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工作常用的时间序列分析案例：

使用 Pandas 构造标准时间序列
可视化每日/每周销售额趋势图
分解时间序列的趋势、季节性与残差（STL分解）
使用移动平均法平滑短期波动
使用指数平滑法（Simple Exponential Smoothing）进行预测
使用 Holt-Winters 季节性模型预测节假日效应
使用 ARIMA 模型预测未来30天销售额
使用 SARIMA 模型处理具有季节性的销售数据
构建多维时间序列模型（按品类 + 区域）
预测促销期间的订单增长曲线

好的，我们将展示如何进行这些常见的时间序列分析任务。为了演示这些方法，我们需要使用一些常用的数据分析库，如 pandas、matplotlib 和 statsmodels。首先，让我们创建一个示例DataFrame来模拟原始数据，并逐步应用这些时间序列分析任务。

创建示例数据

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

# 创建示例时间序列数据
dates = pd.date_range(start='2023-01-01', end='2025-06-30', freq='D')
np.random.seed(42)
sales_data = np.cumsum(np.random.normal(loc=100, scale=20, size=len(dates)))

data = {
    'order_date': dates,
    'amount': sales_data,
    'category_code': np.random.choice(['C{}'.format(i) for i in range(1, 11)], len(dates)),
    'region': np.random.choice(['Beijing', 'Shanghai', 'Guangzhou', 'Shenzhen'], len(dates)),
    'promotion': np.random.choice([True, False], len(dates))
}

df = pd.DataFrame(data)

# 设置时间为索引
df.set_index('order_date', inplace=True)

print("原始数据:")
print(df.head())

1. 使用 Pandas 构造标准时间序列

# 按天聚合销售额
daily_sales = df['amount'].resample('D').sum()

print("\n按天聚合销售额:")
print(daily_sales.head())

2. 可视化每日/每周销售额趋势图

# 绘制每日销售额趋势图
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Daily Sales')
plt.title('Daily Sales Trend')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

# 按周聚合销售额
weekly_sales = daily_sales.resample('W').sum()

# 绘制每周销售额趋势图
plt.figure(figsize=(14, 7))
plt.plot(weekly_sales, label='Weekly Sales')
plt.title('Weekly Sales Trend')
plt.xlabel('Week')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

3. 分解时间序列的趋势、季节性与残差（STL分解）

from statsmodels.tsa.seasonal import STL

# STL分解
stl = STL(daily_sales, period=365)
res = stl.fit()

fig = res.plot()
plt.show()

4. 使用移动平均法平滑短期波动

# 计算移动平均
moving_avg = daily_sales.rolling(window=30).mean()

# 绘制移动平均线
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(moving_avg, label='30-Day Moving Average', color='red')
plt.title('Daily Sales with 30-Day Moving Average')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

5. 使用指数平滑法（Simple Exponential Smoothing）进行预测

from statsmodels.tsa.holtwinters import SimpleExpSmoothing

# 拟合指数平滑模型
model_es = SimpleExpSmoothing(daily_sales)
model_es_fit = model_es.fit(smoothing_level=0.2, optimized=False)

# 预测未来一个月的销售额
forecast_es = model_es_fit.forecast(steps=30)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(forecast_es, label='Forecast', color='red')
plt.title('Simple Exponential Smoothing Forecast')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

6. 使用 Holt-Winters 季节性模型预测节假日效应

from statsmodels.tsa.holtwinters import ExponentialSmoothing

# 添加节假日标志
holidays = pd.to_datetime([
    '2023-01-01', '2023-02-22', '2023-04-05', '2023-05-01', '2023-10-01',
    '2024-01-01', '2024-02-10', '2024-04-04', '2024-05-01', '2024-10-01',
    '2025-01-01', '2025-02-19', '2025-04-04', '2025-05-01', '2025-10-01'
])

df.reset_index(inplace=True)
df['is_holiday'] = df['order_date'].isin(holidays).astype(int)
df.set_index('order_date', inplace=True)

# 拟合Holt-Winters模型
model_hw = ExponentialSmoothing(daily_sales, trend='add', seasonal='add', seasonal_periods=365)
model_hw_fit = model_hw.fit()

# 预测未来一个月的销售额
forecast_hw = model_hw_fit.forecast(steps=30)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(forecast_hw, label='Forecast', color='red')
plt.title('Holt-Winters Seasonal Model Forecast')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

7. 使用 ARIMA 模型预测未来30天销售额

from statsmodels.tsa.arima.model import ARIMA

# 拟合ARIMA模型
model_arima = ARIMA(daily_sales, order=(5, 1, 0))  # 这里使用 (5, 1, 0) 作为示例参数
model_arima_fit = model_arima.fit()

# 预测未来一个月的销售额
forecast_arima = model_arima_fit.forecast(steps=30)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(pd.date_range(start=daily_sales.index[-1] + pd.Timedelta(days=1), periods=30), forecast_arima, label='Forecast', color='red')
plt.title('ARIMA Model Forecast')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

8. 使用 SARIMA 模型处理具有季节性的销售数据

from statsmodels.tsa.statespace.sarimax import SARIMAX

# 拟合SARIMA模型
model_sarima = SARIMAX(daily_sales, order=(5, 1, 0), seasonal_order=(1, 1, 1, 365))
model_sarima_fit = model_sarima.fit()

# 预测未来一个月的销售额
forecast_sarima = model_sarima_fit.forecast(steps=30)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(pd.date_range(start=daily_sales.index[-1] + pd.Timedelta(days=1), periods=30), forecast_sarima, label='Forecast', color='red')
plt.title('SARIMA Model Forecast')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

9. 构建多维时间序列模型（按品类 + 区域）

# 按品类和区域聚合销售额
region_category_sales = df.groupby(['region', 'category_code'])['amount'].sum().unstack(fill_value=0)

# 选择一个组合进行预测
selected_region = region_category_sales.columns.levels[0][0]
selected_category = region_category_sales.columns.levels[1][0]
region_category_series = region_category_sales[(selected_region, selected_category)]

# 拟合SARIMA模型
model_sarima_multi = SARIMAX(region_category_series, order=(5, 1, 0), seasonal_order=(1, 1, 1, 365))
model_sarima_multi_fit = model_sarima_multi.fit()

# 预测未来一个月的销售额
forecast_sarima_multi = model_sarima_multi_fit.forecast(steps=30)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(region_category_series, label='Original')
plt.plot(pd.date_range(start=region_category_series.index[-1] + pd.Timedelta(days=1), periods=30), forecast_sarima_multi, label='Forecast', color='red')
plt.title('Multi-Dimensional SARIMA Model Forecast (Region: {}, Category: {})'.format(selected_region, selected_category))
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

10. 预测促销期间的订单增长曲线

# 按促销状态聚合销售额
promotion_effect = df.groupby('promotion')['amount'].sum()

# 将促销状态转换为数值
df['promotion_numeric'] = df['promotion'].astype(int)

# 拟合SARIMA模型考虑促销影响
model_sarima_promo = SARIMAX(daily_sales, exog=df['promotion_numeric'], order=(5, 1, 0), seasonal_order=(1, 1, 1, 365))
model_sarima_promo_fit = model_sarima_promo.fit()

# 预测未来一个月的销售额并考虑促销影响
future_dates = pd.date_range(start=daily_sales.index[-1] + pd.Timedelta(days=1), periods=30)
future_exog = pd.Series([1]*30, index=future_dates)  # 假设未来都是促销期
forecast_sarima_promo = model_sarima_promo_fit.get_forecast(steps=30, exog=future_exog)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(forecast_sarima_promo.predicted_mean, label='Promotion Forecast', color='red')
plt.title('SARIMA Model Forecast with Promotion Effect')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

综合以上步骤，最终的时间序列分析结果如下：

这段代码展示了从原始数据到经过全面时间序列分析的结果的过程。你可以根据实际需求调整每一步的操作。

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.seasonal import STL
from statsmodels.tsa.holtwinters import SimpleExpSmoothing, ExponentialSmoothing
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.statespace.sarimax import SARIMAX

# 创建示例时间序列数据
dates = pd.date_range(start='2023-01-01', end='2025-06-30', freq='D')
np.random.seed(42)
sales_data = np.cumsum(np.random.normal(loc=100, scale=20, size=len(dates)))

data = {
    'order_date': dates,
    'amount': sales_data,
    'category_code': np.random.choice(['C{}'.format(i) for i in range(1, 11)], len(dates)),
    'region': np.random.choice(['Beijing', 'Shanghai', 'Guangzhou', 'Shenzhen'], len(dates)),
    'promotion': np.random.choice([True, False], len(dates))
}

df = pd.DataFrame(data)

# 设置时间为索引
df.set_index('order_date', inplace=True)

# 按天聚合销售额
daily_sales = df['amount'].resample('D').sum()

# 绘制每日销售额趋势图
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Daily Sales')
plt.title('Daily Sales Trend')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

# 按周聚合销售额
weekly_sales = daily_sales.resample('W').sum()

# 绘制每周销售额趋势图
plt.figure(figsize=(14, 7))
plt.plot(weekly_sales, label='Weekly Sales')
plt.title('Weekly Sales Trend')
plt.xlabel('Week')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

# STL分解
stl = STL(daily_sales, period=365)
res = stl.fit()

fig = res.plot()
plt.show()

# 计算移动平均
moving_avg = daily_sales.rolling(window=30).mean()

# 绘制移动平均线
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(moving_avg, label='30-Day Moving Average', color='red')
plt.title('Daily Sales with 30-Day Moving Average')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

# 拟合指数平滑模型
model_es = SimpleExpSmoothing(daily_sales)
model_es_fit = model_es.fit(smoothing_level=0.2, optimized=False)

# 预测未来一个月的销售额
forecast_es = model_es_fit.forecast(steps=30)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(forecast_es, label='Forecast', color='red')
plt.title('Simple Exponential Smoothing Forecast')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

# 添加节假日标志
holidays = pd.to_datetime([
    '2023-01-01', '2023-02-22', '2023-04-05', '2023-05-01', '2023-10-01',
    '2024-01-01', '2024-02-10', '2024-04-04', '2024-05-01', '2024-10-01',
    '2025-01-01', '2025-02-19', '2025-04-04', '2025-05-01', '2025-10-01'
])

df.reset_index(inplace=True)
df['is_holiday'] = df['order_date'].isin(holidays).astype(int)
df.set_index('order_date', inplace=True)

# 拟合Holt-Winters模型
model_hw = ExponentialSmoothing(daily_sales, trend='add', seasonal='add', seasonal_periods=365)
model_hw_fit = model_hw.fit()

# 预测未来一个月的销售额
forecast_hw = model_hw_fit.forecast(steps=30)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(forecast_hw, label='Forecast', color='red')
plt.title('Holt-Winters Seasonal Model Forecast')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

# 拟合ARIMA模型
model_arima = ARIMA(daily_sales, order=(5, 1, 0))  # 这里使用 (5, 1, 0) 作为示例参数
model_arima_fit = model_arima.fit()

# 预测未来一个月的销售额
forecast_arima = model_arima_fit.forecast(steps=30)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(pd.date_range(start=daily_sales.index[-1] + pd.Timedelta(days=1), periods=30), forecast_arima, label='Forecast', color='red')
plt.title('ARIMA Model Forecast')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

# 拟合SARIMA模型
model_sarima = SARIMAX(daily_sales, order=(5, 1, 0), seasonal_order=(1, 1, 1, 365))
model_sarima_fit = model_sarima.fit()

# 预测未来一个月的销售额
forecast_sarima = model_sarima_fit.forecast(steps=30)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(pd.date_range(start=daily_sales.index[-1] + pd.Timedelta(days=1), periods=30), forecast_sarima, label='Forecast', color='red')
plt.title('SARIMA Model Forecast')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

# 按品类和区域聚合销售额
region_category_sales = df.groupby(['region', 'category_code'])['amount'].sum().unstack(fill_value=0)

# 选择一个组合进行预测
selected_region = region_category_sales.columns.levels[0][0]
selected_category = region_category_sales.columns.levels[1][0]
region_category_series = region_category_sales[(selected_region, selected_category)]

# 拟合SARIMA模型
model_sarima_multi = SARIMAX(region_category_series, order=(5, 1, 0), seasonal_order=(1, 1, 1, 365))
model_sarima_multi_fit = model_sarima_multi.fit()

# 预测未来一个月的销售额
forecast_sarima_multi = model_sarima_multi_fit.forecast(steps=30)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(region_category_series, label='Original')
plt.plot(pd.date_range(start=region_category_series.index[-1] + pd.Timedelta(days=1), periods=30), forecast_sarima_multi, label='Forecast', color='red')
plt.title('Multi-Dimensional SARIMA Model Forecast (Region: {}, Category: {})'.format(selected_region, selected_category))
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()

# 将促销状态转换为数值
df['promotion_numeric'] = df['promotion'].astype(int)

# 拟合SARIMA模型考虑促销影响
model_sarima_promo = SARIMAX(daily_sales, exog=df['promotion_numeric'], order=(5, 1, 0), seasonal_order=(1, 1, 1, 365))
model_sarima_promo_fit = model_sarima_promo.fit()

# 预测未来一个月的销售额并考虑促销影响
future_dates = pd.date_range(start=daily_sales.index[-1] + pd.Timedelta(days=1), periods=30)
future_exog = pd.Series([1]*30, index=future_dates)  # 假设未来都是促销期
forecast_sarima_promo = model_sarima_promo_fit.get_forecast(steps=30, exog=future_exog)

# 绘制预测结果
plt.figure(figsize=(14, 7))
plt.plot(daily_sales, label='Original')
plt.plot(forecast_sarima_promo.predicted_mean, label='Promotion Forecast', color='red')
plt.title('SARIMA Model Forecast with Promotion Effect')
plt.xlabel('Date')
plt.ylabel('Sales Amount')
plt.legend()
plt.show()