时间序列(二)---AI那点小事

一次指数平滑法Python代码如下:

# -*- 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()

二次指数平滑法Python代码如下:

# -*- 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()

三次指数平滑法Python代码如下:

# -*- 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()

一次差分指数平滑法Python代码如下:

# -*- 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()

二阶差分指数平滑法

# -*- 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()

自适应滤波法Python代码如下:

# -*- 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() ---来自腾讯云社区的---AI那点小事