Metode Holt-Winters

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

from statsmodels.tsa.holtwinters import ExponentialSmoothing
from statsmodels.tsa.holtwinters import Holt
from statsmodels.tsa.holtwinters import SimpleExpSmoothing

Data Sampel #

Data yang digunakan adalah Natural Gas Consumption (NATURALGAS). Satuan data adalah BCF (miliar kaki kubik).

data = {
    "value": {
        "2013-01-01": 2878.8,
        "2013-02-01": 2567.2,
        "2013-03-01": 2521.1,
        "2013-04-01": 1967.5,
        "2013-05-01": 1752.5,
        "2013-06-01": 1742.9,
        "2013-07-01": 1926.3,
        "2013-08-01": 1927.4,
        "2013-09-01": 1767.0,
        "2013-10-01": 1866.8,
        "2013-11-01": 2316.9,
        "2013-12-01": 2920.8,
        "2014-01-01": 3204.1,
        "2014-02-01": 2741.2,
        "2014-03-01": 2557.9,
        "2014-04-01": 1961.7,
        "2014-05-01": 1810.2,
        "2014-06-01": 1745.4,
        "2014-07-01": 1881.0,
        "2014-08-01": 1933.1,
        "2014-09-01": 1809.3,
        "2014-10-01": 1912.8,
        "2014-11-01": 2357.5,
        "2014-12-01": 2679.2,
        "2015-01-01": 3115.0,
        "2015-02-01": 2925.2,
        "2015-03-01": 2591.3,
        "2015-04-01": 2007.9,
        "2015-05-01": 1858.2,
        "2015-06-01": 1899.9,
        "2015-07-01": 2067.7,
        "2015-08-01": 2052.7,
        "2015-09-01": 1901.3,
        "2015-10-01": 1987.3,
        "2015-11-01": 2249.1,
        "2015-12-01": 2588.2,
        "2016-01-01": 3091.7,
        "2016-02-01": 2652.3,
        "2016-03-01": 2356.3,
        "2016-04-01": 2083.9,
        "2016-05-01": 1965.8,
        "2016-06-01": 2000.7,
        "2016-07-01": 2186.6,
        "2016-08-01": 2208.4,
        "2016-09-01": 1947.8,
        "2016-10-01": 1925.2,
        "2016-11-01": 2159.5,
        "2016-12-01": 2866.3,
        "2017-01-01": 2913.8,
        "2017-02-01": 2340.2,
        "2017-03-01": 2523.3,
        "2017-04-01": 1932.0,
        "2017-05-01": 1892.0,
        "2017-06-01": 1910.4,
        "2017-07-01": 2141.6,
        "2017-08-01": 2093.8,
        "2017-09-01": 1920.5,
        "2017-10-01": 2031.5,
        "2017-11-01": 2357.3,
        "2017-12-01": 3086.0,
        "2018-01-01": 3340.9,
        "2018-02-01": 2710.7,
        "2018-03-01": 2796.7,
        "2018-04-01": 2350.5,
        "2018-05-01": 2055.0,
        "2018-06-01": 2063.1,
        "2018-07-01": 2350.7,
        "2018-08-01": 2313.8,
        "2018-09-01": 2156.1,
        "2018-10-01": 2285.9,
        "2018-11-01": 2715.9,
        "2018-12-01": 2999.5,
        "2019-01-01": 3424.3,
        "2019-02-01": 3019.1,
        "2019-03-01": 2927.8,
        "2019-04-01": 2212.4,
        "2019-05-01": 2134.0,
        "2019-06-01": 2119.3,
        "2019-07-01": 2393.9,
        "2019-08-01": 2433.9,
        "2019-09-01": 2206.3,
        "2019-10-01": 2306.5,
        "2019-11-01": 2783.8,
        "2019-12-01": 3170.7,
        "2020-01-01": 3320.6,
        "2020-02-01": 3058.5,
        "2020-03-01": 2722.0,
        "2020-04-01": 2256.9,
        "2020-05-01": 2072.2,
        "2020-06-01": 2127.9,
        "2020-07-01": 2464.1,
        "2020-08-01": 2399.5,
        "2020-09-01": 2151.2,
        "2020-10-01": 2315.9,
        "2020-11-01": 2442.0,
        "2020-12-01": 3182.8,
        "2021-01-01": 3343.9,
        "2021-02-01": 3099.2,
        "2021-03-01": 2649.4,
        "2021-04-01": 2265.1,
        "2021-05-01": 2117.4,
        "2021-06-01": 2238.4,
        "2021-07-01": 2412.2,
        "2021-08-01": 2433.8,
        "2021-09-01": 2142.3,
        "2021-10-01": 2262.6,
        "2021-11-01": 2693.3,
        "2021-12-01": 3007.3,
        "2022-01-01": 3612.1,
        "2022-02-01": 3064.2,
        "2022-03-01": 2785.4,
        "2022-04-01": 2379.3,
        "2022-05-01": 2247.8,
        "2022-06-01": 2326.9,
        "2022-07-01": 2597.9,
        "2022-08-01": 2566.1,
        "2022-09-01": 2263.3,
    }
}

data = pd.DataFrame(data)
data.rename(columns={"value": "Natural Gas Consumption(BCF)"}, inplace=True)
data.index = pd.to_datetime(data.index)
data = data.asfreq("MS")
data.head()

	Natural Gas Consumption(BCF)
2013-01-01	2878.8
2013-02-01	2567.2
2013-03-01	2521.1
2013-04-01	1967.5
2013-05-01	1752.5

plt.figure(figsize=(12, 6))
sns.lineplot(data=data)
plt.grid()
plt.show()

png

Pembagian Data #

Data bagian akhir (data setelah tahun 2020) akan digunakan untuk memverifikasi kinerja prediksi.

data_train = data[data.index < "2020-1-1"]
data_test = data[data.index >= "2020-1-1"]

plt.figure(figsize=(12, 6))
plt.plot(data_train.index, data_train.values, label="train", linewidth=2)
plt.plot(data_test.index, data_test.values, "-.", label="test")
plt.legend()
plt.grid()

png

Pelatihan dan Prediksi Model #

Dengan merujuk pada dokumentasi statsmodels.tsa.holtwinters.ExponentialSmoothing, parameter akan ditentukan untuk melatih dan memprediksi menggunakan model.

ses = SimpleExpSmoothing(data_train)
ses = ses.fit(smoothing_level=0.1)
ses_pred = ses.forecast(33)

holt = Holt(data_train)
holt = holt.fit(smoothing_level=0.1, smoothing_trend=0.2)
holt_pred = holt.forecast(33)

hw = ExponentialSmoothing(
    data_train, trend="additive", seasonal="add", seasonal_periods=12
)
hw = hw.fit()
hw_pred = hw.forecast(33)

plt.figure(figsize=(12, 6))
plt.plot(data_train.index, data_train.values, label="train", linewidth=2)
plt.plot(data_test.index, data_test.values, "-.", label="test")
plt.plot(ses_pred.index, ses_pred.values, "-.", label="prediction(ses)")
plt.plot(holt_pred.index, holt_pred.values, "-.", label="prediction(Holt)")
plt.plot(hw_pred.index, hw_pred.values, "-o", label="prediction(Holt-Winters)")
plt.legend()
plt.grid()

png