时间序列(二)

# -*- coding: utf-8 -*-
"""
Created on Sat Jan 14 11:57:34 2017

@author: DaiPuWei
"""
"""
    时间序列一次指数平移法，以电器销售额的预测为例
"""

import pandas as pd
import math

def Index_Translation(data,alpha):
    """
        一次指数平移法函数
        data是样本数据
        alpha为加权系数
    """

    #数据数组长度
    length = len(data)
    forecast_data = []

    #预测初值去顶
    tmp = 0 
    if length > 20:
        tmp = data[0]
    else:
        for i in range(2):
            tmp = tmp + data[i]
        tmp = tmp / 2
    forecast_data.append(tmp)

    #计算预测数据
    for i in range(1,length):
        tmp = 0
        tmp = alpha * data[i-1] + (1-alpha) * forecast_data[i-1]
        forecast_data.append(tmp)

    #相对误差
    error = 0
    for i in range(length):
        error = error + (data[i] - forecast_data[i]) * (data[i] - forecast_data[i])
    error = error * 1.0 / (length - 2)
    error = math.sqrt(error)

    return error,forecast_data

def Index_Translation_Model(data,alpha):
    """
        这是一次指数平移模型
        data是样本数据
        alpha为加权系数数组
        forecast是需要预测的指标年份
    """

    #把数预测据按相对误差进行装饰
    tmp = []
    for i in range(len(alpha)):
        error = 0
        forecast_data = []
        error,forecast_data = Index_Translation(data,alpha[i])
        tmp.append((error,alpha[i],forecast_data))

    #按相对误差从小到大排序
    tmp.sort(reverse = False)

    #获取相关信息
    t = tmp[0]
    Alpha = t[1]
    forecast_data = t[2]

    #对要预测的数据进行预测
    length = len(data)
    last = data[length-1]
    _forecast = forecast_data[length-1]
    forecast = Alpha * last + (1-Alpha) * _forecast     

    return forecast

def run_main():
    '''
        这是主是函数
    '''

    #读取文件中的样例
    sample = pd.read_excel('E:\\Program Files (x86)\\大学数学\\算法大全pdf\\第24章   时间序列模型\\电器销售额.xlsx')
    data = sample[sample.columns[1]]
    year = sample[sample.columns[0]]

    #加权系数
    alpha = []
    for i in range(10):
        alpha.append((i+1)*1.0/10)

    #预测结果
    forecast_result = Index_Translation_Model(data,alpha)
    print(year[len(year)-1]+1,'年的电器销售额预测值为:',forecast_result)

if __name__ == '__main__':
    run_main()

# -*- coding: utf-8 -*-
"""
Created on Sat Jan 14 13:37:09 2017

@author: DaiPuWei
"""

"""
    时间序列二次指数平滑法，以发电量预测为例
"""

import pandas as pd
import math

def Index_Translation(data,alpha):
    """
        指数平移法函数
        data是样本数据
        alpha为加权系数
    """

    #数据数组长度
    length = len(data)
    forecast_data = []

    #预测初值去顶
    tmp = 0 
    if length > 20:
        tmp = data[0]
    else:
        for i in range(2):
            tmp = tmp + data[i]
        tmp = tmp / 2
    forecast_data.append(tmp)

    #计算预测数据
    for i in range(1,length):
        tmp = 0
        tmp = alpha * data[i-1] + (1-alpha) * forecast_data[i-1]
        forecast_data.append(tmp)

    return forecast_data

def Second_Index_Translation_Model(data,alpha,year,forecast_year):
    """
        这是一次指数平移模型
        data是样本数据
        alpha为加权系数
        forecast是需要预测的指标年份
    """

    #一次指数平滑
    forecast_data1 = Index_Translation(data,alpha)

    #二次指数平滑
    forecast_data2 = Index_Translation(forecast_data1,alpha)

    #对要预测的数据进行预测
    A = 2 * forecast_data1[-1] - forecast_data2[-1]
    B = alpha *(forecast_data1[-1] - forecast_data2[-1]) / (1 - alpha)
    first_year = year[len(year)-1]
    print('二次指数平滑模型为:')
    print('Y(t)=',A,'+',B,'(T-',first_year,')')

    forecast = A + B * (forecast_year-first_year)

    return forecast

def run_main():
    '''
        这是主函数
    '''

    #读取数据集
    sample = pd.read_excel('E:\\Program Files (x86)\\大学数学\\算法大全pdf\\第24章   时间序列模型\\1965-1985年发电总量统计.xlsx')
    data = sample['发电总量']
    year = sample['年份']

    #加权系数
    alpha = 0.3

    #模型预测
    forecast_year = 1986
    forecast = Second_Index_Translation_Model(data,alpha,year,forecast_year)
    print(forecast_year,'年的发电总量的预测值为',forecast)

    forecast_year = 1987
    forecast = Second_Index_Translation_Model(data,alpha,year,forecast_year)
    print(forecast_year,'年的发电总量的预测值为',forecast)


if __name__ == '__main__':
    run_main()

# -*- coding: utf-8 -*-
"""
Created on Sat Jan 14 17:34:30 2017

@author: DaiPuWei
"""

"""
    时间序列三次指数平滑法，以固定资产他投资总额预测为例
"""

import pandas as pd

def Index_Translation(data,alpha):
    """
        指数平移法函数
        data是样本数据
        alpha为加权系数
    """

    #数据数组长度
    length = len(data)
    forecast_data = []

    #预测初值去顶
    tmp = 0 
    if length > 20:
        tmp = data[0]
    else:
        for i in range(3):
            tmp = tmp + data[i]
        tmp = tmp / 3
    forecast_data.append(tmp)

    #计算预测数据
    for i in range(1,length):
        tmp = 0
        tmp = alpha * data[i-1] + (1-alpha) * forecast_data[i-1]
        forecast_data.append(tmp)

    return forecast_data

def Third_Index_Translation_Model(data,alpha,year,forecast_year):
    """
        这是一次指数平移模型
        data是样本数据
        year是样本年份
        alpha为加权系数
        forecast是需要预测的指标年份
    """

    #一次指数平滑
    forecast_data1 = Index_Translation(data,alpha)

    #二次指数平滑
    forecast_data2 = Index_Translation(forecast_data1,alpha)

    #三次指数平滑
    forecast_data3 = Index_Translation(forecast_data2,alpha)

    #对要预测的数据进行预测
    A = 3 * forecast_data1[-1] - 3 * forecast_data2[-1] + forecast_data3[-1]
    B = alpha *((6 - 5 * alpha) * forecast_data1[-1] - 2*(5 - 4 * alpha) * forecast_data2[-1] + (4 - 3 * alpha) * forecast_data3[-1]) / (2*(1 - alpha)*(1 - alpha))
    C = alpha * alpha * (forecast_data1[-1] - 2 * forecast_data2[-1] + forecast_data3[-1])
    first_year = year[len(year)-1]
    print('二次指数平滑模型为:')
    print('Y(t)=',A,'+',B,'(T-',first_year,')+',C,'*(T-',first_year,')^2')

    forecast = A + B * (forecast_year-first_year) + C * (forecast_year-first_year) * (forecast_year-first_year)

    return forecast

def run_main():
    """
        这是主函数
    """

    #读取数据集
    sample = pd.read_excel('E:\\Program Files (x86)\\大学数学\\算法大全pdf\\第24章   时间序列模型\\固定资产总额.xlsx')
    data = sample[sample.columns[1]]
    year = sample[sample.columns[0]]

    #加权系数
    alpha = 0.3

    #模型预测
    forecast_year = 1989
    forecast = Third_Index_Translation_Model(data,alpha,year,forecast_year)
    print(forecast_year,'年的发电总量的预测值为',forecast)

    forecast_year = 1990
    forecast = Third_Index_Translation_Model(data,alpha,year,forecast_year)
    print(forecast_year,'年的发电总量的预测值为',forecast)

if __name__ == '__main__':
    run_main()

# -*- coding: utf-8 -*-
"""
Created on Sat Jan 14 19:58:25 2017

@author: DaiPuWei
"""

"""
    时间序列一阶差分指数平滑法，以锅炉燃料消耗量预测为例
"""

import pandas as pd

def Difference_Index(data,alpha):
    '''
        一阶差分函数
        data是样本数据
        alpha为加权系数
    '''

    #差分数值
    length = len(data)
    first_difference = []
    for i in range(length-1):
        difference = data[i+1] - data[i]
        first_difference.append(difference)

    #差分指数平滑
    forecast_difference = []
    forecast_difference.append(first_difference[0])
    for i in range(1,len(first_difference)):
        forecast = alpha * first_difference[i-1] + (1-alpha) * forecast_difference[i-1]
        forecast_difference.append(forecast)
    forecast = forecast_difference[-1] + data[len(data)-1]

    return forecast

def First_Difference_Index_Model(data,year,alpha):
    """
        一阶差分指数平滑法模型
    """

    #模型预测
    forecast = Difference_Index(data,alpha)
    print(year[len(year)-1]+1,'年的锅炉燃料消耗量预测值为:',forecast)

def run_main():
    '''
        这是主函数
    '''

    #读取数据集
    sample = pd.read_excel('E:\\Program Files (x86)\\大学数学\\算法大全pdf\\第24章   时间序列模型\\锅炉燃料消耗量.xlsx')
    data = sample[sample.columns[1]]
    year = sample[sample.columns[0]]

     #加权系数
    alpha = 0.4

    #一阶差分指数平滑法预测
    First_Difference_Index_Model(data,year,alpha)


if __name__ == '__main__':
    run_main()

# -*- coding: utf-8 -*-
"""
Created on Sat Jan 14 20:06:47 2017

@author: DaiPuWei
"""

"""
    时间序列二阶差分指数平滑法，以锅炉燃料消耗量预测为例
"""

import pandas as pd

def Difference_Index(data,alpha):
    '''
        差分函数
        data是样本数据
        alpha为加权系数
    '''

    #差分数值
    length = len(data)
    first_difference = []
    for i in range(length-1):
        difference = data[i+1] - data[i]
        first_difference.append(difference)

    #差分指数平滑
    forecast_difference = []
    forecast_difference.append(first_difference[0])
    for i in range(1,len(first_difference)):
        forecast = alpha * first_difference[i-1] + (1-alpha) * forecast_difference[i-1]
        forecast_difference.append(forecast)

    return forecast_difference

def Second_Difference_Index_Model(data,year,alpha):
    """
        一阶差分指数平滑法模型
    """

    #一阶差分指数平滑
    forecast_difference1 = Difference_Index(data,alpha)

    #二阶差分指数平滑
    forecast_difference2 = Difference_Index(forecast_difference1,alpha)


    #模型预测
    forecast = forecast_difference1[-1] + forecast_difference2[-1] + data[len(data)-1]
    print(year[len(year)-1]+1,'年的锅炉燃料消耗量预测值为:',forecast)

def run_main():
    '''
        这是主函数
    '''

    #读取数据集
    sample = pd.read_excel('E:\\Program Files (x86)\\大学数学\\算法大全pdf\\第24章   时间序列模型\\锅炉燃料消耗量.xlsx')
    data = sample[sample.columns[1]]
    year = sample[sample.columns[0]]

     #加权系数
    alpha = 0.4

    #二阶差分指数平滑法预测
    Second_Difference_Index_Model(data,year,alpha)

if __name__ == '__main__':
    run_main()

# -*- coding: utf-8 -*-
"""
Created on Sun Jan 15 10:16:52 2017

@author: DaiPuWei
"""

"""
    时间序列自适应滤波法
"""

def Forecast(data,weight,N,index):
    '''
        对数据进行预测
    '''

    tmp = []
    forecast = 0
    for i in range(index-N,index):
        tmp.append(data[i])
    tmp = tmp[::-1]
    for i in range(len(tmp)):
        forecast = forecast +tmp[i] * weight[i]

    return forecast,tmp

def Adaptive_Filtering(data,weight,error,N,K,index):
    '''
        一次自适应滤波预测
        data是样本数据
        weight是权值数组
        error为误差数组
        N是权值数组长度
        K为学习系数
        index是需要预测数据的下标
    '''

    #进行预测
    forecast ,tmp = Forecast(data,weight,N,index)

    #进行数据修正
    _error = data[index] - forecast
    error[index] = _error
    #data[index] = forecast
    for i in range(N):
        weight[i] = weight[i] + 2 *K * error[index] * tmp[i] 

    return weight,error

def Adaptive_Filtering_Model(data,weight,error,N,K):
    """
        时间序列自适应滤波法模型
    """    

    #误差的最大值
    weight,error = Adaptive_Filtering(data,weight,error,N,K,N)
    error_max = max(error)

    #开始进行自适应滤波法，进行迭代修改数据
    '''
        第一次循环单独考虑
    '''
    for i in range(N+1,len(data)):
        weight,error = Adaptive_Filtering(data,weight,error,N,K,i)
    error_max = max(error)
    while error_max > 0.00001:
        for i in range(N,len(data)):
            weight,error = Adaptive_Filtering(data,weight,error,N,K,i)
        error_max = max(error)

    #对数据进行预测
    forecast,tmp = Forecast(data,weight,N,len(data))
    j = len(data)+1
    print('第',j,'期数据预测值为:',forecast)

def run_main():
    '''
        这是主函数
    '''

    #10个测试数据
    data = []
    for i in range(10):
        tmp = (i + 1)* 1.0 /10
        data.append(tmp)

    #权值以及权值个数
    weight = [0.5,0.5]
    N = len(weight)

    #学习系数
    K = 0.9

    #误差数组
    error = []
    for i in range(len(data)):
        error.append(0)

    print('权值为:',weight)
    print('数据为:',data,'\n')
    #模型运用
    Adaptive_Filtering_Model(data,weight,error,N,K)


if __name__ == '__main__':
    run_main()