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[深度学习项目] - 时间序列预测 (4)

news 来源：原创 2024/5/20 12:42:16

Prophet 算法

只需要有基本的建模知识即可
有较强的可解释性和可视化支持
能作为大部分时间序列预测的benchmark

模型结构：关于时间的广义线性模型
$y(t)=g(t)+s(t)+h(t)+\epsilon_t$
其中，

g(t)表示趋势 trend，用分段线性函数或者逻辑斯蒂增长（逻辑斯蒂增长相对于线性会有上下界限）函数拟合。
$g(t)=\frac{C}{1+e^{-k(t-m)}}$ ， C 表示上界； k表示增长/下降快慢； m表示增长/下降最快的点。
用户需要给出 C 和分段的段数。
s(t)表示季节性 seasonality，用傅里叶级数拟合。可以叠加多个季节性，比如 weekly, yearly。 $s=s_1+s_2$
$s(t)=\sum_{n=1}^N [a_ncos(\frac{2\pi nt}{T})+b_n sin(\frac{2\pi n t}{T})]$ , T 表示周期长度， N表示阶数。 T表示了数据的周期性； N 表示了采用的傅里叶级数的最高阶数。 N越大，曲线本身的波动也越大，也越容易造成过拟合。
h(t)表示外部变量的影响 regressor，采用线性函数拟合。可以叠加多个外部变量，如节假日，温度，活动。
$h=w_1 h_1 +w_2 h_2 +\dots$ h(t)可以是连续变量，也可以是0-1量。
$\epsilon_t$ 表示模型残差，表示不可知的外部变量造成的影响。

import pandas as pd
import prophet
import matplotlib.pyplot as plt

df_sales = pd.read_csv("store_sales.csv",parse_dates=["week"])
df_prom = pd.read_csv("promotion_data.csv",parse_dates=["week"])
# print(df_sales.head(2))
# print(df_prom.head(2))

df_all = pd.merge(df_sales, df_prom, how="left")
df_all.fillna(0,inplace=True)

dept = 1

df_train = df_all[ (df_all["week"]<="2012-07-30")&
                   (df_all["store"]==1)&
                   (df_all["dept"]==dept)]
df_train.rename(columns={"week":"ds","sales":"y"},inplace=True)

df_test = df_all[ (df_all["week"]<="2012-08-06")&
                   (df_all["store"]==1)&
                   (df_all["dept"]==dept)]
df_test.rename(columns={"week":"ds","sales":"y"},inplace=True)


###### 年周期性
m = prophet.Prophet(yearly_seasonality=True)

####### add regressor
m.add_regressor("promotion_sales")

#####  TRAIN
m.fit(df_train)

######  fit previous data
df_fit = m.predict(df_train)

###### visualize
fig1 = m.plot_components(df_fit)
fig2 = m.plot(df_fit)
plt.show()

trend period regressor

prophet prediction
prophet 只能预测线性模型。

机器学习预测 (LightGBM)

通过滑动窗口获取训练集，验证机，测试集
构建特征：将最原始的特征 $[y_1,x_1,y_2,x_2,\dots,x_T,y_T,x_{T+1},x_{T+2},\dots,x_{T+h}]$ 进行处理

将过去一段时间的特征进行聚合：平均值，标准差，最大值，最小值等等
特定时间点的取值：上一个时间点的x/y , 上一个周期的x/y, …
时间序列的复合特征：自相关性系数，STL分解的结果，差分

import pandas as pd
import prophet
import matplotlib.pyplot as plt

import lightgbm as lgb
from lightgbm.sklearn import LGBMRegressor

df_sales = pd.read_csv("store_sales.csv",parse_dates=["week"])
df_prom = pd.read_csv("promotion_data.csv",parse_dates=["week"])
# print(df_sales.head(2))
# print(df_prom.head(2))
#
df_all = pd.merge(df_sales, df_prom, how="left")
df_all.fillna(0,inplace=True)


#### lightgbm
df_samples = df_all[ (df_all["store"]==1)&
                     (df_all["dept"]==1)].sort_values("week")

###  construct features
feature_cols = []

### first feature:  last week
df_samples["sales_lw"] = df_samples["sales"].shift(1)
df_samples["promotion_lw"] = df_samples["promotion_sales"].shift(1)

feature_cols = feature_cols + ["sales_lw", "promotion_lw"]

#### second features:  last year
df_samples["sales_ly"] = df_samples["sales"].shift(52)
df_samples["promotion_ly"] = df_samples["promotion_sales"].shift(52)

feature_cols += ["sales_ly","promotion_ly"]

#### third features:  variances waiting for prediction
feature_cols = feature_cols + ["promotion_sales"]

#### keep the data that is not nan
for col in feature_cols:
    df_samples = df_samples[ ~df_samples[col].isna() ]

######### construct train data and test data
x_train = df_samples[df_samples["week"]<="2012-07-30"][feature_cols].values
y_train = df_samples[df_samples["week"]<="2012-07-30"]["sales"].values

x_test = df_samples[df_samples["week"]=="2012-08-06"][feature_cols].values
y_test = df_samples[df_samples["week"]=="2012-08-06"]["sales"].values

model = LGBMRegressor()
model.fit(x_train,y_train)

#### prediction
y_pred = model.predict(x_test)

print("actual data:",y_test)
print("prediction:",y_pred)

>>>16119.92
>>>16165.25781465

不同算法区别

特点	ETS	ARIMA	Prophet	LightGBM
是否适合短的时间序列	Y	N	N	N
是否可解释	Y	Y	Y	N
是否支持多条序列批量预测	N	N	N	Y，多条线可以在一个model中
是否支持外部变量	N	N	Y，但只是线性变量	Y

homework

使用Prophet 和 LightGBM算法完成之后所有时间的预测。

prophet

df_sales = pd.read_csv("store_sales.csv",parse_dates=["week"])
df_prom = pd.read_csv("promotion_data.csv",parse_dates=["week"])
# print(df_sales.head(2))
# print(df_prom.head(2))
#
df_all = pd.merge(df_sales, df_prom, how="left")
df_all.fillna(0,inplace=True)
#
dept = 1

print(df_all[ (df_all["store"]==1)&
        (df_all["dept"]==dept)] .sort_values(["week"]).tail(3))

test_date_begin = pd.to_datetime("2012-07-30")
test_date_end = pd.to_datetime("2012-10-22")

test_date = df_all[ (df_all["week"]>=test_date_begin)&
                    (df_all["week"]<=test_date_end)]["week"].unique()

predict_result = []
actual_result = []

print("total prediction num:", len(test_date))
print(test_date)



for i, every_test_date in enumerate(test_date):

    print("predicting: {}".format(i))

    df_train = df_all[ (df_all["week"]<every_test_date)&
                       (df_all["store"]==1)&
                       (df_all["dept"]==dept)]
    df_train.rename(columns={"week":"ds","sales":"y"},inplace=True)


    actual_result.append( df_all[(df_all["week"]==every_test_date)&
                                 (df_all["store"]==1)&
                                 (df_all["dept"]==dept)]["sales"].values[-1] )
    # print(actual_result[-1])

    df_test = df_all[ (df_all["week"]==every_test_date)&
                       (df_all["store"]==1)&
                       (df_all["dept"]==dept)]
    df_test.rename(columns={"week":"ds","sales":"y"},inplace=True)

    m = prophet.Prophet(yearly_seasonality=True)
    m.add_regressor("promotion_sales")
    m.fit(df_train)

    df_predict = m.predict(df_test)
    predict_result.append(df_predict["yhat"].values[0])
    # print(predict_result[-1])


plt.plot(test_date,predict_result,label="prediction")
plt.plot(test_date,actual_result,label="actual")
plt.legend()
plt.xticks(rotation=90)
plt.show()

在这里插入图片描述



#### lightgbm
df_sales = pd.read_csv("store_sales.csv",parse_dates=["week"])
df_prom = pd.read_csv("promotion_data.csv",parse_dates=["week"])
# print(df_sales.head(2))
# print(df_prom.head(2))
#
df_all = pd.merge(df_sales, df_prom, how="left")
df_all.fillna(0,inplace=True)

test_date_begin = pd.to_datetime("2012-07-30")
test_date_end = pd.to_datetime("2012-10-22")

dept = 1

df_samples = df_all[ (df_all["store"]==1)&
                     (df_all["dept"]==dept)].sort_values("week")

###  construct features
feature_cols = []

### first feature:  last week
df_samples["sales_lw"] = df_samples["sales"].shift(1)
df_samples["promotion_lw"] = df_samples["promotion_sales"].shift(1)

feature_cols = feature_cols + ["sales_lw", "promotion_lw"]

#### second features:  last year
df_samples["sales_ly"] = df_samples["sales"].shift(52)
df_samples["promotion_ly"] = df_samples["promotion_sales"].shift(52)

feature_cols += ["sales_ly","promotion_ly"]

#### third features:  variances waiting for prediction
feature_cols = feature_cols + ["promotion_sales"]

#### keep the data that is not nan
for col in feature_cols:
    df_samples = df_samples[ ~df_samples[col].isna() ]

######### construct train data and test data
test_date = df_all[ (df_all["week"]>=test_date_begin)&
                    (df_all["week"]<=test_date_end)]["week"].unique()

predict_result = []
actual_result = []

for i,every_test_date in enumerate(test_date):

    x_train = df_samples[df_samples["week"]<every_test_date][feature_cols].values
    y_train = df_samples[df_samples["week"]<every_test_date]["sales"].values

    x_test = df_samples[df_samples["week"]==every_test_date][feature_cols].values
    y_test = df_samples[df_samples["week"]==every_test_date]["sales"].values

    from lightgbm.sklearn import LGBMRegressor
    model = LGBMRegressor()
    model.fit(x_train,y_train)

    #### prediction
    y_pred = model.predict(x_test)

    predict_result.append(y_pred[0])
    actual_result.append(y_test[0])

print("actual data:",actual_result)
print("prediction:",predict_result)

plt.plot(test_date,predict_result,label="prediction")
plt.plot(test_date,actual_result,label="actual")
plt.legend()
plt.xticks(rotation=90)
plt.show()