7 methods to perform Time Series forecasting

• Method 1 – Start with a Naive Approach
• Method 2 – Simple average
• Method 3 – Moving average
• Method 4 – Single Exponential smoothing
• Method 5 – Holt’s linear trend method
• Method 6 – Holt’s Winter seasonal method
• Method 7 – ARIMA

import pandas as pd import numpy as np import matplotlib.pylab as plt%matplotlib inline # 解决坐标轴刻度负号乱码 plt.rcParams['axes.unicode_minus'] = False # 解决中文乱码问题 plt.rcParams['font.sans-serif'] = ['Simhei']from matplotlib.pylab import rcParams rcParams['figure.figsize'] = 18, 6import warnings warnings.filterwarnings("ignore")

数据：1981-1990年澳大利亚墨尔本每日最低温度

#Importing data df = pd.read_csv('Train_SU63ISt.csv') #Printing head df.head()

	ID	Datetime	Count
0	0	25-08-2012 00:00	8
1	1	25-08-2012 01:00	2
2	2	25-08-2012 02:00	6
3	3	25-08-2012 03:00	2
4	4	25-08-2012 04:00	2

#Printing tail df.tail()

	ID	Datetime	Count
18283	18283	25-09-2014 19:00	868
18284	18284	25-09-2014 20:00	732
18285	18285	25-09-2014 21:00	702
18286	18286	25-09-2014 22:00	580
18287	18287	25-09-2014 23:00	534

#Subsetting the dataset #Index 11856 marks the end of year 2013 df = pd.read_csv('Train_SU63ISt.csv', nrows = 11856)#Creating train and test set #Index 10392 marks the end of October 2013 train=df[0:10392] test=df[10392:]

#Aggregating the dataset at daily level df.Timestamp = pd.to_datetime(df.Datetime,format='%d-%m-%Y %H:%M') df.index = df.Timestamp df = df.resample('D').mean() train.Timestamp = pd.to_datetime(train.Datetime,format='%d-%m-%Y %H:%M') train.index = train.Timestamp train = train.resample('D').mean() test.Timestamp = pd.to_datetime(test.Datetime,format='%d-%m-%Y %H:%M') test.index = test.Timestamp test = test.resample('D').mean()

#Plotting data train.Count.plot(figsize=(18,8), title= 'Daily Ridership', fontsize=14) test.Count.plot(figsize=(18,8), title= 'Daily Ridership', fontsize=14) plt.show()

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Method 1: Start with a Naive Approach **Naive Method：**简单地将最近一个观测值作为下一期的预测值来做预测
[外链图片转存失败(img-ICzME1oI-1562729709188)(attachment:image.png)]

dd= np.asarray(train.Count) y_hat = test.copy() y_hat['naive'] = dd[len(dd)-1] plt.figure(figsize=(18,8)) plt.plot(train.index, train['Count'], label='Train') plt.plot(test.index,test['Count'], label='Test') plt.plot(y_hat.index,y_hat['naive'], label='Naive Forecast') plt.legend(loc='best') plt.title("Naive Forecast") plt.show()

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from sklearn.metrics import mean_squared_error from math import sqrt rms = sqrt(mean_squared_error(test.Count, y_hat.naive)) print(rms)# RMSE = 43.9164061439

43.91640614391676

Method 2: – Simple Average **Simple Average：**用历史全部观测值的均值作为下一期的预测值来做预测
[外链图片转存失败(img-PJRCQxAw-1562729709189)(attachment:image.png)]

y_hat_avg = test.copy() y_hat_avg['avg_forecast'] = train['Count'].mean() plt.figure(figsize=(18,8)) plt.plot(train['Count'], label='Train') plt.plot(test['Count'], label='Test') plt.plot(y_hat_avg['avg_forecast'], label='Average Forecast') plt.legend(loc='best') plt.show()

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rms = sqrt(mean_squared_error(test.Count, y_hat_avg.avg_forecast)) print(rms)# RMSE = 109.545990803

109.88526527082863

Method 3 – Moving Average 移动平均法用近期固定期数的历史观测值的均值作为下一期的预测值来做预测
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y_hat_avg = test.copy() y_hat_avg['moving_avg_forecast'] = train['Count'].rolling(60).mean().iloc[-1] plt.figure(figsize=(18,8)) plt.plot(train['Count'], label='Train') plt.plot(test['Count'], label='Test') plt.plot(y_hat_avg['moving_avg_forecast'], label='Moving Average Forecast') plt.legend(loc='best') plt.show()

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rms = sqrt(mean_squared_error(test.Count, y_hat_avg.moving_avg_forecast)) print(rms)# RMSE = 46.7284072511

46.72840725106963

Weighted moving average 加权移动平均法
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Method 4 – Simple Exponential Smoothing [外链图片转存失败(img-422QEAx8-1562729709190)(attachment:image.png)]
[外链图片转存失败(img-VKsPCRNi-1562729709190)(attachment:image.png)]

""" 在这儿：https://github.com/statsmodels/statsmodels/tree/master/statsmodels/tsa 下载holtwinters.py， 放在当前脚本所在路径下，将tsamodel.py，放在当前脚本所在路径下 """import sys, os sys.path.append(os.getcwd())from statsmodels.tsa.holtwinters import ExponentialSmoothing, SimpleExpSmoothing, Holt

y_hat_avg = test.copy() fit2 = SimpleExpSmoothing(np.asarray(train['Count'])).fit(smoothing_level=0.6,optimized=False) y_hat_avg['SES'] = fit2.forecast(len(test)) plt.figure(figsize=(18,8)) plt.plot(train['Count'], label='Train') plt.plot(test['Count'], label='Test') plt.plot(y_hat_avg['SES'], label='SES') plt.legend(loc='best') plt.show()

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rms = sqrt(mean_squared_error(test.Count, y_hat_avg.SES)) print(rms)# RMSE = 43.3576252252

43.357625225228155

Method 5 – Holt’s Linear Trend method [外链图片转存失败(img-jGMgIePX-1562729709191)(attachment:image.png)]

import statsmodels.api as smsm.tsa.seasonal_decompose(train.Count).plot() result = sm.tsa.stattools.adfuller(train.Count) plt.show()

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y_hat_avg = test.copy()fit1 = Holt(np.asarray(train['Count'])).fit(smoothing_level = 0.3,smoothing_slope = 0.1) y_hat_avg['Holt_linear'] = fit1.forecast(len(test))plt.figure(figsize=(18,8)) plt.plot(train['Count'], label='Train') plt.plot(test['Count'], label='Test') plt.plot(y_hat_avg['Holt_linear'], label='Holt_linear') plt.legend(loc='best') plt.show()

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rms = sqrt(mean_squared_error(test.Count, y_hat_avg.Holt_linear)) print(rms) # RMSE = 43.0562596115

43.056259611507286

Method 6 – Holt-Winters Method [外链图片转存失败(img-EWPH92cP-1562729709192)(attachment:image.png)]

y_hat_avg = test.copy() fit1 = ExponentialSmoothing(np.asarray(train['Count']) ,seasonal_periods=7 ,trend='add', seasonal='add',).fit() y_hat_avg['Holt_Winter'] = fit1.forecast(len(test)) plt.figure(figsize=(18,8)) plt.plot( train['Count'], label='Train') plt.plot(test['Count'], label='Test') plt.plot(y_hat_avg['Holt_Winter'], label='Holt_Winter') plt.legend(loc='best') plt.show()

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rms = sqrt(mean_squared_error(test.Count, y_hat_avg.Holt_Winter)) print(rms)# RMSE = 23.9614925662

23.961492566159794

Method 7 – ARIMA

min(train.index), max(train.index),train.shape

(Timestamp('2012-08-25 00:00:00', freq='D'), Timestamp('2013-10-31 00:00:00', freq='D'), (433, 2))

min(test.index), max(test.index), test.shape

(Timestamp('2013-11-01 00:00:00', freq='D'), Timestamp('2013-12-31 00:00:00', freq='D'), (61, 2))

from pandas import datetime, date_rangestart_index = datetime(2013, 11, 1).date() end_index = datetime(2013, 12, 31).date() start_index, end_index

(datetime.date(2013, 11, 1), datetime.date(2013, 12, 31))

y_hat_avg = test.copy() fit1 = sm.tsa.statespace.SARIMAX(train.Count, order=(2, 1, 4),seasonal_order=(0,1,1,7)).fit() # y_hat_avg['SARIMA'] = fit1.predict(start="2013-11-1", end="2013-12-31", dynamic=True) # y_hat_avg['SARIMA'] = fit1.predict(start=start_index, end=end_index, dynamic=True) y_hat_avg['SARIMA'] = fit1.predict(start=433, end=494, dynamic=True)

plt.figure(figsize=(18,8)) plt.plot(train['Count'], label='Train') plt.plot(test['Count'], label='Test') plt.plot(y_hat_avg['SARIMA'], label='SARIMA') plt.legend(loc='best') plt.show()

【时间序列分析的七种方法】[外链图片转存
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(img-bbHgTnPm-1562729709192)(output_41_0.png)]

rms = sqrt(mean_squared_error(test.Count, y_hat_avg.SARIMA)) print(rms)# RMSE = 25.952261782952643

26.052705330843708

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