使用 statsmodels 进行时间序列分析

Question

我正在尝试对时间序列数据进行多重回归，但是当我将时间序列列添加到我的模型时，它最终会将每个唯一值视为一个单独的变量，就像这样（我的“日期”列是输入日期时间）：

est = smf.ols(formula='r ~ spend + date', data=df).fit()
print est.summary()

coef    std err t   P>|t|   [95.0% Conf. Int.]
Intercept   -6.249e-10  inf -0  nan nan nan
date[T.Timestamp('2014-10-08 00:00:00')]    -2.571e-10  inf -0  nan nan nan
date[T.Timestamp('2014-10-15 00:00:00')]    9.441e-11   inf 0   nan nan nan
date[T.Timestamp('2014-10-22 00:00:00')]    5.619e-11   inf 0   nan nan nan
date[T.Timestamp('2014-10-29 00:00:00')]    -8.035e-12  inf -0  nan nan nan
date[T.Timestamp('2014-11-05 00:00:00')]    6.334e-11   inf 0   nan nan nan
date[T.Timestamp('2014-11-12 00:00:00')]    7.9e+04 inf 0   nan nan nan
date[T.Timestamp('2014-11-19 00:00:00')]    1.58e+05    inf 0   nan nan nan
date[T.Timestamp('2014-11-26 00:00:00')]    1.58e+05    inf 0   nan nan nan
date[T.Timestamp('2014-12-03 00:00:00')]    1.58e+05    inf 0   nan nan nan
date[T.Timestamp('2014-12-10 00:00:00')]    2.28e+05    inf 0   nan nan nan
date[T.Timestamp('2014-12-17 00:00:00')]    3.28e+05    inf 0   nan nan nan
date[T.Timestamp('2014-12-24 00:00:00')]    3.705e+05   inf 0   nan nan nan
spend   2.105e-10   inf 0   nan nan nan

我也尝试了 statsmodel 的 tms 包，但不确定如何处理“频率”：

ar_model = sm.tsa.AR(df, freq='1')

ValueError: Pandas data cast to numpy dtype of object. Check input data with np.asarray(data).

Answer 1

我真的很想看到一个数据样本以及一个代码 sn-p 来重现您的错误。 否则，我的建议将无法解决您的特定错误消息。但是，它可以让您对存储在 pandas 数据框中的一组时间序列进行多元回归分析。假设您在时间序列中使用的是连续值而不是分类值，下面是我使用 pandas 和 statsmodels 的方法：

具有随机值的数据框：

# Imports
import pandas as pd
import numpy as np
import itertools


np.random.seed(1)
rows = 12
listVars= ['y','x1', 'x2', 'x3']
rng = pd.date_range('1/1/2017', periods=rows, freq='D')
df_1 = pd.DataFrame(np.random.randint(100,150,size=(rows, len(listVars))), columns=listVars) 
df_1 = df_1.set_index(rng)

print(df_1)

输出 - 一些可以使用的数据：

              y   x1   x2   x3
2017-01-01  137  143  112  108
2017-01-02  109  111  105  115
2017-01-03  100  116  101  112
2017-01-04  107  145  106  125
2017-01-05  120  137  118  120
2017-01-06  111  142  128  129
2017-01-07  114  104  123  123
2017-01-08  141  149  130  132
2017-01-09  122  113  141  109
2017-01-10  107  122  101  100
2017-01-11  117  108  124  113
2017-01-12  147  142  108  130

下面的函数将让您指定源数据框以及因变量 y 和自变量选择 x1, x2。使用 statsmodels，一些期望的结果将存储在数据框中。在那里，R2 将是数值类型，而回归系数和 p 值将是列表，因为这些估计值的数量会随着您希望包含在分析中的自变量数量而变化。

def LinReg(df, y, x, const):

    betas = x.copy()

    # Model with out without a constant
    if const == True:
        x = sm.add_constant(df[x])
        model = sm.OLS(df[y], x).fit()
    else:
        model = sm.OLS(df[y], df[x]).fit()

    # Estimates of R2 and p
    res1 = {'Y': [y],
            'R2': [format(model.rsquared, '.4f')],
            'p': [model.pvalues.tolist()],
            'start': [df.index[0]], 
            'stop': [df.index[-1]],
            'obs' : [df.shape[0]],
            'X': [betas]}
    df_res1 = pd.DataFrame(data = res1)

    # Regression Coefficients
    theParams = model.params[0:]
    coefs = theParams.to_frame()
    df_coefs = pd.DataFrame(coefs.T)
    xNames = list(df_coefs)
    xValues = list(df_coefs.loc[0].values)
    xValues2 = [ '%.2f' % elem for elem in xValues ]
    res2 = {'Independent': [xNames],
            'beta': [xValues2]}
    df_res2 = pd.DataFrame(data = res2)

    # All results
    df_res = pd.concat([df_res1, df_res2], axis = 1)
    df_res = df_res.T
    df_res.columns = ['results']
    return(df_res)

这是一个测试运行：

df_regression = LinReg(df = df, y = 'y', x = ['x1', 'x2'], const = True)
print(df_regression)

输出：

                                                            results
R2                                                       0.3650
X                                                      [x1, x2]
Y                                                             y
obs                                                          12
p             [0.7417691742514285, 0.07989515781898897, 0.25...
start                                       2017-01-01 00:00:00
stop                                        2017-01-12 00:00:00
Independent                                     [const, x1, x2]
coefficients                                [16.29, 0.47, 0.37]

这是一个简单的复制粘贴的全部内容：

# Imports
import pandas as pd
import numpy as np
import statsmodels.api as sm

np.random.seed(1)
rows = 12
listVars= ['y','x1', 'x2', 'x3']
rng = pd.date_range('1/1/2017', periods=rows, freq='D')
df = pd.DataFrame(np.random.randint(100,150,size=(rows, len(listVars))), columns=listVars) 
df = df.set_index(rng)

def LinReg(df, y, x, const):

    betas = x.copy()

    # Model with out without a constant
    if const == True:
        x = sm.add_constant(df[x])
        model = sm.OLS(df[y], x).fit()
    else:
        model = sm.OLS(df[y], df[x]).fit()

    # Estimates of R2 and p
    res1 = {'Y': [y],
            'R2': [format(model.rsquared, '.4f')],
            'p': [model.pvalues.tolist()],
            'start': [df.index[0]], 
            'stop': [df.index[-1]],
            'obs' : [df.shape[0]],
            'X': [betas]}
    df_res1 = pd.DataFrame(data = res1)

    # Regression Coefficients
    theParams = model.params[0:]
    coefs = theParams.to_frame()
    df_coefs = pd.DataFrame(coefs.T)
    xNames = list(df_coefs)
    xValues = list(df_coefs.loc[0].values)
    xValues2 = [ '%.2f' % elem for elem in xValues ]
    res2 = {'Independent': [xNames],
            'beta': [xValues2]}
    df_res2 = pd.DataFrame(data = res2)

    # All results
    df_res = pd.concat([df_res1, df_res2], axis = 1)
    df_res = df_res.T
    df_res.columns = ['results']
    return(df_res)

df_regression = LinReg(df = df, y = 'y', x = ['x1', 'x2'], const = True)

print(df_regression)

Answer 2

您为每个日期拟合一个线性模型，因为 ols 将日期视为分类变量。我建议你试试：

est = smf.ols(formula='r ~ spend', data=df).fit()
print est.summary()

对于 statsmodel 试试：

ar_model = sm.tsa.AR(df['spend'], freq='1')