Calibrating the Nelson–Siegel–Svensson model

The Nelson–Siegel–Svensson model is widely-used for modelling the yield curve, yet many authors have reported ‘numerical difficulties’ when calibrating the model. We argue that the problem is twofold: firstly, the optimisation problem is not convex and has multiple local optima. Hence standard methods that are readily available in statistical packages are not appropriate. We implement and test an optimisation heuristic, Differential Evolution, and show that it is capable of reliably solving the model. Secondly, we also stress that in certain ranges of the parameters, the model is badly conditioned, thus estimated parameters are unstable given small perturbations of the data. We discuss to what extent these difficulties affect applications of the model.

The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach

This paper seeks to estimate a multifactor volatility model so as to describe the dynamics of interest rate markets, using data from the highly liquid but short term futures markets. The difficult problem of estimating such multifactor models is resolved by using a genetic algorithm to carry out the optimization procedure. The ability to successfully estimate a multifactor volatility model also eliminates the need to include a jump component, the existence of which would create difficulties in the practical use of interest rate models, such as pricing options or producing forecasts.term structure; volatility; mutlifactor; jump; eurodollar futures; genetic algorithm

PV panel modeling and identification

In this chapter, the modelling techniques of PV panels from I-V characteristics are discussed. At the beginning, a necessary review on the various methods are presented, where difficulties in mathematics, drawbacks in accuracy, and challenges in implementation are highlighted. Next, a novel approach based on linear system identification is demonstrated in detail. Other than the prevailing methods of using approximation (analytical methods), iterative searching (classical optimization), or soft computing (artificial intelligence), the proposed method regards the PV diode model as the equivalent output of a dynamic system, so the diode model parameters can be linked to the transfer function coefficients of the same dynamic system. In this way, the problem of solving PV model parameters is equivalently converted to system identification in control theory, which can be perfectly solved by a simple integral-based linear least square method. Graphical meanings of the proposed method are illustrated to help readers understand the underlying principles. As compared to other methods, the proposed one has the following benefits: 1) unique solution; 2) no iterative or global searching; 3) easy to implement (linear least square); 4) accuracy; 5) extendable to multi-diode models. The effectiveness of the proposed method has been verified by indoor and outdoor PV module testing results. In addition, possible applications of the proposed method are discussed like online PV monitoring and diagnostics, noncontact measurement of POA irradiance and cell temperature, fast model identification for satellite PV panels, and etc

Robust aerodynamic design of variable speed wind turbine rotors

This study focuses on the robust aerodynamic design of the bladed rotor of small horizontal axis wind turbines. The optimization process also considers the effects of manufacturing and assembly tolerances on the yearly energy production. The aerodynamic performance of the rotors so designed has reduced sensitivity to manufacturing and assembly errors. The geometric uncertainty affecting the rotor shape is represented by normal distributions of the pitch angle of the blades, and the twist angle and chord of their airfoils. The aerodynamic module is a blade element momentum theory code. Both Monte Carlo-based and the Univariate ReducedQuadrature technique, a novel deterministic uncertainty propagationmethod, are used. The performance of the two approaches is assessed both interms of accuracy and computational speed. The adopted optimization method is based on a hybrid multi-objective evolutionary strategy. The presented results highlight that the sensitivity of the yearly production to geometric uncertainties can be reduced by reducing the rotational speed and increasing the aerodynamic blade loads

The Czech Treasury Yield Curve from 1999 to the Present

The author estimates the Czech Treasury yield curve at a daily frequency from 1999 to the present. He uses the parsimonious yield curve model of Nelson and Siegel (1987), for which he suggests a parameter restriction that avoids abrupt changes in parameter estimates and thus allows for the economic interpretation of the model to hold. The estimation of the model parameters is based on market prices of Czech government bonds. The Nelson-Siegel model is shown to fit the Czech bond price data well without being over-parameterized. Thus, the model provides an accurate and consistent picture of the Czech Treasury yield curve evolution. The estimated parameters can be used to calculate spot rates and hence par rates, forward rates or the discount function for practically any maturity. To eh author´s knowledge, consistent time series of spot rates are not available for the Czech economy.yield curve, spot rates, treasury market, Nelson-Siegel

Generalized Stochastic Gradient Learning

We study the properties of generalized stochastic gradient (GSG) learning in forwardlooking models. We examine how the conditions for stability of standard stochastic gradient (SG) learning both di1er from and are related to E-stability, which governs stability under least squares learning. SG algorithms are sensitive to units of measurement and we show that there is a transformation of variables for which E-stability governs SG stability. GSG algorithms with constant gain have a deeper justification in terms of parameter drift, robustness and risk sensitivity