[2]自我回歸模型.py

# -*- coding: utf-8 -*-
"""[2]自我回歸模型.ipynb

Automatically generated by Colaboratory.

Original file is located at
    https://colab.research.google.com/drive/1zni84oomRNu0tTKKy9lDKTVPuOWhMifN
"""

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Commented out IPython magic to ensure Python compatibility.
# %matplotlib inline

import ffn

import statsmodels.api as sm

"""# 自我回歸模型
- 模擬不同beta下的`AR(1)`序列
- 利用匯率資料估計`AR(1)`模型參數
- 購買力困惑 (PPP puzzle)

## 模擬不同beta下的AR(1)序列
- $ \beta_1 = 0.2$
- $\beta_1 = 0.95$
- $\beta_0 = 0$
- 模型設定
$$
y_t = \beta_0 + \beta_1 y_{t-1} + \epsilon_t
$$
- 設定初始值 $y_0 = 0$
- 生成隨機數 $\epsilon_1\sim N(0,1)$
- 得到序列值 $y_1$
- 依此類推可得所有序列值
"""

len(y)

y = np.zeros(1001)

range(1,1000)

for i in range(1,10):
    print(i)

for i in range(1,10):
    print(i)



# set beta
b_0 = 0
b_11 = 0.2
b_12 = 0.95
sigma = 1
x = np.zeros(1000)
y = np.zeros(1000)
for i in range(1,1000):
    x[i] = b_0 + b_11*x[i-1] + np.random.randn()
    y[i] = b_0 + b_12*y[i-1] + np.random.randn()


plt.plot(x,'--')
plt.plot(y,'-')
plt.title('beta=0.2 & 0.95')
plt.xlabel('Time')
plt.ylabel('Series')

data = ffn.get('EURUSD=X',start='2010-01-01',end='2020-12-31')
data.info()

# AR(1): eurusd
y = data.eurusdx
x = sm.add_constant(data.eurusdx.shift(1))
res = sm.OLS(y,x,missing='drop').fit()
print(res.summary())

res.resid.plot()
#res.fittedvalues.plot()

# generate log return
data['ret'] = np.log(data.eurusdx).diff()
data.head()

data.ret

# AR(1): ret_eurusd
x = sm.add_constant(data.ret.shift(1))
y = data.ret
res = sm.OLS(y,x,missing='drop').fit()
print(res.summary())

# test PPP puzzle

test = pd.read_csv('re_us.csv',index_col='DATE')
test.info()

# set date index
test.index = pd.to_datetime(test.index)

x = sm.add_constant(test.RBUSBIS.shift())
y = test.RBUSBIS
res = sm.OLS(y,x,missing='drop').fit()
print(res.summary())

# calculate the half-life (month frequency)
np.log(0.5)/np.log(0.9888)



# import package
from statsmodels.tsa.ar_model import ar_select_order
# data: y
# ic='aic'/'bic'
mod = ar_select_order(y, ic='aic', maxlag=10)
mod.ar_lags