skewness = np.mean((data-mean)3)/std3 kurtosis = np.mean((data-mean)4)/std4是什么意思

这是计算数据偏度和峰度的公式，其中mean表示数据的平均值，std表示数据的标准差，data表示数据集。偏度用来描述数据分布的不对称性，如果偏度为正，说明数据分布偏向右侧；如果偏度为负，说明数据分布偏向左侧；如果偏度为，说明数据分布对称。峰度用来描述数据分布的峰态，如果峰度大于3，说明数据分布比正态分布更陡峭；如果峰度小于3，说明数据分布比正态分布更平缓。

相关问题

data = pd.read_excel('RESSET_IDXDRET_上证.xls') data.columns = ['code','name','date', 'r'] r = data.loc[:, ['r']].values plt.plot(r) plt.show() print('交易日天数：',len(r)) print('均值、标准差、偏度、峰度、最大值、最小值和自相关系数:',r.mean(),r.std(),r.skew(),r.kurtosis(),r.max(),r.min())这段代码怎么修改

你可以将`r`从numpy数组转换为Pandas数据框，并使用Pandas的函数计算数据的均值、标准差、偏度、峰度、最大值、最小值和自相关系数。修改后的代码如下：

import pandas as pd
import numpy as np
from statsmodels.tsa.stattools import acf
import matplotlib.pyplot as plt

data = pd.read_excel('RESSET_IDXDRET_上证.xls')
data.columns = ['code', 'name', 'date', 'r']

# 将'r'列转换为numpy数组
r = data.loc[:, 'r'].values

# 将r转换为Pandas数据框
r_df = pd.DataFrame({'r': r})

# 计算交易日天数
num_trading_days = len(r_df)

# 计算均值、标准差、偏度、峰度、最大值和最小值
mean = r_df.mean().values[0]
std = r_df.std().values[0]
skewness = r_df.skew().values[0]
kurtosis = r_df.kurtosis().values[0]
max_value = r_df.max().values[0]
min_value = r_df.min().values[0]

# 计算自相关系数
acf_values = acf(r_df, nlags=len(r_df)-1)

# 绘制时间序列图
plt.plot(r)
plt.show()

# 打印结果
print('交易日天数：', num_trading_days)
print('均值：', mean)
print('标准差：', std)
print('偏度：', skewness)
print('峰度：', kurtosis)
print('最大值：', max_value)
print('最小值：', min_value)
print('自相关系数：', acf_values)

注意，`acf()`函数返回一个numpy数组，而不是Pandas数据框，因此无法使用`skew()`和`kurtosis()`函数计算偏度和峰度。如果你需要计算偏度和峰度，可以使用Numpy库中的`numpy.mean()`和`numpy.std()`函数计算样本均值和标准差，并使用`numpy.histogram()`函数计算直方图信息，然后使用`scipy.stats.skew()`和`scipy.stats.kurtosis()`函数计算偏度和峰度。

Daily foreign exchange rates (spot rates) can be obtained from the Federal Reserve Bank in St Louis (FRED). The data are the noon buying rates in New York City certified by the Federal Reserve Bank of New York. Consider the exchange rates between the U.S. dollar and the Euro from January 4, 1999 to March 8, 2013. See the file d-exuseu.txt. (a) Compute the daily log return of the exchange rate. (b) Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the log returns of the exchange rate. (c) Obtain a density plot of the daily long returns of Dollar-Euro exchange rate. (d) Test H0 : µ = 0 versus Ha : µ ̸= 0, where µ denotes the mean of the daily log return of Dollar-Euro exchange rate.

(a) The daily log return of the exchange rate can be calculated using the following formula:

log return = ln(price[t]) - ln(price[t-1])

where price[t] represents the exchange rate at time t and price[t-1] represents the exchange rate at time t-1.

Using the data in the file d-exuseu.txt, we can calculate the daily log returns as follows (assuming the data is stored in a variable called "exchange_rate"):

import numpy as np

log_returns = np.log(exchange_rate[1:]) - np.log(exchange_rate[:-1])

The first element of "exchange_rate" is excluded from the calculation because there is no previous price to compare it to.

(b) The sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the log returns can be calculated using the following code:

mean = np.mean(log_returns)
std_dev = np.std(log_returns)
skewness = stats.skew(log_returns)
kurtosis = stats.kurtosis(log_returns, fisher=False)
minimum = np.min(log_returns)
maximum = np.max(log_returns)

print("Sample mean:", mean)
print("Standard deviation:", std_dev)
print("Skewness:", skewness)
print("Excess kurtosis:", kurtosis - 3) # convert to excess kurtosis
print("Minimum:", minimum)
print("Maximum:", maximum)

This code requires the "scipy.stats" module to be imported at the beginning of the script. The output will show the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the log returns.

(c) To obtain a density plot of the daily log returns, we can use the following code:

import matplotlib.pyplot as plt

plt.hist(log_returns, bins=50, density=True)
plt.xlabel("Daily log return")
plt.ylabel("Density")
plt.show()

This code will create a histogram of the log returns with 50 bins and normalize it to create a density plot. The output will show the density plot of the log returns.

(d) To test the hypothesis H0 : µ = 0 versus Ha : µ ̸= 0, where µ denotes the mean of the daily log return of Dollar-Euro exchange rate, we can use a t-test. The null hypothesis states that the mean log return is equal to zero, while the alternative hypothesis states that the mean log return is not equal to zero.

from scipy.stats import ttest_1samp

t_stat, p_value = ttest_1samp(log_returns, 0)

print("t-statistic:", t_stat)
print("p-value:", p_value)

This code uses the "ttest_1samp" function from the "scipy.stats" module to calculate the t-statistic and the p-value. The output will show the t-statistic and the p-value of the test. If the p-value is less than the significance level (e.g., 0.05), we can reject the null hypothesis and conclude that the mean log return is significantly different from zero.