Time Series: ARIMA/SARIMA with Box-Jenkins Methodology¶
Status: Available
General Description¶
We will learn to model time series using the complete Box-Jenkins Methodology: identification, estimation, diagnostics, and forecasting. We will work with ARIMA and SARIMA models to capture both trends and seasonality.
Level: Advanced Dataset: AirPassengers (144 monthly observations, 1949-1960) Technologies: Python, statsmodels, matplotlib
Learning Objectives¶
- Understand the Box-Jenkins Methodology (4 phases)
- Identify components of a series: trend, seasonality, noise
- Use ACF and PACF to determine orders p, d, q
- Estimate ARIMA and SARIMA models
- Diagnose residuals (Ljung-Box, normality)
- Generate forecasts with confidence intervals
Exercise Content¶
The complete exercise is located at:
ejercicios/04_machine_learning/07_series_temporales_arima/
├── README.md # Complete Box-Jenkins theory (829 lines)
├── serie_temporal_completa.py # 10-part script (1,286 lines)
├── output/ # Directory for generated plots
└── .gitignore # Excludes output/*.png and *.csv
The script serie_temporal_completa.py covers:¶
- Loading and visualization of the original series
- Decomposition (trend + seasonality + residual)
- Stationarity tests (ADF, KPSS)
- Differencing (regular and seasonal)
- ACF/PACF for order identification
- ARIMA estimation with AIC-based selection
- SARIMA estimation with seasonal component
- Residual diagnostics (Ljung-Box, QQ-plot, residual ACF)
- Forecasting with confidence intervals
- Model comparison and metrics (MAPE, RMSE)
Theory: Box-Jenkins Methodology¶
Anatomy of the Signal: The Data Generating Process¶
Stationarity and White Noise¶
Series Decomposition¶
Transformation and Differencing¶
The Classic Decoder: ARIMA¶
Deseasonalization and SARIMA¶
The Box-Jenkins Workflow¶
Phase 1: Identification¶
- Visualize the series and detect trend/seasonality
- Apply differencing to achieve stationarity
- Analyze ACF and PACF to determine orders (p, d, q)
Phase 2: Estimation¶
- Fit ARIMA(p,d,q) or SARIMA(p,d,q)(P,D,Q)[s] model
- Compare candidate models using AIC/BIC
Phase 3: Diagnostics¶
- Verify that residuals are white noise
- Ljung-Box test (autocorrelation)
- Normality test
- QQ plot
Phase 4: Forecasting¶
- Generate predictions with confidence intervals
- Evaluate accuracy with metrics (MAPE, RMSE)
Exercise Results¶
Selected model: SARIMA(1,1,0)(0,1,0)[12]
- AIC: -445.41
- MAPE: 7.41%
- Correctly captures trend and monthly seasonality
Interactive Dashboard¶
You can explore the results in the interactive dashboard:
The dashboard includes 6 tabs with interactive Plotly charts: original series, decomposition, stationarity, ACF/PACF, diagnostics, and forecasting.
Resources¶
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Course: Big Data with Python - From Zero to Production Instructor: Juan Marcelo Gutierrez Miranda | @TodoEconometria Hash ID: 4e8d9b1a5f6e7c3d2b1a0f9e8d7c6b5a4f3e2d1c0b9a8f7e6d5c4b3a2f1e0d9c Methodology: Progressive exercises with real data and professional tools
Academic references:
- Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley.
- Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.
- Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.