Estimating yield curves of the U.S. Treasury securities: An interpolation approach

Following the approach of interpolation, this paper proposes the multiple exponential decay model to fit yield curves for both the U.S. TIPS market and the conventional Treasury security market. Several estimation methods, including the unconstrained/constrained nonlinear minimization, quadratic programming, and the iterative linear least squares, are applied to estimate the unknown parameters according to different curve‐fitting purposes. Comparisons between the proposed model and the alternatives show that the multiple exponential decay successfully (1) adapts to a variety of shapes associated with yield curves, (2) (partially) keeps in line with the economic interpretations of Nelson–Siegel summarized by Diebold and Li ( 2006 ), and (3) dominates the competing models in curve‐fitting performance measured by mean fitted‐price errors over the sample period. In addition, the exact specification of a nonparametric interpolation model is pinned down by applying three statistical tools, which enable us to jointly take into account validity, optimality, and parsimoniousness of the proposed model.     

用基变换方法求多项式的泰勒公式

通过分析多项式函数f(x)在不同点处的泰勒公式与线性空间基变换的联系,得到了多项式在同点处泰勒公式的一种求解方法。     

Numerical issues in threshold autoregressive modeling of time series

This paper analyses the contribution of various numerical approaches to making the estimation of threshold autoregressive time series more efficient. It relies on the computational advantages of QR factorizations and proposes Givens transformations to update these factors for sequential LS problems. By showing that the residual sum of squares is a continuous rational function over threshold intervals it develops a new fitting method based on rational interpolation and the standard necessary optimality condition. Taking as benchmark a simple grid search, the paper illustrates via Monte Carlo simulations the efficiency gains of the proposed tools.     

Exact and approximate D-optimal designs in polynomial regression

If the sample sizen is large enough, then the exact polynomial regression designs obtained by rounding the weights of the approximate D-optimal design to integral multiples of 1/n are D-optimal. This was shown by alaevskiî (1966) and Gaffke (1987). In this note, an efficient algorithm to determine the minimum sample sizen _d for a polynomial model of degreed is derived from a condition given by Huang (1987). Under an additional assumption we show that the conditions of Gaffke and Huang are equivalent; we verify the additional assumption for polynomial degreed40.     

Convergence of numerical methods for valuing path-dependent options using interpolation

One method for valuing path-dependent options is the augmented state space approach described in Hull and White (1993) and Barraquand and Pudet (1996), among others. In certain cases, interpolation is required because the number of possible values of the additional state variable grows exponentially. We provide a detailed analysis of the convergence of these algorithms. We show that it is possible for the algorithm to be non-convergent, or to converge to an incorrect answer, if the interpolation scheme is selected in appropriately. We concentrate on Asian options, due to their popularity and because of some errors in the previous literature. This revised version was published online in June 2006 with corrections to the Cover Date.     

集值函数及向量值函数的两类线性算子逼近

本文得到了利用插值型线性算子列及积分型算子列逼近连续集值函数及连续向量值函数的收敛逼近阶。     

基于泰勒公式的交错级数审敛准则的改进

本文利用泰勒公式,对文献[2]中交错级数的一种收敛准则给出了新的证明,并将此准则进行了改进,使其可以应用于由复合函数构成的更复杂的级数形式。     

Interpolating the Lorenz Curve: Methods to Preserve Shape and Remain Consistent with the Concentration Curves for Components

C¹‐class interpolation methods that preserve monotonicity and convexity and are thus suitable for the estimation of the Lorenz curve from grouped data are not widely known. Instead, parametric models are usually applied for such estimation. Parametric models, however, have difficulty in accurately approximating every part of income/expenditure distributions. This paper proposes two types of C¹‐class shape‐preserving interpolation methods. One is a piecewise rational polynomial interpolation (proposed independently by Stineman and Delbourgo) that enables consistent interpolation of the concentration curves for income/expenditure components, attaining approximately the same accuracy as that of the existing methods when applied to decile‐grouped data or to more detailed aggregation. Another is a Hybrid interpolation that employs pieces of curves derived from parametric models on end intervals. Empirical comparisons show that the Hybrid interpolation (with the assistance of parametric models for class‐boundary estimation) outperforms the existing methods even when applied to quintile‐grouped data without class boundaries.     

Currency substitution,risk premia and the Taylor principle

This paper studies the equilibrium determinacy properties of a simple interest rate rule in a small open economy subject to currency substitution (i.e., the use of a foreign currency for domestic transactions) and risk premia on foreign borrowing. It shows that if currencies are substitute in the provision of liquidity services the rule׳s response to inflation has to be sufficiently above unity for the equilibrium to be locally determinate. This reinforced Taylor principle requirement appears to be more binding in economies characterized by a larger elasticity of currency substitution, more debt-elastic country risk premia, and intermediate degrees of dollarization in transactions.     

Monetary policy rules with PID control features: evidence from the UK,USA and EU

ABSTRACT

This paper considers the extent to which the monetary policy operations of three major central banks can be regarded as an application of Proportional-Integral-Derivative (PID) control rules. The paper outlines the general PID framework and estimates a series of dynamic models to identify how interest rate policy adjustments are affected by the rate of inflation and the level of macroeconomic activity. The paper examines data for the UK, the USA and the Eurozone. The results suggest that the PID rules can provide a useful theoretical and empirical framework for estimating central bank responses to the inflation and macroeconomic activity variables by improving the explanatory power of the Taylor rule model and determining the effect of the parameters.