Python - SARIMAX estimation model - 3/3

ARIMA 에서 파생된 SARIMAX 예측 모델을 사용해 추정해 보는 포스팅

예제 순서

1.US Wholesale Price Index (WPI) 데이터 Set에 ARIMA order (1,1,1)을 넣어서 추정

2.1번 예제에 MA(4) 항을 넣어서 계절적 특성(seasonal effect) 을 추가한다

3.월별 항공사 데이터에 ARIMA order(2,1,0) 과 Seasonal order(1,1,0,12)를 넣기

4.외인성 회귀 변수가 있는 ARIMA (1,1) 모델의 사용

5.Dynamic Forecasting

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Example - 5 - Dynamic Forecasting

Code

# Dataset

raw = pd.read_stata(BytesIO(friedman2))

raw.index = raw.time

raw.index.freq = "QS-OCT"

data = raw.loc[:'1981']

# Variables

endog = data.loc['1959':, 'consump']

exog = sm.add_constant(data.loc['1959':, 'm2'])

nobs = endog.shape[0]

# Fit the model

mod = sm.tsa.statespace.SARIMAX(endog.loc[:'1978-01-01'], exog=exog.loc[:'1978-01-01'], order=(1,0,1))

fit_res = mod.fit(disp=False, maxiter=250)

print(fit_res.summary())

mod = sm.tsa.statespace.SARIMAX(endog, exog=exog, order=(1,0,1))

res = mod.filter(fit_res.params)

# In-sample one-step-ahead predictions

predict = res.get_prediction()

predict_ci = predict.conf_int()

**get_prediction() 에 값이 들어있지 않으면 바로 다음 data를 예측해준다**

# Dynamic predictions

predict_dy = res.get_prediction(dynamic='1978-01-01')

predict_dy_ci = predict_dy.conf_int()

**예측의 시작 날짜를 '1978-01-01'로 지정한다**

# Graph

fig, ax = plt.subplots(figsize=(9,4))

npre = 4

ax.set(title='Personal consumption', xlabel='Date', ylabel='Billions of dollars')

# Plot data points

data.loc['1977-07-01':, 'consump'].plot(ax=ax, style='o', label='Observed')

# Plot predictions

predict.predicted_mean.loc['1977-07-01':].plot(ax=ax, style='r--', label='One-step-ahead forecast')

ci = predict_ci.loc['1977-07-01':]

ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='r', alpha=0.1)

predict_dy.predicted_mean.loc['1977-07-01':].plot(ax=ax, style='g', label='Dynamic forecast (1978)')

ci = predict_dy_ci.loc['1977-07-01':]

ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='g', alpha=0.1)

legend = ax.legend(loc='lower right')

예측의 오차그래프 제작

# Prediction error

# Graph

fig, ax = plt.subplots(figsize=(9,4))

npre = 4

ax.set(title='Forecast error', xlabel='Date', ylabel='Forecast - Actual')

# In-sample one-step-ahead predictions and 95% confidence intervals

predict_error = predict.predicted_mean - endog

predict_error.loc['1977-10-01':].plot(ax=ax, label='One-step-ahead forecast')

ci = predict_ci.loc['1977-10-01':].copy()

ci.iloc[:,0] -= endog.loc['1977-10-01':]

ci.iloc[:,1] -= endog.loc['1977-10-01':]

ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], alpha=0.1)

# Dynamic predictions and 95% confidence intervals

predict_dy_error = predict_dy.predicted_mean - endog

predict_dy_error.loc['1977-10-01':].plot(ax=ax, style='r', label='Dynamic forecast (1978)')

ci = predict_dy_ci.loc['1977-10-01':].copy()

ci.iloc[:,0] -= endog.loc['1977-10-01':]

ci.iloc[:,1] -= endog.loc['1977-10-01':]

ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='r', alpha=0.1)

legend = ax.legend(loc='lower left');

legend.get_frame().set_facecolor('w')