Linear, Machine Learning and Probabilistic Approaches for Time Series Analysis (1703.01977v1)

Abstract: In this paper we study different approaches for time series modeling. The forecasting approaches using linear models, ARIMA alpgorithm, XGBoost machine learning algorithm are described. Results of different model combinations are shown. For probabilistic modeling the approaches using copulas and Bayesian inference are considered.

• The paper demonstrates that combining ARIMA with XGBoost significantly improves forecasting accuracy, achieving lower RMSE values.
• It applies classical, machine learning, and Bayesian techniques to capture both linear trends and non-linear dependencies in retail sales data.
• Quantitative results validate that hybrid models outperform standalone approaches, highlighting their potential in predictive enhancements and risk management.

A Comprehensive Analysis of Time Series Modeling Approaches

The paper presents a comparative paper of linear, machine learning, and probabilistic approaches for time series analysis, highlighting their efficacy on retail sales data from a Kaggle competition. The paper investigates various methodologies, including classical statistical methods like ARIMA, modern machine learning techniques such as XGBoost, and probabilistic models utilizing copulas and Bayesian inference.

Methodological Insights

The paper evaluates multiple approaches to time series modeling, employing root mean squared error (RMSE) for accuracy assessment. Below is a succinct outline of the actual techniques examined:

1. Linear Models and ARIMA: These models are foundational in time series forecasting and serve as a benchmark due to their interpretability and effectiveness for data with a linear trend and seasonal patterns.
2. Machine Learning: XGBoost: This gradient boosting framework is recognized for its scalability and robust performance in predictive accuracy. It's particularly beneficial when the time series exhibits non-linear dependencies.
3. Model Combinations: The paper explores adept combinations of models, such as blending ARIMA and XGBoost, and stacking methods that involve linear regression followed by boosting. These hybrid approaches tend to offer improved RMSE scores, as evidenced by different iterations across various stores.
4. Causal Inference with Copulas: The analysis showcases the use of copulas to model dependencies between multiple variables within a time series. This method is adept at capturing non-linear dependencies, offering insights into the correlation structure independent of the marginal distributions.
5. Bayesian Inference: By employing Bayesian approaches, the research determines parameter distributions for linear models under uncertainty, which is crucial for assessing risks in financial forecasts.

Numerical Results

The quantitative evaluation in the paper reflects that combining ARIMA with XGBoost resulted in superior RMSE values (e.g., 0.093 as opposed to 0.11 for ARIMA alone). This demonstrates the potential advantage of hybrid models over traditional techniques. The Bayesian inference provided meaningful insights into parameter uncertainty, aiding in risk management when dealing with volatile sales data.

Theoretical and Practical Implications

The research has significant implications for both the academic community and industry practitioners:

• Predictive Enhancements: The ability to enhance predictions using model combinations offers a pathway for more accurate and robust forecasting models in retail and similar domains.
• Risk Analysis: Probabilistic modeling approaches such as copulas offer a nuanced understanding of dependencies, which is critical in areas such as risk management where assessing the impact of extreme values or tail distributions is vital.

Future Directions

Looking forward, the paper sets the ground for several interesting avenues in time series analysis:

• Advanced Model Integration: Further exploration of model stacking and blending strategies in different contexts could yield models with superior predictive capabilities.
• Extended Utilization of Probabilistic Models: Expanding the use of vine copulas and Bayesian methods in multivariate settings offers unrealized potential for better capturing complex dependencies.
• Dynamic Model Adaptation: Investigating models that automatically adapt to changing patterns within time series could present a significant advancement in forecasting accuracy.

In conclusion, this paper demonstrates a comprehensive examination of available methodologies in time series analysis, emphasizing the benefits of combining statistical, machine learning, and probabilistic approaches. The results and discussions presented offer valuable insights that can steer future research and practical applications towards more sophisticated predictive modeling frameworks.