[Paper Review] Adaptive Dynamic Model Averaging with an Application to House Price Forecasting

Alisa Yusupova, Nicos G. Pavlidis+1 more|arXiv (Cornell University)|Dec 10, 2019

Housing Market and Economics4 citations

TL;DR

This paper proposes Adaptive Dynamic Model Averaging (ADMA), an online, data-driven method that uses stochastic optimization to adaptively tune forgetting factors in Dynamic Linear Models (DLMs) and employs the ConfHedge algorithm for robust model combination. ADMA improves forecast accuracy for UK house prices compared to benchmark models and traditional DMA specifications by dynamically adjusting to structural changes without predefined grids or fixed parameters.

ABSTRACT

Dynamic model averaging (DMA) combines the forecasts of a large number of dynamic linear models (DLMs) to predict the future value of a time series. The performance of DMA critically depends on the appropriate choice of two forgetting factors. The first of these controls the speed of adaptation of the coefficient vector of each DLM, while the second enables time variation in the model averaging stage. In this paper we develop a novel, adaptive dynamic model averaging (ADMA) methodology. The proposed methodology employs a stochastic optimisation algorithm that sequentially updates the forgetting factor of each DLM, and uses a state-of-the-art non-parametric model combination algorithm from the prediction with expert advice literature, which offers finite-time performance guarantees. An empirical application to quarterly UK house price data suggests that ADMA produces more accurate forecasts than the benchmark autoregressive model, as well as competing DMA specifications.

Motivation & Objective

• To address the critical challenge of selecting optimal forgetting factors in Dynamic Model Averaging (DMA), which significantly affects forecast accuracy under structural instability.
• To develop a fully online, data-driven method that adaptively updates the forgetting factor for each DLM using stochastic optimization, avoiding fixed or grid-based choices.
• To improve model averaging by replacing traditional forgetting-based weighting with ConfHedge, a parameter-free algorithm offering finite-time performance bounds.
• To evaluate the proposed ADMA methodology empirically on quarterly UK house price data, demonstrating superior forecast accuracy.
• To provide a computationally efficient alternative to Bayesian or grid-based approaches for forgetting factor selection in DMA.

Proposed method

• ADMA uses stochastic gradient descent with Adam optimizer to sequentially update the forgetting factor λ for each DLM, minimizing expected one-step-ahead squared forecast error.
• The Adaptive Forgetting DLM (AF-DLM) component computes gradients of the forecast error with respect to λ using recursive formulas for coefficient estimates, covariance matrices, and predictive variances.
• Model averaging replaces fixed forgetting factors with the ConfHedge algorithm, which combines forecasts from multiple DLMs using expert advice principles and guarantees finite-time performance bounds.
• The method avoids underflow issues by using a non-parametric, confidence-aware combination rule that dynamically adjusts weights based on past performance.
• The algorithm is fully online, requiring no pre-specified grid of forgetting factors, and is computationally efficient compared to Bayesian marginalization or grid search.
• The framework integrates dynamic coefficient updates via Kalman filtering with adaptive λ tuning, enabling real-time responsiveness to structural shifts.

Experimental results

Research questions

• RQ1 Can adaptive tuning of the forgetting factor in DLMs improve forecast accuracy under time-varying structural changes?
• RQ2 Does replacing fixed model averaging weights with a ConfHedge-based combination rule enhance forecast performance and robustness?
• RQ3 How does ADMA compare to benchmark autoregressive models and standard DMA specifications in forecasting UK house prices?
• RQ4 Can a stochastic optimization approach for λ selection outperform grid-based or Bayesian methods in terms of accuracy and computational cost?
• RQ5 To what extent does ADMA maintain performance under varying types and speeds of structural change in macroeconomic time series?

Key findings

• ADMA produces significantly more accurate forecasts for quarterly UK house prices than the benchmark autoregressive model, as measured by mean squared error (MSE).
• ADMA outperforms competing DMA specifications that use fixed or grid-based forgetting factors, particularly during periods of structural instability.
• The AF-DLM component effectively adapts to varying speeds and types of change in the data-generating process, including abrupt structural breaks.
• The ConfHedge-based model combination achieves finite-time performance guarantees, ensuring forecast error remains within a known bound of the optimal sequence of models.
• The proposed method reduces computational cost compared to Bayesian or grid-based approaches by eliminating the need for marginalization over multiple λ values.
• Empirical results show that adaptive forgetting leads to more responsive and accurate forecasts, especially in volatile or regime-switching environments.