_double[-1]+b_double[-1]*2#预测下两年
 insert_year = np.array([pre_next_year, pre_next_two_year])
 s_pre_double = np.insert(s_pre_double, len(s_pre_double), values=np.array([pre_next_year, pre_next_two_year]), axis=0)#组合预测值

 s_triple = exponential_smoothing(alpha, s_double)

 a_triple = 3*s_single-3*s_double+s_triple
 b_triple = (alpha/(2*((1-alpha)**2)))*((6-5*alpha)*s_single -2*((5-4*alpha)*s_double)+(4-3*alpha)*s_triple)
 c_triple = ((alpha**2)/(2*((1-alpha)**2)))*(s_single-2*s_double+s_triple)

 s_pre_triple = np.zeros(s_triple.shape)

 for i in range(1, len(initial_time_id)):
  s_pre_triple[i] = a_triple[i-1]+b_triple[i-1]*1 + c_triple[i-1]*(1**2)

 pre_next_year = a_triple[-1]+b_triple[-1]*1 + c_triple[-1]*(1**2)
 pre_next_two_year = a_triple[-1]+b_triple[-1]*2 + c_triple[-1]*(2**2)
 insert_year = np.array([pre_next_year, pre_next_two_year])
 s_pre_triple = np.insert(s_pre_triple, len(s_pre_triple), values=np.array([pre_next_year, pre_next_two_year]), axis=0)

 new_year = np.insert(year, len(year), values=pre_year, axis=0)
 output = np.array([new_year, s_pre_double, s_pre_triple])
 print(output)
 show_data(new_year, pre_year, data, s_pre_double, s_pre_triple)#传入预测值和数据


if __name__ == '__main__':
 main()