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on Econometrics |
| By: | Christian M. Dahl; Henrik Hansen; John Smidt (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | Forecasting using factor models based on large data sets have received ample attention due to the models’ ability to increase forecast accuracy with respect to a range of key macroeconomic variables in the US and the UK. However, forecasts based on such factor models do not uniformly outperform the simple autoregressive model when using data from other countries. In this paper we propose to estimate the factors based on the pure cyclical components of the series entering the large data set. Monte Carlo evidence and an empirical illustration using Danish data shows that this procedure can indeed improve on pseudo real time forecast accuracy. |
| Keywords: | Factor model, Cyclical components, Estimation, Real time forecasting |
| JEL: | C13 C22 C52 |
| Date: | 2008–09–02 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-44&r=ecm |
| By: | Christian M. Dahl; Yu Qin (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | This paper examines the limiting properties of the estimated parameters in the random field regression model recently proposed by Hamilton (Econometrica, 2001). Though the model is parametric, it enjoys the flexibility of the nonparametric approach since it can approximate a large collection of nonlinear functions and it has the added advantage that there is no “curse of dimensionality.”Contrary to existing literature on the asymptotic properties of the estimated parameters in random field models our results do not require that the explanatory variables are sampled on a grid. However, as a consequence the random field model specification introduces non-stationarity and non-ergodicity in the misspecified model and it becomes non-trivial, relative to the existing literature, to establish the limiting behavior of the estimated parameters. The asymptotic results are obtained by applying some convenient new uniform convergence results that we propose. This theory may have applications beyond those presented here. Our results indicate that classical statistical inference techniques, in general, works very well for random field regression models in finite samples and that these models succesfully can fit and uncover many types of nonlinear structures in data. |
| Keywords: | Random fields regressions, Estimation, Inference, Asymptotics |
| JEL: | C12 C13 C14 C45 |
| Date: | 2008–09–02 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-45&r=ecm |
| By: | Roxana Chiriac; Valeri Voev (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | This paper proposes a methodology for modelling time series of realized covariance matrices in order to forecast multivariate risks. The approach allows for flexible dynamic dependence patterns and guarantees positive definiteness of the resulting forecasts without imposing parameter restrictions. We provide an empirical application of the model, in which we show by means of stochastic dominance tests that the returns from an optimal portfolio based on the model’s forecasts second-order dominate returns of portfolios optimized on the basis of traditional MGARCH models. This result implies that any risk-averse investor, regardless of the type of utility function, would be better-off using our model. |
| Keywords: | Forecasting, Fractional integration, Stochastic dominance, Portfolio optimization, Realized covariance |
| JEL: | C32 C53 G11 |
| Date: | 2008–09–02 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-39&r=ecm |
| By: | Han Hong; Bruce Preston |
| Abstract: | This paper studies the asymptotic relationship between Bayesian model averaging and post-selection frequentist predictors in both nested and nonnested models. We derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples. This result depends crucially on the relation between posterior odds and frequentist model selection criteria. Weak conditions are given under which consistent model selection is feasible, regardless of whether models are nested or nonnested and regardless of whether models are correctly specified or not, in the sense that they select the best model with the least number of parameters with probability converging to 1. Under these conditions, Bayesian posterior odds and BICs are consistent for selecting among nested models, but are not consistent for selecting among nonnested models. |
| JEL: | C14 C52 |
| Date: | 2008–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:14284&r=ecm |
| By: | Bent Jesper Christensen; Christian M. Dahl; Emma M. Iglesias (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | A new semiparametric estimator for an empirical asset pricing model with general nonpara- metric risk-return tradeoff and a GARCH process for the underlying volatility is introduced. The estimator does not rely on any initial parametric estimator of the conditional mean func- tion, and this feature facilitates the derivation of asymptotic theory under possible nonlinearity of unspecified form of the risk-return tradeoff. Besides the nonlinear GARCH-in-mean effect, our specification accommodates exogenous regressors that are typically used as conditioning variables entering linearly in the mean equation, such as the dividend yield. Using the profile likelihood approach, we show that our estimator under stated conditions is consistent, asymp- totically normal, and efficient, i.e. it achieves the semiparametric lower bound. A sampling experiment provides evidence on finite sample properties as well as comparisons with the fully parametric approach and the iterative semiparametric approach using a parametric initial esti- mate proposed by Conrad and Mammen (2008). An empirical application to the daily S&P 500 stock market returns suggests that the linear relation between conditional expected return and conditional variance of returns from the literature is misspecified, and this could be the reason for the disagreement on the sign of the relation. |
| Keywords: | Efficiency bound, GARCH-M model, Profile likelihood, Risk-return relation, Semiparametric inference |
| JEL: | C13 C14 C22 G12 |
| Date: | 2008–09–02 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-46&r=ecm |
| By: | Joseph P. Romano; Michael Wolf |
| Abstract: | Consider the problem of testing s hypotheses simultaneously. In this paper, we derive methods which control the generalized familywise error rate given by the probability of k or more false rejections, abbreviated k-FWER. We derive both single-step and stepdown procedures that control the k-FWER in finite samples or asymptotically, depending on the situation. Moreover, the procedures are asymptotically balanced in an appropriate sense. We briefly consider control of the average number of false rejections. Additionally, we consider the false discovery proportion (FDP), defined as the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). Here, the goal is to construct methods which satisfy, for given g and a, P{FDP > g} <= a, at least asymptotically. Special attention attention is paid to the construction of methods which implicitly take into account the dependence structure of the individual test statistics in order to further increase the ability to detect false null hypotheses. A general resampling and subsampling approach is presented which achieves these objectives, at least asymptotically. |
| Keywords: | Bootstrap, False Discovery Proportion, Generalized familywise error rate, Multiple Testing, Stepdown procedure |
| JEL: | C12 C14 |
| Date: | 2008–07 |
| URL: | http://d.repec.org/n?u=RePEc:zur:iewwpx:379&r=ecm |
| By: | Markus Haas (University of Munich, Institute of Statistics); Stefan Mittnik (Department of Statistics, University of Munich, Center for Financial Studies, Frankfurt, and Ifo Institute for Economic Research, Munich); Mark S. Paolella (Swiss Banking Institute, University of Zurich, Switzerland) |
| Abstract: | An asymmetric multivariate generalization of the recently proposed class of normal mixture GARCH models is developed. Issues of parametrization and estimation are discussed. Conditions for covariance stationarity and the existence of the fourth moment are derived, and expressions for the dynamic correlation structure of the process are provided. In an application to stock market returns, it is shown that the disaggregation of the conditional (co)variance process generated by the model provides substantial intuition. Moreover, the model exhibits a strong performance in calculating out–of–sample Value–at–Risk measures. |
| Keywords: | Conditional Volatility, Finite Normal Mixtures, Multivariate GARCH, Leverage Effect |
| JEL: | C32 C51 G10 G11 |
| Date: | 2008–01–18 |
| URL: | http://d.repec.org/n?u=RePEc:cfs:cfswop:wp200807&r=ecm |
| By: | Lars Stentoft (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | In this paper we propose a feasible way to price American options in a model with time varying volatility and conditional skewness and leptokurtosis using GARCH processes and the Normal Inverse Gaussian distribution. We show how the risk neutral dynamics can be obtained in this model, we interpret the effect of the riskneutralization, and we derive approximation procedures which allow for a computationally efficient implementation of the model. When the model is estimated on financial returns data the results indicate that compared to the Gaussian case the extension is important. A study of the model properties shows that there are important option pricing differences compared to the Gaussian case as well as to the symmetric special case. A large scale empirical examination shows that our model outperforms the Gaussian case for pricing options on three large US stocks as well as a major index. In particular, improvements are found when considering the smile in implied standard deviations. |
| Keywords: | GARCH models, Normal Inverse Gaussian distribution, American Options, Least Squares Monte Carlo method |
| JEL: | C22 C53 G13 |
| Date: | 2008–09–02 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-41&r=ecm |
| By: | Todd E. Clark; Michael W. McCracken |
| Abstract: | Recent work suggests VAR models of output, inflation, and interest rates may be prone to instabilities. In the face of such instabilities, a variety of estimation or forecasting methods might be used to improve the accuracy of forecasts from a VAR. The uncertainty inherent in any single representation of instability could mean that combining forecasts from a range of approaches will improve forecast accuracy. Focusing on models of U.S. output, prices, and interest rates, this paper examines the effectiveness of combining various models of instability in improving VAR forecasts made with real-time data. |
| Keywords: | Econometric models ; Economic forecasting |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2008-030&r=ecm |
| By: | Zaman, Asad |
| Abstract: | Applied econometric work takes a superficial approach to causality. Understanding economic affairs, making good policy decisions, and progress in the economic discipline depend on our ability to infer causal relations from data. We review the dominant approaches to causality in econometrics, and suggest why they fail to give good results. We feel the problem cannot be solved by traditional tools, and requires some out-of-the-box thinking. Potentially promising approaches to solutions are discussed. |
| Keywords: | causality; regression; Granger Causality; Exogeneity; Cowles Commission; Hendry Methodology; Natural Experiments |
| JEL: | C59 |
| Date: | 2008–05–31 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:10128&r=ecm |