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on Econometric Time Series |
| By: | Rasmus Søndergaard Pedersen (University of Copenhagen); Anders Rahbek (University of Copenhagen and CREATES) |
| Abstract: | This paper considers asymptotic inference in the multivariate BEKK model based on (co-)variance targeting (VT). By defi?nition the VT estimator is a two-step estimator and the theory presented is based on expansions of the modifi?ed likelihood function, or estimating function, corresponding to these two steps. Strong consistency is established under weak moment conditions, while sixth order moment restrictions are imposed to establish asymptotic normality. Included simulations indicate that the multivariately induced higher-order moment constraints are indeed necessary. |
| Keywords: | Covariance targeting, Variance targeting, Multivariate GARCH, BEKK, Asymptotic theory, Time series. |
| JEL: | C32 C51 C58 |
| Date: | 2012–11–14 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-53&r=ets |
| By: | José Manuel Corcuera (Universitat de Barcelona); Emil Hedevang (Aarhus University); Mikko S. Pakkanen (Aarhus University and CREATES); Mark Podolskij (Heidelberg University and CREATES) |
| Abstract: | This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed in [Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2011): Multipower variation for Brownian semistationary processes. Bernoulli 17(4), 1159-1194; Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2012): Limit theorems for functionals of higher order differences of Brownian semi-stationary processes. In "Prokhorov and Contemporary Probability Theory", Springer.] and present some new connections to fractional diffusion models. We apply our probabilistic results to construct a family of estimators for the smoothness parameter of the BSS process. In this context we develop estimates with gaps, which allow to obtain a valid central limit theorem for the critical region. Finally, we apply our statistical theory to turbulence data. |
| Keywords: | Brownian semi-stationary processes, high frequency data, limit theorems, stable convergence, turbulence |
| JEL: | C10 C13 C14 |
| Date: | 2012–11–16 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-52&r=ets |
| By: | Peter Christoffersen (University of Toronto - Rotman School of Management and CREATES); Christian Dorion (HEC Montreal); Kris Jacobs (University of Houston and Tilburg University); Lotfi Karoui (Goldman, Sachs & Co.) |
| Abstract: | When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi?ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze the potential of the unscented Kalman ?filter to properly capture nonlinearities. To illustrate the advantages of the unscented Kalman ?filter, we analyze the cross section of swap rates, which are relatively simple non-linear instruments, and cap prices, which are highly nonlinear in the states. An extensive Monte Carlo experiment demonstrates that the unscented Kalman fi?lter is much more accurate than its extended counterpart in fi?ltering the states and forecasting swap rates and caps. Our fi?ndings suggest that the unscented Kalman fi?lter may prove to be a good approach for a number of other problems in fi?xed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using coupon bonds and the estimation of quadratic term structure models. |
| Keywords: | Kalman filtering, nonlinearity, term structure models, swaps, caps. |
| JEL: | G12 |
| Date: | 2012–05–14 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-49&r=ets |
| By: | Søren Johansen (University of Copenhagen and CREATES); Morten Ørregaard Nielsen (Queen?s University and CREATES) |
| Abstract: | We consider the nonstationary fractional model $\Delta^{d}X_{t}=\varepsilon _{t}$ with $\varepsilon_{t}$ i.i.d.$(0,\sigma^{2})$ and $d>1/2$. We derive an analytical expression for the main term of the asymptotic bias of the maximum likelihood estimator of $d$ conditional on initial values, and we discuss the role of the initial values for the bias. The results are partially extended to other fractional models, and three different applications of the theoretical results are given. |
| Keywords: | Asymptotic expansion, bias, conditional inference, fractional integration, initial values, likelihood inference. |
| JEL: | C22 |
| Date: | 2012–11–08 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-47&r=ets |
| By: | Peter Christoffersen (University of Toronto - Rotman School of Management and CREATES); Kris Jacobs (University of Houston and Tilburg University); Chayawat Ornthanalai (Georgia Institute of Technology) |
| Abstract: | We survey the theory and empirical evidence on GARCH option valuation models. Our treatment includes the range of functional forms available for the volatility dynamic, multifactor models, nonnormal shock distributions as well as style of pricing kernels typically used. Various strategies for empirical implementation are laid out and we also discuss the links between GARCH and stochastic volatility models. In the appendix we provide Matlab computer code for option pricing via Monte Carlo simulation for nonaffine models as well as Fourier inversion for affine models. |
| Keywords: | GARCH, option valuation. |
| JEL: | G13 |
| Date: | 2012–05–08 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-50&r=ets |
| By: | Gribisch, Bastian |
| Abstract: | This paper generalizes the basic Wishart multivariate stochastic volatility model of Philipov and Glickman (2006) and Asai and McAleer (2009) to encompass regime switching behavior. The latent state variable is driven by a first-order Markov process. The model allows for state-dependent (co)variance and correlation levels and state-dependent volatility spillover effects. Parameter estimates are obtained using Bayesian Markov Chain Monte Carlo procedures and filtered estimates of the latent variances and covariances are generated by particle filter techniques. The model is applied to five European stock index return series. The results show that the proposed regime-switching specification substantially improves the in-sample fit and the VaR forecasting performance relative to the basic model. -- |
| Keywords: | Multivariate stochastic volatility,Dynamic correlations,Wishart distribution,Markov switching,Markov chain Monte Carlo |
| JEL: | C32 C58 G17 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cauewp:201214&r=ets |
| By: | Offick, Sven; Wohltmann, Hans-Werner |
| Abstract: | In a recent paper, Mertens and Ravn (2010) study the effects of anticipated fiscal policy shocks in a structural vector autoregressive model. The authors maintain that (i) the lag polynomial associated with news shocks is a cyclotomic polynomial and (ii) the matrix B(L) which transforms a nonfundamental MA representation into a fundamental one is a Blaschke matrix. Though the results in Mertens and Ravn (2010) are correct, we find that the terms 'cyclotomic' and 'Blaschke matrix' are misused. -- |
| Keywords: | Nonfundamentalness,Cyclotomic polynomial,Blaschke matrix |
| JEL: | C32 E32 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cauewp:201213&r=ets |
| By: | Nyberg , Henri (Department of Political and Economic Studies, and HECER, University of Helsinki); Saikkonen, Pentti (Department of Mathematics and Statistics, and HECER, University of Helsinki, and the Monetary Policy and Research Department of the Bank of Finland) |
| Abstract: | We propose simulation-based forecasting methods for the noncausal vector autoregressive model proposed by Lanne and Saikkonen (2012). Simulation or numerical methods are required because the prediction problem is generally nonlinear and, therefore, its analytical solution is not available. It turns out that different special cases of the model call for different simulation procedures. Simulation experiments demonstrate that gains in forecasting accuracy are achieved by using the correct noncausal VAR model instead of its conventional causal counterpart. In an empirical application, a noncausal VAR model comprised of U.S. inflation and marginal cost turns out superior to the best-fitting conventional causal VAR model in forecasting inflation. |
| Keywords: | noncausal vector autoregression; forecasting; simulation; importance sampling; inflation |
| JEL: | C32 C53 E31 |
| Date: | 2012–11–09 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:bofrdp:2012_033&r=ets |
| By: | Taipalus, Katja (Bank of Finland Research) |
| Abstract: | To promote the financial stability, there is a need for an early warning system to signal the formation of asset price misalignments. This research provides two novel methods to accomplish this task. Results in this research shows that the conventional unit root tests in modified forms can be used to construct early warning indicators for bubbles in financial markets. More precisely, the conventional augmented Dickey-Fuller unit root test is shown to provide a basis for two novel bubble indicators. These new indicators are tested via MC simulations to analyze their ability to signal emerging unit roots in time series and to compare their power with standard stability and unit root tests. Simulation results concerning these two new stability tests are promising: they seem to be more robust and to have more power in the presence of changing persistence than the standard stability and unit root tests. When these new tests are applied to real US stock market data starting from 1871, they are able to signal most of the consensus bubbles, defined as stock market booms for example by the IMF, and they also flash warning signals far ahead of a crash. Also encouraging are the results with these methods in practical applications using equity prices in the UK, Finland and China as the methods seem to be able to signal most of the consensus bubbles from the data. Finally, these early warning indicators are applied to data for several housing markets. In most of the cases the indicators seem to work relatively well, indicating bubbles before the periods which, according to the consensus literature, are seen as periods of sizeable upward or downward movements. The scope of application of these early warning indicators could be wide. They could be used eg to help determine the right timing for the start of a monetary tightening cycle or for an increase in countercyclical capital buffers. |
| Keywords: | asset prices; financial crises; bubbles; indicator; unit-root |
| JEL: | C15 G01 G12 |
| Date: | 2012–11–15 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:bofism:2012_047&r=ets |
| By: | Luis Francisco Rosales (Georg-August-University Göttingen); Tatyana Krivobokova (Georg-August-University Göttingen) |
| Abstract: | We present a nonparametric method to decompose a times series into trend, seasonal and remainder components. This fully data-driven technique is based on penalized splines and makes an explicit characterization of the varying seasonality and the correlation in the remainder. The procedure takes advantage of the mixed model representation of penalized splines that allows for the simultaneous estimation of all model parameters from the corresponding likelihood. Simulation studies and three data examples illustrate the effectiveness of the approach. |
| Keywords: | Penalized splines; Mixed model; Varying coecient; Correlated remainder |
| Date: | 2012–11–20 |
| URL: | http://d.repec.org/n?u=RePEc:got:gotcrc:131&r=ets |
| By: | Katsiaryna Schwarz (Georg-August-University Göttingen); Tatyana Krivobokova (Georg-August-University Göttingen) |
| Abstract: | This article develops a unified framework to study the (asymptotic) properties of (periodic) spline based estimators, that is of regression, penalized and smoothing splines. We obtain an explicit form of the Demmler-Reinsch basis of general degree in terms of exponential splines and corresponding eigenvalues by applying Fourier techniques to periodic smoothers. This allows to derive exact expressions for the equivalent kernels of all spline estimators and get insights into the local and global asymptotic behavior of these estimators. |
| Keywords: | B-splines; Equivalent kernels; Euler-Frobenius polynomials; Exponential splines; Demmler-Reinsch basis |
| Date: | 2012–11–20 |
| URL: | http://d.repec.org/n?u=RePEc:got:gotcrc:130&r=ets |
| By: | Søren Johansen (Department of Economics, University of Copenhagen and CREATES, University of Aarhus); Marco Riani (Dipartimento di Economia, Universita di Parma); Anthony C. Atkinson (Department of Statistics, London School of Economics, UK) |
| Abstract: | We develop a Cp statistic for the selection of regression models with stationary and nonstationary ARIMA error term. We derive the asymptotic theory of the maximum likelihood estimators and show they are consistent and asymptotically Gaussian. We also prove that the distribution of the sum of squares of one step ahead standardized prediction errors, when the parameters are estimated, differs from the chi-squared distribution by a term which tends to infinity at a lower rate than X (2/n). We further prove that, in the prediction error decomposition, the term involving the sum of the variance of one step ahead standardized prediction errors is convergent. Finally, we provide a small simulation study. Empirical comparisons of a consistent version of our Cp statistic with BIC and a generalized RIC show that our statistic has superior performance, particularly for small signal to noise ratios. A new plot of our time series Cp statistic is highly informative about the choice of model. On the way we introduce a new version of AIC for regression models, show that it estimates a Kullback-Leibler distance and provide a version for small samples that is bias corrected. We highlight the connections with standard Mallows Cp. |
| Keywords: | AIC; ARMA models; bias correction; BIC; Cp plot; generalized RIC; Kalman filter; Kullback-Leibler distance; state-space formulation |
| JEL: | C22 |
| Date: | 2012–11–08 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1217&r=ets |
| By: | Monica Billio (University of Venice, GRETA Assoc. and School for Advanced Studies in Venice); Roberto Casarin (University of Venice, GRETA Assoc. and School for Advanced Studies in Venice); Francesco Ravazzolo (Norges Bank and BI Norwegian Business School); Herman K. van Dijk (Erasmus University Rotterdam, VU University Amsterdam) |
| Abstract: | We propose a Bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights. Several specifications of multivariate time-varying weights are introduced with a particular focus on weight dynamics driven by the past performance of the predictive densities and the use of learning mechanisms. In the proposed approach the model set can be incomplete, meaning that all models can be individually misspecified. A Sequential Monte Carlo method is proposed to approximate the filtering and predictive densities. The combination approach is assessed using statistical and utility-based performance measures for evaluating density forecasts. Simulation results indicate that, for a set of linear autoregressive models, the combination strategy is successful in selecting, with probability close to one, the true model when the model set is complete and it is able to detect parameter instability when the model set includes the true model that has generated subsamples of data. For the macro series we find that incompleteness of the models is relatively large in the 70's, the beginning of the 80's and during the recent financial crisis, and lower during the Great Moderation. With respect to returns of the S&P 500 series, we find that an investment strategy using a combination of predictions from professional forecasters and from a white noise model puts more weight on the white noise model in the beginning of the 90's and switches to giving more weight to the professional forecasts over time. |
| Keywords: | Density Forecast Combination; Survey Forecast; Bayesian Filtering; Sequential Monte Carlo |
| JEL: | C11 C15 C53 E37 |
| Date: | 2012–11–07 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20120118&r=ets |
| By: | Marc Hallin; Ramon van den Akker; Bas Werker |
| Abstract: | This paper introduces rank-based tests for the cointegrating rank in an Error CorrectionModel with i.i.d. elliptical innovations. The tests are asymptotically distribution-free,and their validity does not depend on the actual distribution of the innovations. Thisresult holds despite the fact that, depending on the alternatives considered, the model exhibitsa non-standard Locally Asymptotically Brownian Functional (LABF) and LocallyAsymptotically Mixed Normal (LAMN) local structure—a structure which we completelycharacterize. Our tests, which have the general form of Lagrange multiplier tests, dependon a reference density that can freely be chosen, and thus is not restricted to be Gaussianas in traditional quasi-likelihood procedures. Moreover, appropriate choices of the referencedensity are achieving the semiparametric efficiency bounds. Simulations show thatour asymptotic analysis provides an accurate approximation to finite-sample behavior.Our results are based on an extension, of independent interest, of two abstract resultson the convergence of statistical experiments and the asymptotic linearity of statistics tothe context of, possibly non-stationary, time series |
| Keywords: | Cointegration model; Cointegration Rank; Elliptical densities; error correction model; Lagrange Multiplier test; local asymptotic Brownian Functional; Local asymptotic Mixed Normality; Local asymptotic Normality; Multivariate Ranks; non-Gaussian Quasi-Likelihood Procedures |
| JEL: | C14 C32 |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/132503&r=ets |
| By: | Stelios Arvanitis; Antonis Demos (www.aueb.gr/users/demos) |
| Abstract: | In this paper we are concerned with the issue of the existence of locally uniform Edgeworth expansions for the distributions of parameterized random vectors. Our motivation resides on the fact that this could enable subsequent polynomial asymptotic expansions of moments. These could be useful for the establishment of asymptotic properties for estimators based on these moments. We derive sufficient conditions either in the case of stochastic processes exhibiting weak dependence, or in the case of smooth transformations of such expansions. |
| Keywords: | Locally uniform Edgeworth expansion, formal Edgeworth distribution, weak dependence, smooth transformations, moment approximations, GMM estimators, Indirect estimators, GARCH model |
| JEL: | C10 C13 |
| Date: | 2012–06–05 |
| URL: | http://d.repec.org/n?u=RePEc:aue:wpaper:1229&r=ets |
| By: | Neil R. Ericsson (Board of Governors of the Federal Reserve System); Erica L. Reisman (Board of Governors of the Federal Reserve System) |
| Abstract: | Global vector autoregressions (GVARs) have several attractive features: multiple potential channels for the international transmission of macroeconomic and financial shocks, a standardized economically appealing choice of variables for each country or region examined, systematic treatment of long-run properties through cointegration analysis, and flexible dynamic specification through vector error correction modeling. Pesaran, Schuermann, and Smith (2009) generate and evaluate forecasts from a paradigm GVAR with 26 countries, based on Dées, di Mauro, Pesaran, and Smith (2007). The current paper empirically assesses the GVAR in Dées, di Mauro, Pesaran, and Smith (2007) with impulse indicator saturation (IIS)—a new generic procedure for evaluating parameter constancy, which is a central element in model-based forecasting. The empirical results indicate substantial room for an improved, more robust specification of that GVAR. Some tests are suggestive of how to achieve such improvements. |
| Keywords: | cointegration, error correction, forecasting, GVAR, impulse indicator saturation, model design, model evaluation, model selection, parameter constancy, VAR |
| JEL: | C32 F41 |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:gwc:wpaper:2012-006&r=ets |