时间序列(三)---AI那点小事

修正指数曲线法Python代码如下:

# -*- coding: utf-8 -*- """ Created on Sun Jan 15 15:36:15 2017 @author: DaiPuWei """ ''' 时间序列修正指数曲线法，以收音机销售量为例 ''' import pandas as pd import numpy as np import math def Check_Data(data): ''' 检查数据增长率函数,即检查增长率是否稳定在某一常数 data是数据样本 ''' error = [] flag = False for i in range(1,len(data)-1): err1 = data[i+1] - data[i] err2 = data[i] - data[i-1] error.append(err1/err2) tmp = np.array(error) _range = sum(tmp) / len(tmp) if all(tmp>_range-0.2) and all(tmp<_range+0.2): flag = True return flag def subarrsum(data,start,end): ''' 数组切片求和 ''' tmp = [] for i in range(start,end): tmp.append(data[i]) return sum(tmp) def Index_Curve_Model(data,year,T): """ 修正指数曲线方法 模型为: Y(t) = K + a * b^(t-t0+1) data为数据集 T为预测年份 """ forecast = 0 #增长率若稳定在某一常数则进行模型求解 if Check_Data(data) == True: #将数据分成3份 len1 = (int)(len(data) / 3) len2 = len(data) - len1 len3 = len(data) #各份数据的总和 tmp = [] for i in range(len(data)): tmp.append(data[i]) sum1 = subarrsum(data,0,len1) sum2 = subarrsum(data,len1,len2) sum3 = subarrsum(data,len2,len3) #各个参数值的求解 b = math.pow((sum3-sum2)/(sum2-sum1),1.0/len1) a = (sum2-sum1) * (b-1) / (b * (math.pow(b,len1)-1) * (math.pow(b,len1)-1)) K = (sum1 - a*b*(math.pow(b,len1)-1)/(b-1)) / len1 if a > 0: print('修正指数曲线模型: Y(t)=',K,'+',a,'*',b,'^(T-',year[0],')') elif a == 0: print('修正指数曲线模型: Y(t)=',K) elif a < 0: print('修正指数曲线模型: Y(t)=',K,a,'*',b,'^(',T,'-',year[0],'+1)') forecast = K + a * math.pow(b,T-year[0]+1) else: print("数据不真实，重新输入数据!") 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\收音机销售量.xlsx') data = sample[sample.columns[1]] year = sample[sample.columns[0]] #模型预测 T = 1986 forecast = Index_Curve_Model(data,year,T) print(T,'年的收音机销售额预测值为:',forecast) if __name__ == '__main__': run_main()

Compertz曲线法Python代码如下:

# -*- coding: utf-8 -*- """ Created on Sun Jan 15 21:54:47 2017 @author: DaiPuWei """ ''' 时间序列Compertz曲线法，以收音机销售量为例 ''' import pandas as pd import numpy as np import math def Check_Data(data): ''' 检查数据增长率函数,即检查增长率是否稳定在某一常数 data是数据样本 ''' error = [] flag = False for i in range(1,len(data)-1): err1 = data[i+1] - data[i] err2 = data[i] - data[i-1] error.append(err1/err2) tmp = np.array(error) _range = sum(tmp) / len(tmp) if all(tmp>_range-0.2) and all(tmp<_range+0.2): flag = True return flag def subarrsum(data,start,end): ''' 数组切片求和 ''' tmp = [] for i in range(start,end): tmp.append(data[i]) return sum(tmp) def Compertz_Model(data,year,T): """ 修正指数曲线方法 模型为: Y(t) = e^(K + a * b^(t-t0+1)) data为数据集 T为预测年份 """ forecast = 0 #增长率若稳定在某一常数则进行模型求解 if Check_Data(data) == True: #将数据分成3份 len1 = (int)(len(data) / 3) len2 = len(data) - len1 len3 = len(data) #各份数据的总和 tmp = [] for i in range(len(data)): tmp.append(data[i]) sum1 = subarrsum(data,0,len1) sum2 = subarrsum(data,len1,len2) sum3 = subarrsum(data,len2,len3) #各个参数值的求解 b = math.pow((sum3-sum2)/(sum2-sum1),1.0/len1) a = (sum2-sum1) * (b-1) / (b * (math.pow(b,len1)-1) * (math.pow(b,len1)-1)) K = (sum1 - a*b*(math.pow(b,len1)-1)/(b-1)) / len1 if a > 0: print('Compertz曲线模型: Y(t)=',K,'*',a,'^(',b,'^(T-',year[0],'+1))') elif a == 0: print('Compertz曲线模型: Y(t)=',K) elif a < 0: print('Compertz曲线模型: Y(t)=',K,'*(',a,')^(',b,'^(T','-',year[0],'+1))') tmp = math.pow(b,T-year[0]+1) forecast = K + a*tmp forecast = math.exp(forecast) else: print("数据不真实，重新输入数据!") 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\收音机销售量.xlsx') data = sample[sample.columns[1]] _data = [] for i in range(len(data)): _data.append(math.log(data[i])) year = sample[sample.columns[0]] #模型预测 T = 1986 forecast = Compertz_Curve_Model(_data,year,T) print(T,'年的收音机销售额预测值为:',forecast) if __name__ == '__main__': run_main()

Logistic曲线（生长曲线）法Python代码如下:

# -*- coding: utf-8 -*- """ Created on Sun Jan 15 22:07:39 2017 @author: DaiPuWei """ ''' 时间序列Compertz曲线法，以收音机销售量为例 ''' import pandas as pd import numpy as np import math def Check_Data(data): ''' 检查数据增长率函数,即检查增长率是否稳定在某一常数 data是数据样本 ''' error = [] flag = False for i in range(1,len(data)-1): err1 = data[i+1] - data[i] err2 = data[i] - data[i-1] error.append(err1/err2) tmp = np.array(error) _range = sum(tmp) / len(tmp) if all(tmp>_range-0.2) and all(tmp<_range+0.2): flag = True return flag def subarrsum(data,start,end): ''' 数组切片求和 ''' tmp = [] for i in range(start,end): tmp.append(data[i]) return sum(tmp) def Logistic_Model(data,year,T): """ 修正指数曲线方法 模型为: Y(t) = 1/(K + a * b^(t-t0)) data为数据集 T为预测年份 """ forecast = 0 #增长率若稳定在某一常数则进行模型求解 if Check_Data(data) == True: #将数据分成3份 len1 = (int)(len(data) / 3) len2 = len(data) - len1 len3 = len(data) #各份数据的总和 tmp = [] for i in range(len(data)): tmp.append(data[i]) sum1 = subarrsum(data,0,len1) sum2 = subarrsum(data,len1,len2) sum3 = subarrsum(data,len2,len3) #各个参数值的求解 b = math.pow((sum3-sum2)/(sum2-sum1),1.0/len1) a = (sum2-sum1) * (b-1) / (b * (math.pow(b,len1)-1) * (math.pow(b,len1)-1)) K = (sum1 - a*b*(math.pow(b,len1)-1)/(b-1)) / len1 if a > 0: print('Logistic曲线模型: Y(t)=1/(',K,'+',a,'*',b,'^(T-',year[0],'+1))') elif a == 0: print('Logistic曲线模型: Y(t)=',K) elif a < 0: print('Logistic曲线模型: Y(t)=1/(',K,'+',a,'*',b,'^(T','-',year[0],'+1))') tmp = math.pow(b,T-year[0]+1) forecast = K + a*tmp forecast = 1.0 / forecast else: print("数据不真实，重新输入数据!") 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\收音机销售量.xlsx') data = sample[sample.columns[1]] _data = [] for i in range(len(data)): _data.append(1.0/data[i]) year = sample[sample.columns[0]] #模型预测 T = 1986 forecast = Logistic_Model(_data,year,T) print(T,'年的收音机销售额预测值为:',forecast) if __name__ == '__main__': run_main()

(时间序列模型中的ARMA模型由于原理对我来说理解有些困难，加之最近的北美数学建模大赛即将开始，自己为了顾全大局，多看掌握几个重要模型，所以ARMA模型的Python代码暂时不更新，等比赛过后有时间再更新！！！！)

---来自腾讯云社区的---AI那点小事