INAR(1)模型參數估計的電腦實現

標籤：

1. 估計方法：Yule-Walker估計

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2. 運行環境spyder2(python科學計算編輯器)

3. 實現代碼

# -*- coding: utf-8 -*-import numpy as np#建立數組用的包#設定初值A=9f = open(‘/Users/gaojiaxing/desktop/data.txt‘,‘a‘,encoding = ‘utf-8‘)f.write(‘時間跨度‘+‘ ‘+‘p值‘+‘ ‘+‘lamb值‘+‘ ‘+‘p均方誤差‘+‘ ‘+‘lamb均方誤差‘+‘ ‘+‘p的估計‘+‘ ‘+‘p的估計‘+‘ ‘+‘p的估計‘+‘ ‘+‘lamb的估計‘+‘ ‘+‘lamb的估計‘+‘ ‘+‘lamb的估計‘+‘\n‘)f.close()def sample_cov(alist,k):    ‘‘‘    這個函數是用來計算樣本的自共變數函數    ‘‘‘    n = len(alist)    sum1 = 0    for i in range(n-k):        sum1 = sum1 + (alist[i]-np.mean(alist))*(alist[i+k]-np.mean(alist))    return sum1/n    def calc_lamb(alist):    ‘‘‘    yule-walker估計求誤差項的    ‘‘‘    n = len(alist)    error_sum = 0    for j in range(n-1):        error_sum = error_sum + alist[j+1]-p*alist[j]    return error_sum  for time_len in range(50,250,50):#時間序列長度    for p in np.arange(0,1,0.1):#讓p值取0,0.1，0.2，...0.9的所有結果        for lamb in np.arange(0.2,1.4,0.4):#lamb取值0.2，0.6，1                        claim_time_series = []#類比的最終1000組時間序列的存放在這裡                for i in range(1000):                one_case = list(range(time_len))#one_case是一個理賠時間序列                one_case[0] = int(lamb/(1-p))                for j in range(1,time_len):                    one_case[j] = (np.random.binomial(one_case[j-1],p,size=1)+                    np.random.poisson(lamb*np.random.gamma(shape=A,scale=1/A,size=1)))[0]                                    claim_time_series.append(one_case)                            p_hat = []#根據樣本估計出來的P估計值將要存放的地方            for j in range(1000):                p_hat.append(sample_cov(claim_time_series[j],1)/sample_cov(claim_time_series[j],0))                            p_array = np.array(p_hat).reshape(1000)#轉換成數組，便於運算            p_mse = sum((p_array-p*np.ones(1000))**2)/1000#均方誤差            lamb_hat = []            for i in range(1000):                lamb_hat.append(calc_lamb(claim_time_series[i])/(time_len-1))                            lamb_array = np.array(lamb_hat).reshape(1000)                        lamb_mse = sum((lamb_array-lamb*np.ones(1000))**2)/1000            f = open(‘/Users/gaojiaxing/desktop/data.txt‘,‘a‘,encoding = ‘utf-8‘)            f.write(str(time_len)+‘ ‘+str(p)+‘ ‘+str(lamb)+‘ ‘+str(p_mse)+‘ ‘+            str(lamb_mse)+‘ ‘+str(p_array[0])+‘ ‘+str(p_array[1])+‘ ‘+str(p_array[2])+‘ ‘+            str(lamb_array[0])+‘ ‘+str(lamb_array[1])+‘ ‘+str(lamb_array[2])+‘\n‘)            f.close()

 

INAR(1)模型參數估計的電腦實現