pandas 傅立叶级数列未出现在Deterministicprocess()中

9cbw7uwe 于 2022-12-16 发布在其他

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我一直在刷新我的时间序列技能，但我在创建傅立叶级数时遇到了麻烦。以下是数据（如果你把所有数据都放在一起运行，它会给予你同样的图和最终表格）：

import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.deterministic import CalendarFourier, DeterministicProcess
from sklearn.linear_model import LinearRegression

df = pd.DataFrame({'Pax': {Period('1949-01', 'M'): 112,  Period('1949-02', 'M'): 118,  Period('1949-03', 'M'): 132,  Period('1949-04', 'M'): 129,  Period('1949-05', 'M'): 121,  Period('1949-06', 'M'): 135,  Period('1949-07', 'M'): 148,  Period('1949-08', 'M'): 148,  Period('1949-09', 'M'): 136,  Period('1949-10', 'M'): 119,  Period('1949-11', 'M'): 104,  Period('1949-12', 'M'): 118,  Period('1950-01', 'M'): 115,  Period('1950-02', 'M'): 126,  Period('1950-03', 'M'): 141,  Period('1950-04', 'M'): 135,  Period('1950-05', 'M'): 125,  Period('1950-06', 'M'): 149,  Period('1950-07', 'M'): 170,  Period('1950-08', 'M'): 170,  Period('1950-09', 'M'): 158,  Period('1950-10', 'M'): 133,  Period('1950-11', 'M'): 114,  Period('1950-12', 'M'): 140,  Period('1951-01', 'M'): 145,  Period('1951-02', 'M'): 150,  Period('1951-03', 'M'): 178,  Period('1951-04', 'M'): 163,  Period('1951-05', 'M'): 172,  Period('1951-06', 'M'): 178,  Period('1951-07', 'M'): 199,  Period('1951-08', 'M'): 199,  Period('1951-09', 'M'): 184,  Period('1951-10', 'M'): 162,  Period('1951-11', 'M'): 146,  Period('1951-12', 'M'): 166,  Period('1952-01', 'M'): 171,  Period('1952-02', 'M'): 180,  Period('1952-03', 'M'): 193,  Period('1952-04', 'M'): 181,  Period('1952-05', 'M'): 183,  Period('1952-06', 'M'): 218,  Period('1952-07', 'M'): 230,  Period('1952-08', 'M'): 242,  Period('1952-09', 'M'): 209,  Period('1952-10', 'M'): 191,  Period('1952-11', 'M'): 172,  Period('1952-12', 'M'): 194,  Period('1953-01', 'M'): 196,  Period('1953-02', 'M'): 196,  Period('1953-03', 'M'): 236,  Period('1953-04', 'M'): 235,  Period('1953-05', 'M'): 229,  Period('1953-06', 'M'): 243,  Period('1953-07', 'M'): 264,  Period('1953-08', 'M'): 272,  Period('1953-09', 'M'): 237,  Period('1953-10', 'M'): 211,  Period('1953-11', 'M'): 180,  Period('1953-12', 'M'): 201,  Period('1954-01', 'M'): 204,  Period('1954-02', 'M'): 188,  Period('1954-03', 'M'): 235,  Period('1954-04', 'M'): 227,  Period('1954-05', 'M'): 234,  Period('1954-06', 'M'): 264,  Period('1954-07', 'M'): 302,  Period('1954-08', 'M'): 293,  Period('1954-09', 'M'): 259,  Period('1954-10', 'M'): 229,  Period('1954-11', 'M'): 203,  Period('1954-12', 'M'): 229,  Period('1955-01', 'M'): 242,  Period('1955-02', 'M'): 233,  Period('1955-03', 'M'): 267,  Period('1955-04', 'M'): 269,  Period('1955-05', 'M'): 270,  Period('1955-06', 'M'): 315,  Period('1955-07', 'M'): 364,  Period('1955-08', 'M'): 347,  Period('1955-09', 'M'): 312,  Period('1955-10', 'M'): 274,  Period('1955-11', 'M'): 237,  Period('1955-12', 'M'): 278,  Period('1956-01', 'M'): 284,  Period('1956-02', 'M'): 277,  Period('1956-03', 'M'): 317,  Period('1956-04', 'M'): 313,  Period('1956-05', 'M'): 318,  Period('1956-06', 'M'): 374,  Period('1956-07', 'M'): 413,  Period('1956-08', 'M'): 405,  Period('1956-09', 'M'): 355,  Period('1956-10', 'M'): 306,  Period('1956-11', 'M'): 271,  Period('1956-12', 'M'): 306,  Period('1957-01', 'M'): 315,  Period('1957-02', 'M'): 301,  Period('1957-03', 'M'): 356,  Period('1957-04', 'M'): 348,  Period('1957-05', 'M'): 355,  Period('1957-06', 'M'): 422,  Period('1957-07', 'M'): 465,  Period('1957-08', 'M'): 467,  Period('1957-09', 'M'): 404,  Period('1957-10', 'M'): 347,  Period('1957-11', 'M'): 305,  Period('1957-12', 'M'): 336,  Period('1958-01', 'M'): 340,  Period('1958-02', 'M'): 318,  Period('1958-03', 'M'): 362,  Period('1958-04', 'M'): 348,  Period('1958-05', 'M'): 363,  Period('1958-06', 'M'): 435,  Period('1958-07', 'M'): 491,  Period('1958-08', 'M'): 505,  Period('1958-09', 'M'): 404,  Period('1958-10', 'M'): 359,  Period('1958-11', 'M'): 310,  Period('1958-12', 'M'): 337,  Period('1959-01', 'M'): 360,  Period('1959-02', 'M'): 342,  Period('1959-03', 'M'): 406,  Period('1959-04', 'M'): 396,  Period('1959-05', 'M'): 420,  Period('1959-06', 'M'): 472,  Period('1959-07', 'M'): 548,  Period('1959-08', 'M'): 559,  Period('1959-09', 'M'): 463,  Period('1959-10', 'M'): 407,  Period('1959-11', 'M'): 362,  Period('1959-12', 'M'): 405,  Period('1960-01', 'M'): 417,  Period('1960-02', 'M'): 391,  Period('1960-03', 'M'): 419,  Period('1960-04', 'M'): 461,  Period('1960-05', 'M'): 472,  Period('1960-06', 'M'): 535,  Period('1960-07', 'M'): 622,  Period('1960-08', 'M'): 606,  Period('1960-09', 'M'): 508,  Period('1960-10', 'M'): 461,Period('1960-11', 'M'): 390,Period('1960-12', 'M'): 432}})
df.head()

我创建了一个常量和一个趋势：

dp = DeterministicProcess(
        index=df.index,
        constant=True,
        order=1,
        seasonal=False,
        #additional_terms=[fourier],
        drop=True,
    )

X = dp.in_sample()
y = df.squeeze()

我用线性回归拟合，去趋势化时间序列，并绘制结果：

model_pax = LinearRegression().fit(X, y)
y_pred_pax = pd.Series(model_pax.predict(X), index=X.index)
y_detrended = y-y_pred_pax

fig, (ax1, ax2) = plt.subplots(2,1, sharex=True, figsize=(10, 4))

ax1 = y.plot(label='Pax', ax=ax1)
ax1 = y_pred_pax.plot(label='trend', ax=ax1)
ax1.legend()

ax2 = y_detrended.plot(label='Pax detrended', ax=ax2)
ax2.legend()
plt.show()

现在我想捕捉季节性，为此我需要做一个傅立叶序列，但是当我创建确定性过程并包括傅立叶序列时，傅立叶序列列没有出现。

fourier =  CalendarFourier(freq="M", order=4)
dp = DeterministicProcess(
        index=y_detrended.index,
        constant=True,
        order=0,
        seasonal=False,
        additional_terms=[fourier]
        drop=True,
    )

dp.in_sample().head()