Estimating Functions and Equations: An Essay on Historical Developments with Applications to Econometrics

The idea of using estimating functions goes a long way back, at least to Karl Pearson's introduction to the method of moments in 1894. It is now a very active area of research in the statistics literature. One aim of this chapter is to provide an account of the developments relating to the theory of estimating functions. Starting from the simple case of a single parameter under independence, we cover the multiparameter, presence of nuisance parameters and dependent data cases. Application of the estimating functions technique to econometrics is still at its infancy. However, we illustrate how this estimation approach could be used in a number of time series models, such as random coefficient, threshold, bilinear, autoregressive conditional heteroscedasticity models, in models of spatial and longitudinal data, and median regression analysis. The chapter is concluded with some remarks on the place of estimating functions in the history of estimation.

Stock returns, size, and book-to-market equity

Purpose – The purpose of this paper is to reinvestigate the performance of common stock returns with respect to two popularly known firm level characteristics: size and book-to-market ratio. Design/methodology/approach – All of New York Stock Exchange, American Stock Exchange, and National Association of Securities Dealers Automated Quotations stocks between July 1926 and June 2007 are used, and divided into various size and book-to-market equity groups. The extension of the various versions of the simple Fama-French model is implemented. Findings – From the findings, it is inferred that: two risk factors based on the mimicking return for the size and book-to-market ratio play a significant role in capturing strong variation in stock returns; and volatility persistence can significantly improve the common risk factors' impact in explaining the time series variation in size and book-to-market sorted portfolios. Research limitations/implications – In some sense, the model is based on only two firm level variables. In reality there exists plenty of other sources of average return anomalies. For a clearer understanding, an integration of various firm level characteristics would be an interesting issue to explore. A general equilibrium model that incorporates volatility exposure in a Fama-French framework would be a challenging task as well. Practical implications – The approach will help scholars and investment professionals make robust quantification of risk and average returns with respect to various measures of fundamental value. Originality/value – The patterns in the monthly and yearly average excess returns with respect to two firm level characteristics, which documented are consistent with earlier studies. Even though the important role of firm level characteristics on the average-return anomalies of common stocks is widely known, the approach is the very first that extends its support with respect to volatility models.Financial risk, Stock returns, Volatility

Modeling Conditional Heteroskedasticity in Time Series and Spatial Analysis

136 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.My fourth chapter investigates heterogeneity in the assessment of spatial dependence by exploring (jointly) two main mechanisms: distributional misspecification and conditional heteroskedasticity. I first derive a simple specification test for spatial autoregressive model using the information matrix (IM) test principle. As a byproduct of my test development, I obtain a general model that has similar features like autoregressive conditional heteroskedasticity (ARCH) in time series context. My suggested spatial ARCH (SARCH) model can take account of some of the stylized facts observed in spatial data. To illustrate the usefulness of our test and SARCH model, I apply our theoretical result to Boston housing price data and show the importance of modeling the conditional second moment in spatial context.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Modeling Conditional Heteroskedasticity in Time Series and Spatial Analysis

136 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.My fourth chapter investigates heterogeneity in the assessment of spatial dependence by exploring (jointly) two main mechanisms: distributional misspecification and conditional heteroskedasticity. I first derive a simple specification test for spatial autoregressive model using the information matrix (IM) test principle. As a byproduct of my test development, I obtain a general model that has similar features like autoregressive conditional heteroskedasticity (ARCH) in time series context. My suggested spatial ARCH (SARCH) model can take account of some of the stylized facts observed in spatial data. To illustrate the usefulness of our test and SARCH model, I apply our theoretical result to Boston housing price data and show the importance of modeling the conditional second moment in spatial context.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD