1 时间序列
时间序列是指将某种现象某一个统计指标在不同时间上的各个数值，按时间先后顺序排列而形成的序列。典型的时间序列问题，例如股价预测、制造业中的电力预测、传统消费品行业的销售预测、客户日活跃量预测等等。(本文以客户日活跃量预测为例。)
2 预测方法
时间序列的预测方法可以归纳为三类：1、时间序列基本规则法-周期因子法；2、传统序列预测方法，如均值回归、ARIMA等线性模型；3、机器学习方法，将序列预测转为有监督建模预测，如XGBOOST集成学习方法，LSTM长短期记忆神经网络模型。
2.1 周期因子法
当序列存在周期性时，通过加工出数据的周期性特征预测。这种比较麻烦，简述下流程不做展开。1、计算周期的因子 。2、计算base 3、预测结果=周期因子*base
2.1 Ariama
ARIMA模型，差分整合移动平均自回归模型，又称整合移动平均自回归模型 （移动也可称作滑动），时间序列预测分析方法之一。ARIMA（p，d，q）中， AR是"自回归"，p为自回归项数；MA为"滑动平均"，q为滑动平均项数， d为使之成为平稳序列所做的差分次数（阶数）。建模的主要步骤是：1、数据需要先做平稳法处理：采用（对数变换或差分）平稳化后，并检验符合平稳非白噪声序列；2、观察PACF和ACF截尾/信息准则定阶确定(p, q); 3、 建立ARIMA（p，d，q）模型做预测;
代码语言：javascript复制"""
ARIMA（ 差分自回归移动平均模型）预测DAU指标
"""
import numpy as np
import pandas as pd
import seaborn as sns
import scipy
import matplotlib.pyplot as plt
import statsmodels.api as sm
import warnings
from math import sqrt
from pandas import Series
from sklearn.metrics import mean_squared_error
from statsmodels.graphics.tsaplots import acf, pacf,plot_acf, plot_pacf
from statsmodels.stats.diagnostic import acorr_ljungbox
from statsmodels.tsa.arima_model import ARIMA, ARMA, ARIMAResults
from statsmodels.tsa.stattools import adfuller as ADF
from keras.models import load_model
warnings.filterwarnings("ignore")
df = pd.read_csv('DAU.csv')
dau = df["dau"]
# 折线图
df.plot()
plt.show()
# 箱线图
ax = sns.boxplot(y=dau)
plt.show()
# pearsonr时间相关性
# a = df['dau']
# b = df.index
# print(scipy.stats.pearsonr(a,b))
# 自相关性
plot_acf(dau)
plot_pacf(dau)
plt.show()
print('raw序列的ADF')
# p值大于0.05为非平衡时间序列
print(ADF(dau))
#对数变换平稳处理
# dau_log = np.log(dau)
# dau_log = dau_log.ewm(com=0.5, span=12).mean()
# plot_acf(dau_log)
# plot_pacf(dau_log)
# plt.show()
# print('log序列的ADF')
# print(ADF(dau_log))
# print('log序列的白噪声检验结果')
# # 大于0.05为白噪声序列
# print(acorr_ljungbox(dau_log, lags=1))
#差分平稳处理
diff_1_df = dau.diff(1).dropna(how=any)
diff_1_df = diff_1_df
diff_1_df.plot()
plot_acf(diff_1_df)
plot_pacf(diff_1_df)
plt.show()
print('差分序列的ADF')
print(ADF(diff_1_df))
print('差分序列的白噪声检验结果')
# 大于0.05为白噪声序列
print(acorr_ljungbox(diff_1_df, lags=1))
# # 在满足检验条件后，给出最优p q值 ()
r, rac, Q = sm.tsa.acf(diff_1_df, qstat=True)
prac = pacf(diff_1_df, method='ywmle')
table_data = np.c_[range(1,len(r)), r[1:], rac, prac[1:len(rac) 1], Q]
table = pd.DataFrame(table_data, columns=['lag', "AC","Q", "PAC", "Prob(>Q)"])
order = sm.tsa.arma_order_select_ic(diff_1_df, max_ar=7, max_ma=7, ic=['aic', 'bic', 'hqic'])
p, q =order.bic_min_order
print("p,q")
print(p, q)
# 建立ARIMA(p, d, q)模型 d=1
order = (p, 1, q)
train_X = diff_1_df[:]
arima_model = ARIMA(train_X, order).fit()
# 模型报告
# print(arima_model.summary2())
# 保存模型
arima_model.save('./data/arima_model.h5')
# # load model
arima_model = ARIMAResults.load('./data/arima_model.h5')
# 预测未来两天数据
predict_data_02 = arima_model.predict(start=len(train_X), end=len(train_X) 1, dynamic = False)
# 预测历史数据
predict_data = arima_model.predict(dynamic = False)
# 逆log化
# original_series = np.exp(train_X.values[1:] np.log(dau.values[1:-1]))
# predict_series = np.exp(predict_data.values np.log(dau.values[1:-1]))
# 逆差分
original_series = train_X.values[1:] dau.values[1:-1]
predict_series = predict_data.values dau.values[1:-1]
# comp = pd.DataFrame()
# comp['original'] = original_series
# comp['predict'] = predict_series
split_num = int(len(dau.values)/3) or 1
rmse = sqrt(mean_squared_error(original_series[-split_num:], predict_series[-split_num:]))
print('Test RMSE: %.3f' % rmse)
# (0,1,0)Test RMSE
plt.title('ARIMA RMSE: %.3f' % rmse)
plt.plot(original_series[-split_num:], label="original_series")
plt.plot(predict_series[-split_num:], label="predict_series")
plt.legend()
plt.show()
2.2 lstm
Long Short Term 网络是一种 RNN 特殊的类型，可以学习长期依赖序列信息。LSTM区别于RNN的地方，主要就在于它在算法中加入了一个判断信息有用与否的“处理器”，这个处理器作用的结构被称为cell。一个cell当中被放置了三扇门，分别叫做输入门、遗忘门和输出门。一个信息进入LSTM的网络当中，只有符合信息才会留下，不符的信息则通过遗忘门被遗忘。通过这机制减少梯度爆炸/消失的风险。
建模主要的步骤：1、数据处理：差分法数据平稳化；MAX-MIN法数据标准化；构建监督学习训练集；（对于LSTM，差分及标准化不是必要的） 2、模型训练并预测；
代码语言：javascript复制"""
LSTM预测DAU指标
"""
import numpy as np
from pandas import DataFrame, datetime, concat,read_csv, Series
from matplotlib import pyplot as plt
from sklearn.metrics import mean_squared_error
from math import sqrt
from sklearn.preprocessing import MinMaxScaler
from keras.models import Sequential
from keras.models import load_model
from keras.layers import Dense
from keras.layers import LSTM
from keras.callbacks import EarlyStopping
from keras import regularizers
from statsmodels.stats.diagnostic import acorr_ljungbox
from statsmodels.tsa.stattools import adfuller as ADF
# convert date
def parser(x):
return datetime.strptime(x,"%Y-%m-%d")
#supervised
def timeseries_to_supervised(data, lag=1):
df = DataFrame(data)
columns = [df.shift(1) for i in range(1, lag 1)]
columns.append(df)
df = concat(columns, axis=1)
df.fillna(0, inplace=True)
return df
# diff series
def difference(dataset, interval=1):
diff = list()
for i in range(interval, len(dataset)):
value = dataset[i] - dataset[i - interval]
diff.append(value)
return Series(diff)
# invert diff value
def inverse_difference(history, yhat, interval=1):
return yhat history[-interval]
# max_min标准化 [-1, 1]
def scale(train, test):
# fit scaler
scaler = MinMaxScaler(feature_range=(-1, 1))
scaler = scaler.fit(train)
# transform train
train = train.reshape(train.shape[0], train.shape[1])
train_scaled = scaler.transform(train)
# transform test
test = test.reshape(test.shape[0], test.shape[1])
test_scaled = scaler.transform(test)
return scaler, train_scaled, test_scaled
# invert scale transform
def invert_scale(scaler, X, value):
new_row = [x for x in X] [value]
array = np.array(new_row)
array = array.reshape(1, len(array))
inverted = scaler.inverse_transform(array)
return inverted[0, -1]
# model train
def fit_lstm(train, batch_size, nb_epoch, neurons):
X, y = train[:,0:-1], train[:,-1]
# reshp
X = X.reshape(X.shape[0], 1, X.shape[1])
model = Sequential()
# stateful
# input(samples:batch row, time steps:1, features:one time observed)
model.add(LSTM(neurons,
batch_input_shape=(batch_size, X.shape[1], X.shape[2]),
stateful=True, return_sequences=True, dropout=0.2))
model.add(Dense(1))
model.compile(loss="mean_squared_error", optimizer="adam")
# train
train_loss = []
val_loss = []
for i in range(nb_epoch):
# shuffle=false
history = model.fit(X, y, batch_size=batch_size, epochs=1,verbose=0,shuffle=False,validation_split=0.3)
train_loss.append(history.history['loss'][0])
val_loss.append(history.history['val_loss'][0])
# clear state
model.reset_states()
# 提前停止训练
if i > 50 and sum(val_loss[-10:]) < 0.3:
print(sum(val_loss[-5:]))
print("better epoch", i)
break
# print(history.history['loss'])
plt.plot(train_loss)
plt.plot(val_loss)
plt.title('model train vs validation loss')
plt.ylabel('loss')
plt.xlabel('epoch')
plt.legend(['train', 'validation'], loc='upper right')
plt.show()
return model
# model predict
def forecast_lstm(model, batch_size, X):
X = X.reshape(1, 1, len(X))
yhat = model.predict(X, batch_size=batch_size)
return yhat[0,0]
# 开始加载数据
series = read_csv('DAU.csv')["dau"]
print(series.head())
series.plot()
plt.show()
# 数据平稳化
raw_values = series.values
diff_values = difference(raw_values, 1)
print(diff_values.head())
plt.plot(raw_values, label="raw")
plt.plot(diff_values, label="diff")
plt.legend()
plt.show()
print('差分序列的ADF')
print(ADF(diff_values)[1])
print('差分序列的白噪声检验结果')
# (array([13.95689179]), array([0.00018705]))
print(acorr_ljungbox(diff_values, lags=1)[1][0])
# 序列转监督数据
supervised = timeseries_to_supervised(diff_values, 1)
print(supervised.head())
supervised_values = supervised.values
# split data
split_num = int(len(supervised_values)/3) or 1
train, test = supervised_values[0:-split_num], supervised_values[-split_num:]
# 标准化
scaler, train_scaled, test_scaled = scale(train, test)
#fit model
lstm_model = fit_lstm(train_scaled, 1, 200, 5)
train_reshaped = train_scaled[:, 0].reshape(len(train_scaled), 1, 1)
train_predict = lstm_model.predict(train_reshaped, batch_size=1)
train_raw = train_scaled[:, 0]
# # train RMSE plot
# train_raw = raw_values[0:-split_num]
# predictions = list()
# for i in range(len(train_scaled)):
# # make one-step forecast
# X, y = train_scaled[i, 0:-1], train_scaled[i, -1]
# yhat = forecast_lstm(lstm_model, 1, X)
# # invert scaling
# yhat = invert_scale(scaler, X, yhat)
# # invert differencing
# yhat = inverse_difference(raw_values, yhat, len(train_scaled) 1-i)
# # store forecast
# predictions.append(yhat)
# expected = train_raw[i]
# mae = abs(yhat-expected)
# print('data=%d, Predicted=%f, Expected=%f, mae=%.3f' % (i 1, yhat, expected,mae))
# print(mae)
# plt.plot(train_raw, label="train_raw")
# plt.plot(predictions, label="predict")
# plt.legend()
# plt.show()
# 保存模型
lstm_model.save('./data/lstm_model_epoch50.h5')
# # load model
lstm_model = load_model('./data/lstm_model_epoch50.h5')
# validation
predictions = list()
for i in range(len(test_scaled)):
# make one-step forecast
X, y = test_scaled[i, 0:-1], test_scaled[i, -1]
yhat = forecast_lstm(lstm_model, 1, X)
# invert scaling
yhat = invert_scale(scaler, X, yhat)
# invert differencing
yhat = inverse_difference(raw_values, yhat, len(test_scaled) 1-i)
# store forecast
predictions.append(yhat)
expected = raw_values[len(train) i 1]
mae = abs(yhat-expected)
print('data=%d, Predicted=%f, Expected=%f, mae=%.3f' % (i 1, yhat, expected, mae))
mae = np.average(abs(predictions - raw_values[-split_num:]))
print("Test MAE: %.3f",mae)
#report performance
rmse = sqrt(mean_squared_error(raw_values[-split_num:], predictions))
print('Test RMSE: %.3f' % rmse)
# line plot of observed vs predicted
plt.plot(raw_values[-split_num:], label="raw")
plt.plot(predictions, label="predict")
plt.title('LSTM Test RMSE: %.3f' % rmse)
plt.legend()
plt.show()
# 附数据集dau.csv
log_date,dau
2018-06-01,257488
2018-06-02,286612
2018-06-03,287405
2018-06-04,246955
2018-06-05,249926
2018-06-06,252951
2018-06-07,255467
2018-06-08,262498
2018-06-09,288368
2018-06-10,288440
2018-06-11,255447
2018-06-12,251316
2018-06-13,251654
2018-06-14,250515
2018-06-15,262155
2018-06-16,288844
2018-06-17,296143
2018-06-18,298142
2018-06-19,264124
2018-06-20,262992
2018-06-21,263549
2018-06-22,271631
2018-06-23,296452
2018-06-24,296986
2018-06-25,271197
2018-06-26,270546
2018-06-27,271208
2018-06-28,275496
2018-06-29,284218
2018-06-30,307498
2018-07-01,316097
2018-07-02,295106
2018-07-03,290675
2018-07-04,292231
2018-07-05,297510
2018-07-06,298839
2018-07-07,302083
2018-07-08,301238
2018-07-09,296398
2018-07-10,300986
2018-07-11,301459
2018-07-12,299865
2018-07-13,289830
2018-07-14,297501
2018-07-15,297443
2018-07-16,293097
2018-07-17,293866
2018-07-18,292902
2018-07-19,292368
2018-07-20,290766
2018-07-21,294669
2018-07-22,295811
2018-07-23,297514
2018-07-24,297392
2018-07-25,298957
2018-07-26,298101
2018-07-27,298740
2018-07-28,304086
2018-07-29,305269
2018-07-30,304827
2018-07-31,299689
2018-08-01,300526
2018-08-02,59321
2018-08-03,31731
2018-08-04,36838
2018-08-05,42043
2018-08-06,42366
2018-08-07,37209
