七、置信区间

import pandas as pd
import numpy as np
from scipy.stats import norm
ms = pd.read_csv('data/microsoft.csv',index_col=0)
ms.index=pd.to_datetime(ms.index)
ms.head()

Estimate the average stock return with 90% Confidence Interval

# we will use log return for average stock return of Microsoft

ms['logReturn'] = np.log(ms['Close'].shift(-1)) - np.log(ms['Close'])
# Lets build 90% confidence interval for log return
sample_size = ms['logReturn'].shape[0]
sample_mean = ms['logReturn'].mean()
sample_std = ms['logReturn'].std(ddof=1) / sample_size**0.5

# left and right quantile
z_left =norm.ppf(0.05)
z_right = norm.ppf(0.95)

# upper and lower bound
interval_left = sample_mean+z_left*sample_std
interval_right = sample_mean+z_right*sample_std
# 90% confidence interval tells you that there will be 90% chance that the average stock return lies between "interval_left"
# and "interval_right".

print('90% confidence interval is ', (interval_left, interval_right))

Expected output: 90% confidence interval is (-1.5603253899378836e-05, 0.001656066226145423)