[ML] 전통적 시계열 모델링 - ARIMA

전처리

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

import scipy.stats as stats
import statsmodels.api as sm
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

from sklearn.metrics import *

# 검증 함수
def residual_diag(residuals, lags = 20) :

    print('* 정규성 검정(> 0.05) : ', round(stats.shapiro(residuals)[1],5))
    print('* 정상성 검정(< 0.05) : ', round(sm.tsa.stattools.adfuller(residuals)[1],5))
    print('* 자기상관성 확인(ACF, PACF)')
    fig,ax = plt.subplots(1,2, figsize = (15,5))
    plot_acf(residuals, lags = lags, ax = ax[0])
    plot_pacf(residuals, lags = lags, ax = ax[1])
    plt.show()
    
path = 'retail_demand2.csv'
data = pd.read_csv(path, usecols = ['date', 'sales', 'tot_sales', 'comp_sales'])
data = data.loc[data['date']<= '2015-10-31'].reset_index(drop = True)

# 날짜 -> 인덱스
data['DT'] = data['date']
data.set_index('DT', inplace=True)

# 날짜 단위 정하기
df = data.asfreq('D')

# y만들기
df['y'] = df['sales'].shift(-1)
df.dropna(axis = 0, inplace = True)

 

 

데이터 분할

# x,y 데이터 분할
target = 'y'

x = df.drop([target, 'date'], axis = 1)
y = df.loc[:, target]

from sklearn.model_selection import TimeSeriesSplit

val_size = 30
nfold = 3

#시계열 데이터 분할
tscv = TimeSeriesSplit(n_splits = nfold, test_size = val_size)

 

ARIMA

#y 값 분리
train = y[:-30]
val = y[-30:]

#모델 학습
model1_1 = sm.tsa.SARIMAX(train, order=(1,0,1)).fit() #ARMA
model1_2 = sm.tsa.SARIMAX(train, order=(1,1,1)).fit() #ARIMA

# 잔차 진단
residuals = model1_2.resid
residual_diag(residuals)

# AIC
print('model1 AIC :', model1_1.aic)
print('model2 AIC :', model1_2.aic)

# Validation
pred = model1_2.forecast(30)
mean_absolute_error(val, pred)

 

hyper parameter tuning

from itertools import product

# product 함수를 이용하여 값의 조합을 구성
p = [0,1,2,3,4]
q = [0,1,2,3,4]
d = [0,1]
iter = list(product(p,d,q))

# Grid Search
mae, aic = [],[]
for i in iter :
    model_fit = sm.tsa.SARIMAX(train, order=(i[0],i[1],i[2])).fit()
    pred = model_fit.forecast(30)
    mae.append( mean_absolute_error(val, pred))
    aic.append(model_fit.aic)
    print(i)
    
    
result = pd.DataFrame({'params(p,d,q)' : iter, 'mae' : mae, 'aic':aic})

model2_1 = sm.tsa.SARIMAX(train, order=(3,1,3)).fit()
model2_2 = sm.tsa.SARIMAX(train, order=(4,1,4)).fit()

# 잔차 진단
residuals = model2_2.resid
residual_diag(residuals)

# AIC
print('model2 AIC :', model2_2.aic)

# Validation
pred = model2_2.forecast(30)
mean_absolute_error(val, pred)

Cross Validation

rmse, mae, mape, aic = [],[],[],[]
residuals = []
preds = []
p,d,q = 4,1,4

for train_index, val_index in tscv.split(x):

    # 인덱스로 데이터 분할
    train = y[train_index]
    val = y[val_index]

    # 학습
    model = sm.tsa.SARIMAX(train, order=(p,d,q)).fit()

    # 예측
    pred = model.forecast(val_size)
    preds += list(pred)

    # 잔차 저장
    residuals += list(model.resid)

    # 평가
    rmse.append(mean_squared_error(val, pred, squared = False))
    mae.append(mean_absolute_error(val, pred))
    mape.append(mean_absolute_percentage_error(val, pred))
    aic.append(model.aic)