Python 基于Stats模型的Holt-Winters时间序列预测

我尝试使用霍尔特温特斯模型进行预测，如下所示，但我一直得到一个与我预期不一致的预测。我还展示了情节的可视化

Train = Airline[:130]
Test = Airline[129:]

from statsmodels.tsa.holtwinters import Holt

y_hat_avg = Test.copy()
fit1 = Holt(np.asarray(Train['Passengers'])).fit()
y_hat_avg['Holt_Winter'] = fit1.predict(start=1,end=15)
plt.figure(figsize=(16,8))
plt.plot(Train.index, Train['Passengers'], label='Train')
plt.plot(Test.index,Test['Passengers'], label='Test')
plt.plot(y_hat_avg.index,y_hat_avg['Holt_Winter'], label='Holt_Winter')
plt.legend(loc='best')
plt.savefig('Holt_Winters.jpg')

我不确定我错过了什么

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预测似乎与训练数据的早期部分相吻合。错误的主要原因是您的起始值和结束值。它预测第一次观测到15日的数值。然而，即使你纠正了这一点，霍尔特只包括趋势成分，你的预测也不会带来季节性影响。相反，使用季节参数的

指数平滑

以下是数据集的工作示例：

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.holtwinters import ExponentialSmoothing

df = pd.read_csv('/home/ayhan/international-airline-passengers.csv', 
                 parse_dates=['Month'], 
                 index_col='Month'
)
df.index.freq = 'MS'
train, test = df.iloc[:130, 0], df.iloc[130:, 0]
model = ExponentialSmoothing(train, seasonal='mul', seasonal_periods=12).fit()
pred = model.predict(start=test.index[0], end=test.index[-1])

plt.plot(train.index, train, label='Train')
plt.plot(test.index, test, label='Test')
plt.plot(pred.index, pred, label='Holt-Winters')
plt.legend(loc='best')

由此得出以下曲线图：

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这是上述答案的即兴创作

以下是我如何获得最佳参数的方法

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摘要： 新模型结果：

旧模型结果：

奖金： 您将得到一个很好的数据帧，您可以将原始值与预测值进行比较

df_pass_pred['1960':]

输出

            Passengers     pred_HW
Month                             
1960-01-01         417  417.826543
1960-02-01         391  400.452916
1960-03-01         419  461.804259
1960-04-01         461  450.787208
1960-05-01         472  472.695903
1960-06-01         535  528.560823
1960-07-01         622  601.265794
1960-08-01         606  608.370401
1960-09-01         508  508.869849
1960-10-01         461  452.958727
1960-11-01         390  407.634391
1960-12-01         432  437.385058

---

你能在这里发布时间序列数据吗？可以在这里找到数据，单击导出。我对数据做了一些预处理，并将月份列转换为索引。我猜你的索引start=1，end=15是错误的。在图中，预测似乎是针对前几次观测。尝试使用start=129或start=130进行预测。嘿，你能告诉我

df.index.freq='MS'

在你的代码中的作用吗？为了建立平滑模型，statsmodels需要知道数据的频率（无论是每日、每月还是其他）。MS是指月初，所以我们说的是我们在每个月初观察到的月度数据。感谢您的回复。我的数据点滞后5分钟。那么，我的数据的频率应该是多少？有什么想法吗？如果我有一个月的数据，频率是10T，并且每天都有一个趋势，即（24小时），那么我的

季节性

和

季节性

参数应该是什么？我是否应该在一个月内使用季节性be‘mul’和季节性_周期=1。

edf = df['Passengers']
ts = edf[:'1959-12-01'].copy()
ts_v = edf['1960-01-01':].copy()
ind = edf.index[-12:]  # this will select last 12 months' indexes

print("Holt's Winter Model")
best_RMSE = np.inf
best_config = []
t1 = d1 = s1 = p1 = b1 = r1 = ''
for j in range(len(cfg_list)):
    print(j)
    try:
        cg = cfg_list[j]
        print(cg)
        t,d,s,p,b,r = cg
        train = edf[:'1959'].copy()
        test = edf['1960-01-01':'1960-12-01'].copy()
        # define model
        if (t == None):
            model = ExponentialSmoothing(ts, trend=t, seasonal=s, seasonal_periods=p)
        else:
            model = ExponentialSmoothing(ts, trend=t, damped=d, seasonal=s, seasonal_periods=p)
        # fit model
        model_fit = model.fit(optimized=True, use_boxcox=b, remove_bias=r)
        # make one step forecast
        y_forecast = model_fit.forecast(12)
        rmse = np.sqrt(mean_squared_error(ts_v,y_forecast))
        print(rmse)
        if rmse < best_RMSE:
            best_RMSE = rmse
            best_config = cfg_list[j]
    except:
       continue

def model_eval(y, predictions):

    # Import library for metrics
    from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error

    # Mean absolute error (MAE)
    mae = mean_absolute_error(y, predictions)

    # Mean squared error (MSE)
    mse = mean_squared_error(y, predictions)


    # SMAPE is an alternative for MAPE when there are zeros in the testing data. It
    # scales the absolute percentage by the sum of forecast and observed values
    SMAPE = np.mean(np.abs((y - predictions) / ((y + predictions)/2))) * 100


    # Calculate the Root Mean Squared Error
    rmse = np.sqrt(mean_squared_error(y, predictions))

    # Calculate the Mean Absolute Percentage Error
    # y, predictions = check_array(y, predictions)
    MAPE = np.mean(np.abs((y - predictions) / y)) * 100

    # mean_forecast_error
    mfe = np.mean(y - predictions)

    # NMSE normalizes the obtained MSE after dividing it by the test variance. It
    # is a balanced error measure and is very effective in judging forecast
    # accuracy of a model.

    # normalised_mean_squared_error
    NMSE = mse / (np.sum((y - np.mean(y)) ** 2)/(len(y)-1))


    # theil_u_statistic
    # It is a normalized measure of total forecast error.
    error = y - predictions
    mfe = np.sqrt(np.mean(predictions**2))
    mse = np.sqrt(np.mean(y**2))
    rmse = np.sqrt(np.mean(error**2))
    theil_u_statistic =  rmse / (mfe*mse)


    # mean_absolute_scaled_error
    # This evaluation metric is used to over come some of the problems of MAPE and
    # is used to measure if the forecasting model is better than the naive model or
    # not.


    # Print metrics
    print('Mean Absolute Error:', round(mae, 3))
    print('Mean Squared Error:', round(mse, 3))
    print('Root Mean Squared Error:', round(rmse, 3))
    print('Mean absolute percentage error:', round(MAPE, 3))
    print('Scaled Mean absolute percentage error:', round(SMAPE, 3))
    print('Mean forecast error:', round(mfe, 3))
    print('Normalised mean squared error:', round(NMSE, 3))
    print('Theil_u_statistic:', round(theil_u_statistic, 3))

print(best_RMSE, best_config)

t1,d1,s1,p1,b1,r1 = best_config

if t1 == None:
    hw_model1 = ExponentialSmoothing(ts, trend=t1, seasonal=s1, seasonal_periods=p1)
else:
    hw_model1 = ExponentialSmoothing(ts, trend=t1, seasonal=s1, seasonal_periods=p1, damped=d1)

fit2 = hw_model1.fit(optimized=True, use_boxcox=b1, remove_bias=r1)

pred_HW = fit2.predict(start=pd.to_datetime('1960-01-01'), end = pd.to_datetime('1960-12-01'))
# pred_HW = fit2.forecast(12)

pred_HW = pd.Series(data=pred_HW, index=ind)
df_pass_pred = pd.concat([df, pred_HW.rename('pred_HW')], axis=1)

print(model_eval(ts_v, pred_HW))
print('-*-'*20)

# 15.570830579664698 ['add', True, 'add', 12, False, False]
# Mean Absolute Error: 10.456
# Mean Squared Error: 481.948
# Root Mean Squared Error: 15.571
# Mean absolute percentage error: 2.317
# Scaled Mean absolute percentage error: 2.273
# Mean forecast error: 483.689
# Normalised mean squared error: 0.04
# Theil_u_statistic: 0.0
# None
# -*--*--*--*--*--*--*--*--*--*--*--*--*--*--*--*--*--*--*--*-

Mean Absolute Error: 10.456
Mean Squared Error: 481.948
Root Mean Squared Error: 15.571
Mean absolute percentage error: 2.317
Scaled Mean absolute percentage error: 2.273
Mean forecast error: 483.689
Normalised mean squared error: 0.04
Theil_u_statistic: 0.0

Mean Absolute Error: 20.682
Mean Squared Error: 481.948
Root Mean Squared Error: 23.719
Mean absolute percentage error: 4.468
Scaled Mean absolute percentage error: 4.56
Mean forecast error: 466.704
Normalised mean squared error: 0.093
Theil_u_statistic: 0.0

df_pass_pred['1960':]

            Passengers     pred_HW
Month                             
1960-01-01         417  417.826543
1960-02-01         391  400.452916
1960-03-01         419  461.804259
1960-04-01         461  450.787208
1960-05-01         472  472.695903
1960-06-01         535  528.560823
1960-07-01         622  601.265794
1960-08-01         606  608.370401
1960-09-01         508  508.869849
1960-10-01         461  452.958727
1960-11-01         390  407.634391
1960-12-01         432  437.385058