nep-ecm New Economics Papers
on Econometrics
Issue of 2007‒02‒24
twenty-six papers chosen by
Sune Karlsson
Orebro University

  1. Forecasting with Panel Data By Badi H. Baltagi
  2. GMM for panel count data models By Frank Windmeijer
  3. Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities By Adam Rosen
  4. Covariance-based orthogonality tests for regressors with unknown persistence By Alex Maynard; Katsumi Shimotsu
  5. Methods for estimating a conditional distribution function By Rodney C Wolff; Peter Hall; Qiwei Yao
  6. Adaptive orthogonal series estimation in additive stochastic regression models By Rodney C Wolff; Jiti Gao; Howell Tong
  7. A time-domain test for some types of non-linearity By Rodney C Wolff; Adrian G Barnett
  8. Bayesian Likelihoods for Moment Condition Models By Giuseppe Ragusa
  9. Evaluating the Empirical Performance of Alternative Econometric Models for Oil Price Forecasting By Matteo Manera; Chiara Longo; Anil Markandya; Elisa Scarpa
  10. Phase randomisation: a convergence diagnostic test for MCMC By Rodney C Wolff; Darfiana Nur; Kerrie L Mengersen
  11. Exact critical value and power functions for the conditional likelihood ratio and related tests in the IV regression model with known covariance By Grant Hillier
  12. Statistical tests for Lyapunov exponents of deterministic systems By Rodney C Wolff; Qiwei Yao; Howell Tong
  13. Estimators of integrals of powers of density derivatives By Rodney C Wolff; Peter Hall
  14. Properties of distributions and correlation integrals for generalised versions of the logistic map By Rodney C Wolff; Peter Hall
  15. Estimation with many instrumental variables By Christian Hansen; Jerry Hausman; Whitney Newey
  16. Forming Priors for DSGE Models (and How It Affects the Assessment of Nominal Rigidities) By Del Negro, Marco; Schorfheide, Frank
  17. Using a Laplace approximation to estimate the random coefficients logit model by non-linear least squares By Matthew Harding; Jerry Hausman
  18. Non parametric Fractional Cointegration Analysis By Mauro Costantini; Roy Cerqueti
  19. Tourism in the Canary Islands: Forecasting Using Several Seasonal Time Series Models By Juncal Cuñado; Luis A. Gil-Alaña
  20. Properties of invariant distributions and Lyapunov exponents for chaotic logistic maps By Rodney C Wolff; Peter Hall
  21. On the conditional likelihood ratio test for several parameters in IV regression By Grant Hillier
  22. On Least Squares Estimation When the Dependent Variable is Grouped By Mark. B. Stewart
  23. Predicting Sovereign Debt Crises Using Artificial Neural Networks: A Comparative Approach By Marco Fioramanti
  24. Predictive Systems: Living with Imperfect Predictors By Pástor, Lubos; Stambaugh, Robert F
  25. A New Continuous Distribution and Two New Families of Distributions Based on the Exponential By Guillermina Jasso; Samuel Kotz
  26. Genetic algorithm estimation of interest rate term structure By Ricardo Gimeno; Juan M. Nave

  1. By: Badi H. Baltagi (Center for Policy Research, Maxwell School, Syracuse University, Syracuse, NY 13244-1020)
    Abstract: This paper gives a brief survey of forecastiang with panel data. Starting with a simple error component regression model and surveying best linear unbiased prediction under various assumptions of the disturbance term. This includes various ARMA models as well as spatial autoregressive models. The paper also surveys how these forecasts have been used in panel data applications, running horse races between heterogeneous and homogeneous panel data models using out of sample forecasts.
    Keywords: forecasting; BLUP; panel data; spatial dependence; serial correlation; heterogeneous panels.
    JEL: C33
  2. By: Frank Windmeijer (Institute for Fiscal Studies and University of Bristol)
    Abstract: This paper gives an account of the recent literature on estimating models for panel count data. Specifically, the treatment of unobserved individual heterogeneity that is correlated with the explanatory variables and the presence of explanatory variables that are not strictly exogenous are central. Moment conditions are discussed for these type of problems that enable estimation of the parameters by GMM. As standard Wald tests based on efficient two-step GMM estimation results are known to have poor finite sample behaviour, alternative test procedures that have recently been proposed in the literature are evaluated by means of a Monte Carlo study.
    Keywords: GMM, exponential models, hypothesis testing
    JEL: C12 C13 C23
    Date: 2006–10
  3. By: Adam Rosen (Institute for Fiscal Studies and University College London)
    Abstract: This paper proposes a new way to construct confidence sets for a parameter of interest in models comprised of finitely many moment inequalities. Building on results from the literature on multivariate one-sided tests, I show how to test the hypothesis that any particular parameter value is logically consistent with the maintained moment inequalities. The associated test statistic has an asymptotic chi-bar-square distribution, and can be inverted to construct an asymptotic confidence set for the parameter of interest, even if that parameter is only partially identified. The confidence sets are easily computed, and Monte Carlo simulations demonstrate good finite sample performance.
    Keywords: Partial identification, inference, moment inequalities
    JEL: C3 C12
    Date: 2006–12
  4. By: Alex Maynard (Wilfrid Laurier University); Katsumi Shimotsu (Queen's University)
    Abstract: This paper develops a new test of orthogonality based on a zero restriction on the covariance between the dependent variable and the predictor. The test provides a useful alternative to regression-based tests when conditioning variables have roots close or equal to unity. In this case standard predictive regression tests can suffer from well-documented size distortion. Moreover, under the alternative hypothesis, they force the dependent variable to share the same order of integration as the predictor, whereas in practice the dependent variable often appears stationary while the predictor may be near-nonstationary. By contrast, the new test does not enforce the same orders of integration and is therefore capable of detecting alternatives to orthogonality that are excluded by the standard predictive regression model. Moreover, the test statistic has a standard normal limit distribution for both unit root and local-to-unity conditioning variables, without prior knowledge of the local-to-unity parameter. If the conditioning variable is stationary, the test remains conservative and consistent. Thus the new test requires neither size correction nor unit root pre-test. Simulations suggest good small sample performance. As an empirical application, we test for the predictability of stock returns using two persistent predictors, the dividend-price-ratio and short-term interest rate.
    Keywords: orthogonality test, covariance estimation, local-to-unity, unit roots, market efficiency, predictive regression, regression imbalance
    JEL: C12 C22
    Date: 2007–02
  5. By: Rodney C Wolff; Peter Hall; Qiwei Yao (School of Economics and Finance, Queensland University of Technology)
    Abstract: Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for conditional distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation. It produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1. The second method involves an adjusted form of the Nadaraya--Watson estimator. It preserves the bias and variance properties of a class of second-order estimators introduced by Yu and Jones but has the added advantage of always being a distribution itself. Our methods also have application outside the time series setting; for example, to quantile estimation for independent data. This problem motivated the work of Yu and Jones.
    Keywords: Absolutely regular; bandwidth; biased bootstrap; conditional distribution; kernel methods; local linear methods; local logistic methods; Nadaraya-Watson estimator; prediction; quantile estimation; time series analysis; weighted bootstrap
    Date: 2006–06–15
  6. By: Rodney C Wolff; Jiti Gao; Howell Tong (School of Economics and Finance, Queensland University of Technology)
    Abstract: In this paper, we consider additive stochastic nonparametric regression models. By approximating the nonparametric components by a class of orthogonal series and using a generalized cross-validation criterion, an adaptive and simultaneous estimation procedure for the nonparametric components is constructed. We illustrate the adaptive and simultaneous estimation procedure by a number of simulated and real examples.
    Keywords: Adaptive estimation; additive model; dependent process; mixing condition; nonlinear time series; nonparametric regression; orthogonal series; strict stationarity; truncation parameter
    Date: 2006–06–15
  7. By: Rodney C Wolff; Adrian G Barnett (School of Economics and Finance, Queensland University of Technology)
    Abstract: The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third-order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third-order moment is required to construct the Fourier transform. In this paper, we propose a test for nonlinearity based upon the estimated third-order moment. We use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study, we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of nonstationarity.
    Keywords: Third-order moment; bispectrum; non-linear; non-stationary; time series; bootstrap; phase scrambling
    Date: 2006–06–15
  8. By: Giuseppe Ragusa (Department of Economics, University of California-Irvine)
    Abstract: Bayesian inference in moment condition models is difficult to implement. For these models, a posterior distribution cannot be calculated because the likelihood function has not been fully specified. In this paper, we obtain a class of likelihoods by formal Bayesian calculations that take into account the semiparametric nature of the problem. The likelihoods are derived by integrating out the nuisance parameters with respect to a maximum entropy tilted prior on the space of distribution. The result is a unification that uncovers a mapping between priors and likelihood functions. We show that there exist priors such that the likelihoods are closely connected to Generalized Empirical Likelihood (GEL) methods.
    Keywords: Moment condition; GMM; GEL; Likelihood functions; Bayesian inference
    JEL: C1 C11 C14 C21
    Date: 2007–01
  9. By: Matteo Manera (University of Milan Bicocca); Chiara Longo (Fondazione Eni Enrico Mattei); Anil Markandya (University of Bath and Fondazione Eni Enrico Mattei); Elisa Scarpa (Risk Management Department, Intesa-San Paolo)
    Abstract: The relevance of oil in the world economy explains why considerable effort has been devoted to the development of different types of econometric models for oil price forecasting. Several specifications have been proposed in the economic literature. Some are based on financial theory and concentrate on the relationship between spot and futures prices (“financial” models). Others assign a key role to variables explaining the characteristics of the physical oil market (“structural” models). The empirical literature is very far from any consensus about the appropriate model for oil price forecasting that should be implemented. Relative to the previous literature, this paper is novel in several respects. First of all, we test and systematically evaluate the ability of several alternative econometric specifications proposed in the literature to capture the dynamics of oil prices. Second, we analyse the effects of different data frequencies on the coefficient estimates and forecasts obtained using each selected econometric specification. Third, we compare different models at different data frequencies on a common sample and common data. Fourth, we evaluate the forecasting performance of each selected model using static and dynamic forecasts, as well as different measures of forecast errors. Finally, we propose a new class of models which combine the relevant aspects of the financial and structural specifications proposed in the literature (“mixed” models). Our empirical findings can be summarized as follows. Financial models in levels do not produce satisfactory forecasts for the WTI spot price. The financial error correction model yields accurate in-sample forecasts. Real and strategic variables alone are insufficient to capture the oil spot price dynamics in the forecasting sample. Our proposed mixed models are statistically adequate and exhibit accurate forecasts. Different data frequencies seem to affect the forecasting ability of the models under analysis.
    Keywords: Oil Price, WTI Spot And Futures Prices, Forecasting, Econometric Models
    JEL: C52 C53 Q32 Q43
    Date: 2007–01
  10. By: Rodney C Wolff; Darfiana Nur; Kerrie L Mengersen (School of Economics and Finance, Queensland University of Technology)
    Abstract: Most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. Potentially useful diagnostics may be borrowed from diverse areas such as time series. One such method is phase randomisation. The aim of this paper is to describe this method in the context of MCMC, summarise its characteristics, and contrast its performance with those of the more common diagnostic tests for MCMC. It is observed that the new tool contributes information about third and higher order cumulant behaviour which is important in characterising certain forms of nonlinearity and nonstationarity.
    Keywords: Convergence diagnostics; higher cumulants; Markov Chain Monte Carlo; non-linear time series; stationarity; surrogate series
    Date: 2006–06–15
  11. By: Grant Hillier (Institute for Fiscal Studies and University of Southampton)
    Abstract: For a simplified structural equation/IV regression model with one right-side endogenous variable, we obtain the exact conditional distribution function for Moreira's (2003) conditional likelihood ratio (CLR) test. This is then used to obtain the critical value function needed to implement the CLR test, and reasonably comprehensive graphical versions of the function are provided for practical use. The analogous functions are also obtained for the case of testing more than one right-side endogenous coefficient, but only for an approximation to the true likelihood ratio test. We then go on to provide an exact analysis of the power functions of the CLR test, the Anderson-Rubin test, and the LM test suggested by Kleibergen (2002). The CLR test is shown to clearly conditionally dominate the other two tests for virtually all parameter configurations, but none of these test is either inadmissible or uniformly superior to the other two.
    Date: 2006–10
  12. By: Rodney C Wolff; Qiwei Yao; Howell Tong (School of Economics and Finance, Queensland University of Technology)
    Abstract: In order to develop statistical tests for the Lyapunov exponents of deterministic dynamical systems, we develop bootstrap tests based on empirical likelihood for percentiles and expectiles of strictly stationary processes. The percentiles and expectiles are estimated in terms of asymmetric least deviations and asymmetric least squares methods. Asymptotic distributional properties of the estimators are established.
    Keywords: Bootstrap; chaos; empirical likelihood; expectile; percentile
    Date: 2006–06–15
  13. By: Rodney C Wolff; Peter Hall (School of Economics and Finance, Queensland University of Technology)
    Abstract: Simple kernel-type estimators of integrals of general powers of general derivatives of probability densities are proposed. They are based on two simple properties, and in many circumstances enjoy optimal convergence rate.
    Keywords: Kernel estimators; nonparametric density estimation; wavelets
    Date: 2006–06–15
  14. By: Rodney C Wolff; Peter Hall (School of Economics and Finance, Queensland University of Technology)
    Abstract: We study a generalised version of the logistic map of the unit interval $(0,1)$, in which the point $x$ is taken to $1-|2x-1|^\nu$. Here, $\nu >0$ is a parameter of the map, which has received attention only when $\nu =1$ and 2. We obtain the invariant density when $\nu = \frac12$, and derive properties of invariant distributions in all other cases. These are obtained by a mixture of analytic and numerical argument. In particular, we develop a technique for combining "parametric" information, available from the functional form of the map, with "non-parametric" information, from a Monte Carlo study. Properties of the correlation integral under the invariant distribution are also derived. It is shown that classical behaviour of this test statistic, which demands that the logarithm of the integral have slope equal to the lag, is valid if and only if $\nu \leq 2$.
    Keywords: Chaos; correlation integral; invariant distribution; logistic map
    Date: 2006–06–15
  15. By: Christian Hansen (Institute for Fiscal Studies and Chicago GSB); Jerry Hausman (Institute for Fiscal Studies and Massachussets Institute of Technology); Whitney Newey (Institute for Fiscal Studies and Massachussets Institute of Technology)
    Abstract: Using many valid instrumental variables has the potential to improve efficiency but makes the usual inference procedures inaccurate. We give corrected standard errors, an extension of Bekker (1994) to nonnormal disturbances, that adjust for many instruments. We find that this adujstment is useful in empirical work, simulations, and in the asymptotic theory. Use of the corrected standard errors in t-ratios leads to an asymptotic approximation order that is the same when the number of instrumental variables grow as when the number of instruments is fixed. We also give a version of the Kleibergen (2002) weak instrument statistic that is robust to many instruments.
    Date: 2006–09
  16. By: Del Negro, Marco; Schorfheide, Frank
    Abstract: In Bayesian analysis of dynamic stochastic general equilibrium (DSGE) prior distributions for some of the taste-and-technology parameters can be obtained from microeconometric or pre-sample evidence, but it is difficult to elicit priors for the parameters that govern the law of motion of unobservable exogenous processes. Moreover, since it is challenging to formulate beliefs about the correlation of parameters, most researchers assume that all model parameters are independent of each other. We provide a simple method of constructing prior distributions for (a subset of) DSGE model parameters from beliefs about the moments of the endogenous variables. We use our approach to investigate the importance of nominal rigidities and show how the specification of prior distributions affects our assessment of the relative importance of different frictions.
    Keywords: Bayesian analysis; DSGE models; model comparisons; nominal rigidities; prior elicitation
    JEL: C32 E3
    Date: 2007–02
  17. By: Matthew Harding (Institute for Fiscal Studies and MIT); Jerry Hausman (Institute for Fiscal Studies and Massachussets Institute of Technology)
    Abstract: Current methods of estimating the random coefficients logit model employ simulations of the distribution of the taste parameters through pseudo-random sequences. These methods suffer from difficulties in estimating correlations between parameters and computational limitations such as the curse of dimensionality. This paper provides a solution to these problems by approximating the integral expression of the expected choice probability using a multivariate extension of the Laplace approximation. Simulation results reveal that our method performs very well, both in terms of accuracy and computational time. This paper is a revised version of CWP01/06.
    Date: 2006–10
  18. By: Mauro Costantini (ISAE - Institute for Studies and Economic Analyses); Roy Cerqueti (Università degli Studi di Roma “La Sapienza”, Italy)
    Abstract: This paper provides a theoretical fractional cointegration analysis in a nonparametric framework. We solve a generalized eigenvalues problem. To this end, a couple of random matrices are constructed taking into account the stationarity properties of the differencesof a fractional p-variate integrated process. These difference orders are assumed to vary in a continuous and discrete range. The random matrices are defined by some weight functions. Asymptotic behaviors of these random matrices are obtained by stating some conditions on the weight functions, and by using Bierens (1997) and Andersen et al.(1983) results. In this way, a nonparametric analysis is provided. Moving from the solution of the generalized eigenvalue problem, a fractional nonparametric VAR model for cointegration is also presented.
    Keywords: Fractional integrated process, Nonparametric methods, Cointegration, Asymptotic distribution, Generalized eigenvalues problem.
    JEL: C14 C22 C65
    Date: 2007–02
  19. By: Juncal Cuñado (Universidad de Navarra); Luis A. Gil-Alaña (Universidad de Navarra)
    Abstract: This paper deals with the analysis of the number of tourists travelling to the Canary Islands by means of using different seasonal statistical models. Deterministic and stochastic seasonality is considered. For the latter case, we employ seasonal unit roots and seasonally fractionally integrated models. As a final approach, we also employ a model with possibly different orders of integration at zero and the seasonal frequencies. All these models are compared in terms of their forecasting ability in an out-of-sample experiment. The results in the paper show that a simple deterministic model with seasonal dummy variables and AR(1) disturbances produce better results than other approaches based on seasonal fractional and integer differentiation over short horizons. However, increasing the time horizon, the results cannot distinguish between the model based on seasonal dummies and another using fractional integration at zero and the seasonal frequencies.
  20. By: Rodney C Wolff; Peter Hall (School of Economics and Finance, Queensland University of Technology)
    Abstract: Statistical scientists have recently focused sharp attention on properties of iterated chaotic maps, with a view to employing such processes to model naturally occurring phenomena. In the present paper we treat the logistic map, which has earlier been studied in the context of modelling biological systems. We derive theory describing properties of the 'invariant' or 'stationary' distribution under logistic maps and apply those results in conjunction with numerical work to develop further properties of invariant distributions and Lyapunov exponents. We describe the role that poles play in determining properties of densities' iterated distributions and show how poles arise from iterated mappings of the centre of the interval to which the map is applied. Particular attention is paid to the shape of the invariant distribution in the tails or in the neighbourhood of a pole of its density. A new technique is developed for this application. it enables us to combine 'parametric' information, available from the structure of the map, with 'nonparametric' information obtainable from numerical experiments.
    Keywords: Bandwidth; chaos; density estimation; invariant distribution; kernel method; logistic map; Lyapunov exponent; pole; stationary distribution
    Date: 2006–06–15
  21. By: Grant Hillier (Institute for Fiscal Studies and University of Southampton)
    Abstract: For the problem of testing the hypothesis that all <i>m</i> coefficients of the RHS endogenous variables in an IV regression are zero, the likelihood ratio (LR) test can, if the reduced form covariance matrix is known, be rendered similar by a conditioning argument. To exploit this fact requires knowledge of the relevant conditional <i>cdf</i> of the LR statistic, but the statistic is a function of the smallest characteristic root of an (<i>m</i> + 1)−square matrix, and is therefore analytically difficult to deal with when <i>m</i> > 1. We show in this paper that an iterative conditioning argument used by Hillier (2006) and Andrews, Moreira, and Stock (2007) to evaluate the cdf in the case <i>m</i> = 1 can be generalized to the case of arbitrary <i>m</i>. This means that we can completely bypass the difficulty of dealing with the smallest characteristic root. Analytic results are obtained for the case <i>m</i> = 2, and a simple and efficient simulation approach to evaluating the <i>cdf</i> is suggested for larger values of <i>m</i>.
    Date: 2006–12
  22. By: Mark. B. Stewart
  23. By: Marco Fioramanti (ISAE - Institute for Studies and Economic Analyses; University of Pescara, Faculty of Economics)
    Abstract: Recent episodes of financial crises have revived the interest in developing models that are able to timely signal their occurrence. The literature has developed both parametric and non parametric models to predict these crises, the so called Early Warning Systems. Using data related to sovereign debt crises occurred in developing countries from 1980 to 2004, this paper shows that a further progress can be done applying a less developed non-parametric method, i.e. Artificial Neural Networks (ANN). Thanks to the high flexibility of neural networks and to the Universal Approximation Theorem an ANN based early warning system can, under certain conditions, outperform more consolidated methods.
    Keywords: Early Warning System; Financial Crisis; Sovereign Debt Crises; Artificial Neural Network.
    JEL: F34 F37 C45 C14
    Date: 2006–10
  24. By: Pástor, Lubos; Stambaugh, Robert F
    Abstract: The standard regression approach to modeling return predictability seems too restrictive in one way but too lax in another. A predictive regression models expected returns as an exact linear function of a given set of predictors but does not exploit the likely economic property that innovations in expected returns are negatively correlated with unexpected returns. We develop an alternative framework---a predictive system---that accommodates imperfect predictors and beliefs about that negative correlation. In this framework, the predictive ability of imperfect predictors is supplemented by information in lagged returns as well as lags of the predictors. Compared to predictive regressions, predictive systems deliver different and substantially more precise estimates of expected returns as well as different assessments of a given predictor's usefulness.
    Keywords: expected stock return; predictability; predictive regression; predictive system; state space model
    JEL: G1
    Date: 2007–02
  25. By: Guillermina Jasso (New York University and IZA); Samuel Kotz (George Washington University)
    Abstract: Recent work on social status led to derivation of a new continuous distribution based on the exponential. The new variate, termed the ring(2)-exponential, in turn leads to derivation of two closely-related new families of continuous distributions, which we call the mirrorexponential and the ring-exponential. Both the standard exponential and the ring(2)- exponential are special cases of both the new families. In this paper, we first focus on the ring(2)-exponential, describing its derivation and examining its properties, and next introduce the two new families, describing their derivation and initiating exploration of their properties. The mirror-exponential arises naturally in the study of status; the ring-exponential arises from the mathematical structure of the ring(2)-exponential. Both have potential for broad application in diverse contexts across science and engineering, including the physical and social sciences as well as finance, information processing, and communication. Within sociobehavioral contexts, the new mirror-exponential may have application to the problem of approximating the form and inequality of the wage distribution.
    Keywords: continuous univariate distributions, Erlang distribution, general Erlang distribution, gamma distribution, general gamma distribution, folded distributions, Gini coefficient, social status, social inequality, wage function, wage distribution, wage inequality
    JEL: C02 C16 D31 D6 I3
    Date: 2007–02
  26. By: Ricardo Gimeno (Banco de España); Juan M. Nave (Universidad CEU Cardenal Herrera)
    Abstract: The term structure of interest rates is an instrument that gives us the necessary information for valuing deterministic financial cash flows, measuring the economic market expectations and testing the effectiveness of monetary policy decisions. However, it is not directly observable and needs to be measured by smoothing data obtained from asset prices through statistical techniques. Adjusting parsimonious functional forms - as proposed by Nelson and Siegel (1987) and Svensson (1994) - is the most popular technique. This method is based on bond yields to maturity and the high degree of non linearity of the functions to be optimised make it very sensitive to the initial values employed. In this context, this paper proposes the use of genetic algorithms to find these values and reduce the risk of false convergence, showing that stable time series parameters are obtained without the need to impose any kind of restrictions.
    Keywords: forward and spot interest rates, nelson and siegel model, non-linear optimization, numerical methods, svensson model, yield curve estimation
    JEL: G12 C51 C63
    Date: 2006–12

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