Efficient Estimation of Linear Asset-Pricing Models with Moving Average Errors

For most continuous time models formulated in finance, there is no closed form for the likelihood function and estimation of the parameters on the basis of discrete data will be based on an approximation rather than an exact discretization. For example, the Euler method introduces discretization bias because it ignores the internal dynamics that can be excessively erratic. We view the approximation as a difference equation and note that the solution of the continuous time model does not satisfy this difference equation. The effectiveness of the approximation will depend on the rate at which the underlying process is sampled. We investigate how much it matters: can we get significantly different estimates of the same structural parameter when we use say hourly data as compared with using monthly data under given discretization? If yes, then that discretization when applied to a data set in hand, as is done in practice, cannot be said to give robust results. We compare numerically the application of methods by Yu and Phillips (2001), Shoji and Ozaki (1998) and Ait-Sahalia (2002) in the maximum likelihood estimation of the unrestricted interest rate model proposed by Chan et al. (1992). We find that reducing the sampling rate yield large biases in the estimation of the parameters. The AitSahalia method is shown to offer a good approximation and has the advantage of reducing some of the temporal aggregation bias.

Many important factors affect the spread of childhood infectious disease. To better understand the fundamental drivers of infectious disease spread, several researchers have estimated seasonal transmission coefficients in discrete-time models. In this paper, we build upon this previous work and also develop a framework for efficient estimation using continuous differential equation models. We introduce nonlinear programming formulations to efficiently estimate model parameters and seasonal transmission profiles from existing case count data for the childhood disease, measles. We compare results from discrete time and continuous time models and address several shortcomings of the discrete-time method, including removing the need for the data reporting interval to match the time between successive cases in the chain of transmission or serial interval of the disease. Using a simultaneous approach for optimization of differential equation systems, we demonstrate that seasonal transmission parameters can be effectively estimated using continuous time models instead of discrete-time models.

Beside the wide success of discrete time models in system identification, some advantages of continuous time models have also been acknowledged, in particular, the ability of fully benefiting from fast sampling devices. This paper proposes a continuous time black-box model structure for nonlinear system identification, together with an efficient model estimation method. This model structure belongs to the class of continuous time nonlinear ARX (AutoRegressive with eXogenous input) models, with the particularity of being integrable. By applying techniques of adaptive observer, models of the proposed structure can be efficiently estimated from input-output data, without requiring computing the time derivatives of the data. The proposed model structure and estimation method are illustrated through the identification of a magneto-rheological fluid damper system.

We describe two approaches to instrumental variable estimation in binary regression measurement error models. The methods entail constructing approximate mean models for the binary response as a function of the measured predictor, the instrument, and any covariates in the model. Estimates are obtained by exploiting relationships between regression parameters, just as in linear instrumental variable estimation. In the course of deriving the approximate mean models, we obtain an alternative characterization of instrumental variable estimation in linear measurement error models.

This paper deals with asymptotic properties of the Least-Square Estimator and of two-stage estimators in multiariate linear models where the case of singular experimental matrices is included. Fristly we prove the asymptotic optimality of the best linear unbiased estimator (BLUE) when the convariance matrix is assumed to be known in a partial class of linear asymptotically unbiased and consistent sequences of estimators. Comparison of two sequences is made by the help of limits of covariance matrices. Secondly conditions are given under which sequence of Blue's. Furthermore there are a lot of cases in which the ineffienent ordinary Least-Square Estimator (OLSE) becomes asymptotically an efficient estimator when the sample size increases. General conditions are obtained under which this fact holds. Certain examples are discussed for illustration.

Contents: Acknowledgements General Introduction PART I HARRY M. MARKOWITZ Introduction to Part I Howard R. Vane and Chris Mulhearn 1. Harry Markowitz (1952a), 'Portfolio Selection' 2. Harry Markowitz (1952b), 'The Utility of Wealth' 3. H. Levy and H.M. Markowitz (1979), 'Approximating Expected Utility by a Function of Mean and Variance' 4. Harry M. Markowitz and Eric L. van Dijk (2003), 'Single-Period Mean-Variance Analysis in a Changing World' PART II MERTON H. MILLER Introduction to Part II Howard R. Vane and Chris Mulhearn 5. Franco Modigliani and Merton H. Miller (1958), 'The Cost of Capital, Corporation Finance and the Theory of Investment' 6. Franco Modigliani and Merton H. Miller (1959), 'The Cost of Capital, Corporation Finance and the Theory of Investment: Reply' 7. Merton H. Miller and Franco Modigliani (1961), 'Dividend Policy, Growth, and the Valuation of Shares' 8. Franco Modigliani and Merton H. Miller (1963), 'Corporate Income Taxes and the Cost of Capital: A Correction' 9. Merton H. Miller and Franco Modigliani (1966), 'Some Estimates of the Cost of Capital to the Electric Utility Industry, 1954-57' 10. Merton H. Miller (1977), 'Debt and Taxes' PART III WILLIAM F. SHARPE Introduction to Part III Howard R. Vane and Chris Mulhearn 11. William F. Sharpe (1963), 'A Simplified Model For Portfolio Analysis' 12. William F. Sharpe (1964), 'Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk' 13. William F. Sharpe (1966), 'Mutual Fund Performance' 14. William F. Sharpe (1978), 'Bank Capital Adequacy, Deposit Insurance, and Security Values' PART IV ROBERT C. MERTON Introduction to Part IV Howard R. Vane and Chris Mulhearn 15. Robert C. Merton (1969), 'Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case' 16. Robert C. Merton (1971), 'Optimum Consumption and Portfolio Rules in a Continuous-Time Model' 17. Robert C. Merton (1973a), 'Theory of Rational Option Pricing' 18. Robert C. Merton (1973b), 'An Intertemporal Capital Asset Pricing Model' 19. Robert C. Merton (1974), 'On the Pricing of Corporate Debt: The Risk Structure of Interest Rates' 20. Robert C. Merton (1977), 'On the Pricing of Contingent Claims and the Modigliani-Miller Theorem' PART V MYRON S. SCHOLES Introduction to Part V Howard R. Vane and Chris Mulhearn 21. Fischer Black and Myron Scholes (1972), 'The Valuation of Option Contracts and a Test of Market Efficiency' 22. Fischer Black and Myron Scholes (1973), 'The Pricing of Options and Corporate Liabilities' 23. Fischer Black and Myron Scholes (1974), 'The Effects of Dividend Yield and Dividend Policy on Common Stock Prices and Returns' 24. Myron Scholes and Joseph Williams (1977), 'Estimating Betas from Nonsynchronous Data' 25. Merton H. Miller and Myron S. Scholes (1978), 'Dividends and Taxes' Name Index

Instrumental variable estimation of dynamic linear panel data models with defactored regressors and a multifactor error structure

Efficient Estimation of Second Moment Parameters in ARCH Models

In this paper, we consider two‐stage least squares (2SLS) and simple instrumental variable (IV) type estimation of dynamic panel data models with both individual‐specific effects and heterogeneous time trend when both N and T tend to infinity. We consider the forward orthogonal deviations (FOD) proposed by (Hayakawa, et al. Econometric Reviews, 2019. Vol. 38, pp. 1055–1088) and the double first difference (2FD) to remove both the individual‐specific effects and heterogeneous trend. As the main theoretical contribution, we establish the asymptotic properties of the 2SLS estimation of the lag coefficient and find that the 2SLS estimation using FOD and optimal 2SLS estimation using 2FD are asymptotically biased of order , while the 2SLS based on 2FD using non‐optimal weighting matrix is asymptotically biased of order . We also establish the asymptotic unbiasedness of the simple IV estimation using first differenced lagged dependent variable as instrument, and establish the invalidity of using level lagged dependent variable as instrument for the simple IV estimation. Monte Carlo simulations confirm our findings in this paper.

Three-stage semi-parametric inference: Control variables and differentiability

This paper proposes a version of the generalized method of moments procedure that handles both the case where the number of moment conditions is finite and the case where there is a continuum of moment conditions. Typically, the moment conditions are indexed by an index parameter that takes its values in an interval. The objective function to minimize is then the norm of the moment conditions in a Hilbert space. The estimator is shown to be consistent and asymptotically normal. The optimal estimator is obtained by minimizing the norm of the moment conditions in the reproducing kernel Hilbert space associated with the covariance. We show an easy way to calculate this estimator. Finally, we study properties of a specification test using overidentifying restrictions. Results of this paper are useful in many instances where a continuum of moment conditions arises. Examples include efficient estimation of continuous time regression models, cross-sectional models that satisfy conditional moment restrictions, and scalar diffusion processes.

Estimation of spatial autoregressive panel data models with fixed effects

Undirected graphical models such as Markov random fields or Boltzmann machines prove useful in many signal processing and machine learning tasks. However, parameter estimation in these models is difficult due to the intractable normalising constant in their probability density functions. One powerful technique for parameter estimation in such models is score matching. This technique makes use of an objective function which is independent of the normalising constant and constitutes locally consistent estimators for the parameters of such models. However, score matching is only applicable to fully-observed models. In this paper, we extend the applicability of score matching to models with latent variables. Our estimators are unbiased, based on Monte Carlo integration. Unbiased gradient estimators open the way to optimisation through stochastic approximation. We demonstrate the performance of our methodology on two synthetic problems.

A Penalty Function Approach to Bias Reduction in Non-linear Panel Models with Fixed Effects

In order to solve the problem of parameter estimation of nonlinear model in chemical engineering, a novel heuristic optimization approach is presented. The proposed approach develops and employs particle swarm optimization (PSO) technique to search for optimal solution of the parameter estimation. Firstly, the proposed approach converts the problem of parameter estimation of nonlinear model into an equation solving problem that is prone to be optimized. Secondly, two extrema of PSO are used as the target, and all the particles synchronously move through the solution space roundly and efficiently to find the optimum parameter estimation. The feasibility of the proposed method is demonstrated by the parameter estimation example of the pyrolysis model for fir.