python 时间序列处理

作者: 安徒生 | 来源:发表于2019-05-16 21:47 被阅读0次

数据说明：’./data/raw/pm25.csv’文件为某地2017年一段时间内的PM2.5的每小时监测数据，数据按时间顺序记录（从2017-01-01 00:00:00开始，中间不间断），由于各种原因造成了某些时刻的数据缺失。

要求：

1.利用已有的记录数据进行建模，将缺失值填充完整，评估指标采用RMSE、MAE和；

2.尝试多种方法进行建模，对比各种模型的性能;

3.希望你不要直接用中值、均值、前一时刻、后一时刻等常数填充法进行填充（方法对比中可用做简单对比，如表 2所示）；

4.将数据填充完整后保存至’pm25_predicted.csv’文件（只保存缺失时刻的数据，不按要求则作废），数据格式如表 3所示（列名、文件名不按要求则作废）。

题解：

（1）完成时间序列缺失数据填充，一般来说有如下几种方式：常数填充有均值填充，中位数填充，众数填充，前一时刻和后一时刻填充，传统回归模型方式有自回归模型，移动平均模型，自回归移动平均模型和差分自回归移动平均模型，一般采用插值法填充数据，插值办法一般有滑动平均插值，线性插值，拉格朗日多项式插值；

（2）每个函数对应一种办法，先将数据用pandas从csv文件中读取为df,然后进行数据插值的算法操作，最后将插值后的数据集用matplotlib呈现出来，最后将插值的数据转化为df，用pandas重新写回csv之中；

代码：

1.time_series_fill.py

# -*- coding:utf-8 -*-

from pandas.compat import reduce

__author__ = 'gin.chen'

import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

from scipy.interpolate import lagrange

# from fbprophet import Prophet

#

# 加载数据

def load_data():

df = pd.read_csv('F:/muke/super_mali/data/raw/pm25.csv')

# return df.head(100)

return df

# 画散点图

def draw_scatte_diagram(df):

plt.plot(df['index'].to_list(), df['PM2.5'].to_list())

plt.show()

# 均值填充

def mean_method():

df = load_data()

df.fillna(df['PM2.5'].mean(), inplace=True)

draw_scatte_diagram(df)

# 中位数填充

def median_method():

df = load_data()

df.fillna(df['PM2.5'].median(), inplace=True)

draw_scatte_diagram(df)

# 众数填充

def mode_method():

df = load_data()

df.fillna(df['PM2.5'].mode(), inplace=True)

draw_scatte_diagram(df)

# 前一时刻填充

def ffill_method():

df = load_data()

df['PM2.5'].fillna(method='ffill', inplace=True)

draw_scatte_diagram(df)

# 后一时刻填充

def bfill_method():

df = load_data()

df['PM2.5'].fillna(method='bfill', inplace=True)

draw_scatte_diagram(df)

# 前后时刻平均值插值

def mean_by_before_after_method():

df = load_data()

# data_index = df['index'].to_list()

# data_value = df['PM2.5'].to_list()

fill = []

for i in range(len(df)):

if np.math.isnan(df.iloc[i - 1][1]):

left = df.iloc[i - 2][1]

for j in range(i, len(df)):

if np.math.isnan(df.iloc[j][1]):

continue

else:

right = df.iloc[j][1]

break

df.iloc[i - 1, 1] = (left + right) / 2

fill_tuple = i, df.iloc[i - 1][1]

fill.append(fill_tuple)

draw_scatte_diagram(df)

df = pd.DataFrame(fill, columns=['index', 'PM2.5'])

df.to_csv('pm25_predicted_mean.csv', index=False)

# 线性插值详细

def linear_detail(x1, y1, x2, y2):

k = (y2 - y1) / (x2 - x1)

b = y1 - k * x1

return lambda x: b + k * x

# 线性插值

def linear_method():

# global j

df = load_data()

fill = []

for i in range(len(df)):

if np.isnan(df.iloc[i][1]):

for j in range(i, len(df)):

if np.isnan(df.iloc[j][1]):

continue

else:

break

df.iloc[i, 1] = (linear_detail(i, df.iloc[i - 1][1], j + 1, df.iloc[j][1]))(i + 1)

fill_tuple = i + 1, df.iloc[i][1]

fill.append(fill_tuple)

draw_scatte_diagram(df)

df = pd.DataFrame(fill, columns=['index', 'PM2.5'])

df.to_csv('pm25_predicted_linear.csv', index=False)

# 平滑插值详细

def smooth_detail(series, pos, window=5):

"""

:param series: 列向量

:param pos: 被插值的位置

:param window: 为取前后的数据个数

:return:

"""

y = series[list(range(pos - window, pos)) + list(range(pos + 1, pos + 1 + window))] # 取数

y = y[y.notnull()]

return reduce(lambda a, b: a + b, y) / len(y)

# 平滑插值

def smooth_method(show=1):

df_raw = load_data()

df = df_raw['PM2.5'].copy()

full = []

for j in range(len(df)):

if (df.isnull())[j]: # 如果为空即插值。

df[j] = smooth_detail(df, j)

df_raw.loc[j, 'PM2.5'] = df[j]

# print(j, df_raw.loc[j, 'index'], df_raw.loc[j, 'PM2.5'])

full_tuple = df_raw.loc[j, 'index'], df_raw.loc[j, 'PM2.5']

full.append(full_tuple)

if show:

draw_scatte_diagram(df_raw)

df = pd.DataFrame(full, columns=['index', 'PM2.5'])

df.to_csv('pm25_predicted_smooth.csv', index=False)

return df_raw

# 拉格朗日插值详细

def lagrange_detail(series, pos, window=5):

"""

:param series: 列向量

:param pos: 被插值的位置

:param window: 为取前后的数据个数

:return:

"""

y = series[list(range(pos - window, pos)) + list(range(pos + 1, pos + 1 + window))] # 取数

y = y[y.notnull()] # 剔除空值

return lagrange(y.index, list(y))(pos) # 插值并返回插值结果

# 拉格朗日插值

def lagrange_method():

df_raw = load_data()

df = df_raw['PM2.5'].copy()

full = []

for j in range(len(df)):

if (df.isnull())[j]: # 如果为空即插值。

df[j] = lagrange_detail(df, j)

df_raw.loc[j, 'PM2.5'] = df[j]

# print(j, df.loc[j, 'index'], df[j])

full_tuple = df_raw.loc[j, 'index'], df_raw.loc[j, 'PM2.5']

full.append(full_tuple)

draw_scatte_diagram(df_raw)

df = pd.DataFrame(full, columns=['index', 'PM2.5'])

df.to_csv('pm25_predicted_lagrange.csv', index=False)

# 计算RMSE

def calculate_RMSE(target, prediction):

error = []

for i in range(len(target)):

error.append(target[i] - prediction[i])

return (sum([n * n for n in error]) / len(error)) ** 0.5

# 计算MAE

def calculate_MAE(target, prediction):

error = []

for i in range(len(target)):

error.append(target[i] - prediction[i])

return sum([abs(n) for n in error]) / len(error)

# 计算R-square

def calculate_R_Square(target, prediction):

error = []

a = calculate_MAE(target, prediction) * len(error)

mean = np.mean(np.array(target))

for i in range(len(target)):

error.append(prediction[i] - mean)

b = sum([n * n for n in error])

return 1 - a / b

if __name__ == '__main__':

# mean_method()

# median_method()

# mode_method()

# ffill_method()

# bfill_method()

# mean_by_before_after_method()

# linear_method()

# lagrange_method()

smooth_method()

2.fbprophet_fill.py

# -*- coding:utf-8 -*-

from pandas.io.sas.sas7bdat import _column

from time_series_fill import smooth_method

__author__ = 'gin.chen'

import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

import datetime

from fbprophet import Prophet

if __name__ == '__main__':

def load_data():

# df = pd.read_csv('F:/muke/super_mali/data/raw/pm25.csv')

# return df.head(100)

df = smooth_method(0)

return df.head(3129)

df = load_data()

first_value = datetime.datetime.strptime('2017-01-01 00:00:00', '%Y-%m-%d %H:%M:%S')

for i in range(len(df)):

df.iloc[i, 0] = (first_value + datetime.timedelta(hours=i)).strftime("%Y-%m-%d %H:%M:%S")

# df = pd.DataFrame(, columns=['ds', 'y'])

# df.to_csv('pm25_predicted_mean.csv', index=False)

# print(df.iloc[1,0])

df.rename(columns={'index': 'ds', 'PM2.5': 'y'}, inplace=True)

m = Prophet()

# df['y'] = np.log(df['y'])

df = m.fit(df)

future = m.make_future_dataframe(freq='H', periods=5428)

future.tail()

forecast = m.predict(future)

forecast[['ds', 'yhat', 'yhat_lower', 'yhat_upper']].tail()

fig1 = m.plot(forecast)

fig2 = m.plot_components(forecast)

plt.show()