Feature Matching in Time Series Modeling

TL;DR

This paper advocates for a feature matching approach in time series modeling, focusing on capturing global data features like cycles and long memory rather than just short-term prediction accuracy, addressing limitations of conventional methods.

Contribution

It introduces a novel feature matching methodology that emphasizes fitting models to match the joint distribution and long-term features of time series data, moving beyond traditional prediction-based fitting.

Findings

Conventional methods often fail to capture global features of data.

Feature matching improves the ability to replicate cycles and long memory.

The approach offers a more robust alternative to traditional model fitting.

Abstract

Using a time series model to mimic an observed time series has a long history. However, with regard to this objective, conventional estimation methods for discrete-time dynamical models are frequently found to be wanting. In fact, they are characteristically misguided in at least two respects: (i) assuming that there is a true model; (ii) evaluating the efficacy of the estimation as if the postulated model is true. There are numerous examples of models, when fitted by conventional methods, that fail to capture some of the most basic global features of the data, such as cycles with good matching periods, singularities of spectral density functions (especially at the origin) and others. We argue that the shortcomings need not always be due to the model formulation but the inadequacy of the conventional fitting methods. After all, all models are wrong, but some are useful if they are fitted properly. The practical issue becomes one of how to best fit the model to data. Thus, in the absence of a true model, we prefer an alternative approach to conventional model fitting that typically involves one-step-ahead prediction errors. Our primary aim is to match the joint probability distribution of the observable time series, including long-term features of the dynamics that underpin the data, such as cycles, long memory and others, rather than short-term prediction. For want of a better name, we call this specific aim feature matching.