Online Generalized Method of Moments for Time Series

TL;DR

This paper introduces the online generalized method of moments (OGMM), a new framework for efficient, real-time estimation and inference in time series analysis, suitable for large-scale streaming data.

Contribution

The paper develops OGMM, an online estimation method that retains GMM's properties while significantly reducing time and memory costs for streaming data applications.

Findings

OGMM achieves semiparametric efficiency under temporal dependence.

Encouraging finite-sample performance in various online regression and testing scenarios.

Effective applications demonstrated in stochastic volatility and sensor calibration.

Abstract

Online learning has gained popularity in recent years due to the urgent need to analyse large-scale streaming data, which can be collected in perpetuity and serially dependent. This motivates us to develop the online generalized method of moments (OGMM), an explicitly updated estimation and inference framework in the time series setting. The OGMM inherits many properties of offline GMM, such as its broad applicability to many problems in econometrics and statistics, natural accommodation for over-identification, and achievement of semiparametric efficiency under temporal dependence. As an online method, the key gain relative to offline GMM is the vast improvement in time complexity and memory requirement. Building on the OGMM framework, we propose improved versions of online Sargan--Hansen and structural stability tests following recent work in econometrics and statistics. Through Monte Carlo simulations, we observe encouraging finite-sample performance in online instrumental variables regression, online over-identifying restrictions test, online quantile regression, and online anomaly detection. Interesting applications of OGMM to stochastic volatility modelling and inertial sensor calibration are presented to demonstrate the effectiveness of OGMM.