Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations

Maximum-likelihood estimates of the parameters of stochasticdifferential equations are consistent and asymptotically efficient,but unfortunately difficult to obtain if a closed-form expressionfor the transitional probability density function of the processis not available. As a result, a large number of competing estimationprocedures have been proposed. This article provides a criticalevaluation of the various estimation techniques. Special attentionis given to the ease of implementation and comparative performanceof the procedures when estimating the parameters of the Cox–Ingersoll–Rossand Ornstein–Uhlenbeck equations respectively.     

Extending the Lee–Carter model: a three-way decomposition

In this paper, we focus on a Multi-dimensional Data Analysis approach to the Lee–Carter (LC) model of mortality trends. In particular, we extend the bilinear LC model and specify a new model based on a three-way structure, which incorporates a further component in the decomposition of the log-mortality rates. A multi-way component analysis is performed using the Tucker3 model. The suggested methodology allows us to obtain combined estimates for the three modes: (1) time, (2) age groups and (3) different populations. From the results obtained by the Tucker3 decomposition, we can jointly compare, in both a numerical and graphical way, the relationships among all three modes and obtain a time-series component as a leading indicator of the mortality trend for a group of populations. Further, we carry out a correlation analysis of the estimated trends in order to assess the reliability of the results of the three-way decomposition. The model's goodness of fit is assessed using an analysis of the residuals. Finally, we discuss how the synthesised mortality index can be used to build concise projected life tables for a group of populations. An application which compares 10 European countries is used to illustrate the approach and provide a deeper insight into the model and its implementation.     

A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances

Cross-sectional spatial models frequently contain a spatial lag of the dependent variable as a regressor or a disturbance term that is spatially autoregressive. In this article we describe a computationally simple procedure for estimating cross-sectional models that contain both of these characteristics. We also give formal large-sample results.     

On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation

Recent studies in the empirical finance literature have reportedevidence of two types of asymmetries in the joint distributionof stock returns. The first is skewness in the distributionof individual stock returns. The second is an asymmetry in thedependence between stocks: stock returns appear to be more highlycorrelated during market downturns than during market upturns.In this article we examine the economic and statistical significanceof these asymmetries for asset allocation decisions in an out-of-samplesetting. We consider the problem of a constant relative riskaversion (CRRA) investor allocating wealth between the risk-freeasset, a small-cap portfolio, and a large-cap portfolio. Weuse models that can capture time-varying moments up to the fourthorder, and we use copula theory to construct models of the time-varyingdependence structure that allow for different dependence duringbear markets than bull markets. The importance of these twoasymmetries for asset allocation is assessed by comparing theperformance of a portfolio based on a normal distribution modelwith a portfolio based on a more flexible distribution model.For investors with no short-sales constraints, we find thatknowledge of higher moments and asymmetric dependence leadsto gains that are economically significant and statisticallysignificant in some cases. For short sales-constrained investorsthe gains are limited.     

Gaussian Estimation and Forecasting of Multi-Factor Term Structure Models with an Application to Japan and the United Kingdom

In this paper we extend the exact discrete model of Bergstrom (1966) first used in empirical finance by Brennan and Schwartz (1979) to estimate their two-factor term structure model to estimate other two-factor term structure models using the recent assumption in Nowman (1997) for single factor models. Following Nowman (1997) we use the exact Gaussian estimation methods of Bergstrom (1983–1986, 1990) to estimate two-factor CKLS, Vasicek and CIR models. We estimate the models using monthly UK and Japanese interest rate data and our results indicate that the estimation method works well in practice.     

Double Entry Bookkeeping and the Distributional Properties of a Firm's Financial Ratios

Our purpose here is to assess whether the innate properties of the double entry bookkeeping system are such that financial ratios, calculated from the balance sheet summary measures implied by it, will be generated by distributional forms with non‐convergent moments. Our analysis begins with a brief summary of some important analytical properties of the debt and equity components of the double entry bookkeeping system. We then use these to determine the time series and distributional properties of the debt to equity ratio itself. Our analysis shows that even when the evolution of balance sheet summary measures like debt and equity can be described by 'well behaved' distributional processes, there is a distinct possibility that ratios derived from them will evolve in terms of distributional forms with non‐convergent moments. We argue that this has serious implications for parameter estimation as well as the integrity of the regression and/or discriminant procedures which underscore bankruptcy and financial distress prediction models based on financial ratios derived from the double entry bookkeeping system.     

Equality of Real Returns on Canadian and US Treasury Bills: A Fractional Cointegration Analysis

This paper empirically analyzes the long memory relationship between the real returns on Canadian and US Treasury bills. A fractional cointegration approach, instead of conventional integer integration (unit root) and cointegration approaches, is used in analyzing the relationship. The advantage of fractionally integrated models is that they allow a smooth transition from a stationary process to a unit-root process. Furthermore, such models embody unit-root models as a special case. The models are therefore more general and appropriate for empirical analysis. By using fractionally integrated models, one also resolves the problems of an inconsistency in test results associated with using unit root and cointegration approaches. Briefly, it is found that the real returns on Canadian and US Treasury bills are fractionally integrated and the order of integration is significantly less than unity. Furthermore, the difference between the real returns follows a stationary process. This indicates that the Canadian and the US capital markets as well as product markets are well integrated. Furthermore, the domestic monetary authorities will not be able to influence the domestic real interest rate independent of the other market in the long-run.     

On discontinuous frequency functions of two variables

The theory of discontinuous frequency functions of one variable has been well elaborated, especially due to the important researches of Professor Steffensen ¹ See f. i. Steffensen: Matematisk Iagtagelseslære, p. 32 f. while the theory of discontinuous frequency functions of two and more variables has been almost neglected, in spite of the fact that all statisticians agree as to the importance of this topic.     

经典波动模型下的最优债券投资组合

文章认为,由于利率和股价兼有相同的趋势性和波动性属性,股价经典波动模型对利率建模具有研究价值。通过引入经典的波动模型,结合极大似然估计的方法,本文探讨了无风险债券的最优投资方案,并将该成果运用于全球主要国债市场进行实证模拟投资,结果表明,该模型在全球主要国债市场均能取得较好的超额收益。     

Bivariate Nonparametric Density Estimation of Stock Prices and Volume

This paper comprehensively investigates the joint movement of stock prices and trading volume of New York and Tokyo stock markets by undertaking nonparametric density estimation. Bivariate nonparametric density estimation has been reported as a powerful tool for revealing complicated relations between two variables. In application to finance, it is important to use a method robust for heavy-tailed densities, since the distributions of asset price changes are known to have heavy tails, and information about sudden and large price changes is contained in the tails. The empirical regularities found in this paper are mostly consistent with previous literature, but partially disagrees with the work of Gallant et al. (1992).     

Boundary Conditions for Ratios with Positively Distributed Components

This paper describes the statistical properties of the ratio of two positively distributed variables where the numerator is a component of the denominator and where, therefore, the ratio has implicit boundaries of 0 and 1. Johnson's bounded distribution (the S_B) is suggested as a model for ratios of this type, and is derived in this paper as a ratio of lognormal variates. An empirical analysis of bounded financial ratios of UK companies confirms the goodness of fit.