السلاسل الزمنية والتنبؤ للتخطيط المؤسسي بلغتي Python وR

import numpy as np
import statsmodels.api as sm
from statsmodels.tsa.statespace.sarimax import SARIMAX

# Built-in weekly CO2 series aggregated to monthly
y = (sm.datasets.co2.load_pandas().data["co2"]
     .resample("MS").mean().ffill())
train, test = y[:-24], y[-24:]

# Backtest: fit on training window, score last 24 months
fit = SARIMAX(train, order=(1, 1, 1),
              seasonal_order=(0, 1, 1, 12)).fit(disp=False)
pred = fit.forecast(len(test))
naive = y.shift(12)[-24:]  # seasonal naive benchmark
mae = lambda f: np.mean(np.abs(test - f))
print(f"MAE  sarima={mae(pred):.3f}  naive={mae(naive):.3f}")

# Same parameters on full data: 12 months, 95% interval
fc = fit.apply(y).get_forecast(12).summary_frame(alpha=0.05)
print(fc[["mean", "mean_ci_lower", "mean_ci_upper"]].round(2))

library(fable)
library(tsibble)
library(dplyr)

# Built-in AirPassengers as a monthly tsibble
ap <- as_tsibble(AirPassengers)
train <- ap |> filter(index < yearmonth("1959 Jan"))

# Competing models fitted on the training window
fit <- train |> model(
  ets    = ETS(log(value)),
  arima  = ARIMA(log(value)),
  snaive = SNAIVE(log(value)))

# Backtest on 1959-1960: RMSE, MAE, MAPE, MASE
fit |> forecast(h = 24) |> accuracy(ap)

# Refit on full data: 12-month forecast, 95% interval
ap |> model(ETS(log(value))) |>
  forecast(h = 12) |> hilo(level = 95)