将非线性单变量回归拟合到 Python 中的时间序列数据

Question

我最近开始使用 python 进行机器学习。下面是我选择的一个数据集作为示例，以及我到目前为止所使用的代码。选择 [2000....2015] 作为测试数据和训练数据 [2016, 2017]。

Dataset  
      Years        Values
    0    2000      23.0
    1    2001      27.5
    2    2002      46.0
    3    2003      56.0
    4    2004      64.8
    5    2005      71.2
    6    2006      80.2
    7    2007      98.0
    8    2008     113.0
    9    2009     155.8
    10   2010     414.0
    11   2011    2297.8
    12   2012    3628.4
    13   2013   16187.8
    14   2014   25197.8
    15   2015   42987.8
    16   2016   77555.5
    17   2017  130631.9

import pandas as pd
import numpy as np

import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split

from sklearn.ensemble import RandomForestClassifier

df = pd.DataFrame([[i for i in range(2000,2018)], 
[23.0,27.5,46.0,56.0,64.8,71.2,80.2,98.0,113.0,155.8,414.0,2297.8,3628.4,16187.8,25197.8,42987.8,77555.5,130631.9]])


df = df.T
df.columns = ['Years', 'Values']

上面的代码创建了DataFrame。要记住的另一件重要事情是我的Years 列是一个时间序列，而不仅仅是一个连续值。我没有进行任何更改来适应这一点。

我想拟合可能有帮助的非线性模型，并像我为线性模型示例所做的那样打印绘图。这是我尝试使用线性模型的方法。此外，在我自己的示例中，我似乎没有考虑到我的 Years 列是时间序列而不是连续的这一事实。

一旦我们有了模型，就想用它来预测至少未来几年的值。

X = df.iloc[:, :-1].values
y = df.iloc[:, 1].values
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.1, random_state = 0, shuffle = False)
lm = LinearRegression()
lm.fit(X_train, y_train)
y_pred = lm.predict(X_test)
plt.scatter(X_train, y_train, color = 'red')
plt.plot(X_train, lm.predict(X_train), color = 'blue')
plt.title('Years vs Values (training set)')
plt.xlabel('Years')
plt.ylabel('Values')
plt.show()

Answer 1

试试这个。您也可以打印预测值。 预计 5 年。

import numpy.polynomial.polynomial as poly
import pandas as pd
import numpy as np

import matplotlib.pyplot as plt

df = pd.DataFrame([[i for i in range(2000,2018)],
[23.0,27.5,46.0,56.0,64.8,71.2,80.2,98.0,113.0,155.8,414.0,2297.8,3628.4,16187.8,25197.8,42987.8,77555.5,130631.9]])
df = df.T
df.columns = ['Year', 'Values']
df['Year'] = df['Year'].astype(int)
df['Values'] = df['Values'].astype(int)
no_of_predictions = 5


X = np.array(df.Year, dtype = float)
y = np.array(df.Values, dtype = float)
Z = [2019,2020,2021,2022]
coefs = poly.polyfit(X, y, 4)
X_new = np.linspace(X[0], X[-1]+no_of_predictions, num=len(X)+no_of_predictions)
ffit = poly.polyval(X_new, coefs)
pred = poly.polyval(Z, coefs)
predictions = pd.DataFrame(Z,pred)
print predictions
plt.plot(X, y, 'ro', label="Original data")
plt.plot(X_new, ffit, label = "Fitted data")
plt.legend(loc='upper left')
plt.show()

Answer 2

编辑：我的回答是错误的，我习惯使用分类器而不是回归器；不删除它，因为我害怕被禁止发布更多答案。不要使用这个答案。

试试这个

import pandas as pd
import numpy as np

import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split

from sklearn.ensemble import RandomForestClassifier

df = pd.DataFrame([[i for i in range(2000,2018)], 
[23.0,27.5,46.0,56.0,64.8,71.2,80.2,98.0,113.0,155.8,414.0,2297.8,3628.4,16187.8,25197.8,42987.8,77555.5,130631.9]])


df = df.T
df.columns = ['Year', 'Values']
df['Year'] = df['Year'].astype(int)
df['Values'] = df['Values'].astype(int)

你的数据框

X = df[['Year']]
y = df[['Values']]

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.1, random_state = 0, shuffle = False)
print(X_train.shape, y_train.shape, X_test.shape, y_test.shape)

clf = RandomForestClassifier(n_estimators=10)
clf.fit(X_train, y_train)


y_pred = clf.predict(X_test)

plt.scatter(X_train, y_train, color = 'red')
plt.plot(X_train, clf.predict(X_train), color = 'blue')
plt.title('Years vs Values (training set)')
plt.xlabel('Years')

plt.xticks(rotation=90)
plt.ylabel('Values')
plt.show()

Answer 3

同时，我也试过了

import numpy.polynomial.polynomial as poly
X = np.array(df.Years, dtype = float)
y = np.array(df.Values, dtype = float)
coefs = poly.polyfit(X, y, 4)
X_new = np.linspace(X[0], X[-1], num=17)
ffit = poly.polyval(X_new, coefs)
plt.plot(X, y, 'ro', label="Original data")
plt.plot(X_new, ffit, label = "Fitted data")
plt.legend(loc='upper left')
plt.show()

它确实提供了几乎完美的契合度。但现在我不清楚如何使用这些来预测未来五年的价值。