nep-ecm 2025-04-07 papers

on Econometrics

Issue of 2025–04–07
two papers chosen by
Sune Karlsson, Örebro universitet

Maximum Likelihood Estimation of Fractional Ornstein-Uhlenbeck Process with Discretely Sampled Data By Xiaohu Wang; Weilin Xiao; Jun Yu; Chen Zhang
Optimal formula instruments By Kirill Borusyak; Peter Hull

Maximum Likelihood Estimation of Fractional Ornstein-Uhlenbeck Process with Discretely Sampled Data

By:	Xiaohu Wang (School of Economics, Fudan University, Shanghai, China); Weilin Xiao (School of Management, Zhejiang University, Hangzhou, 310058, China); Jun Yu (Faculty of Business Administration, University of Macau, Macao, China); Chen Zhang (Faculty of Business Administration, University of Macau, Macao, China)
Abstract:	This paper first derives two analytic formulae for the autocovariance of the discretely sampled fractional Ornstein-Uhlenbeck (fOU) process. Utilizing the analytic formulae, two main applications are demonstrated: (i) investigation of the accuracy of the likelihood approximation by the Whittle method; (ii) the optimal forecasts with fOU based on discretely sampled data. The finite sample performance of the Whittle method and the derived analytic formula motivate us to introduce a feasible exact maximum likelihood (ML) method to estimate the fOU process. The long-span asymptotic theory of the ML estimator is established, where the convergence rate is a smooth function of the Hurst parameter (i.e., H) and the limiting distribution is always Gaussian, facilitating statistical inference. The asymptotic theory is different from that of some existing estimators studied in the literature, which are discontinuous at H = 3/4 and involve non-standard limiting distributions. The simulation results indicate that the ML method provides more accurate parameter estimates than all the existing methods, and the proposed optimal forecast formula offers a more precise forecast than the existing formula. The fOU process is applied to fit daily realized volatility (RV) and daily trading volume series. When forecasting RVs, it is found that the forecasts generated using the optimal forecast formula together with the ML estimates outperform those generated from all possible combinations of alternative estimation methods and alternative forecast formula.
Keywords:	Fractional Ornstein-Uhlenbeck process; Hurst parameter; Out-of-sample forecast; Maximum likelihood; Whittle likelihood; Composite likelihood
JEL:	C15 C22 C32
Date:	2025–03
URL:	https://d.repec.org/n?u=RePEc:boa:wpaper:202527

Optimal formula instruments

By:	Kirill Borusyak; Peter Hull
Abstract:	When estimating the effects of treatments defined by complex formulas, researchers often use simple functions of exogenous shocks as instruments. A leading example is â€œsimulated instrumentsâ€ for public policy eligibility, which capture variation in state-level policy generosity. We show how more powerful instruments can be constructed by incorporating heterogeneous shock exposure while using a recentering procedure to avoid bias. We characterize the asymptotically efficient instruments in this class and propose an algorithm for constructing feasible approximations to them. Compared to a simulated instrument approach, our approach yields a 44% smaller standard error on the private insurance crowd-out effect of Medicaid enrollment from the 2014 Affordable Care Act expansions.
Date:	2025–03–28
URL:	https://d.repec.org/n?u=RePEc:azt:cemmap:09/25

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