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on Econometric Time Series |
| By: | Behzad Mehrdad; Lingjiong Zhu |
| Abstract: | The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has immigration-birth representation. Based on that, Fierro et al. recently introduced a generalized linear Hawkes model with different exciting functions. In this paper, we study the convergence to equilibrium, large deviation principle, and moderate deviation principle for this generalized model. This model also has connections to the multivariate linear Hawkes process. Some applications to finance are also discussed. |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1403.0994&r=ets |
| By: | Michael McAleer (University of Canterbury) |
| Abstract: | This note discusses some aspects of the paper by Hu and Tsay (2014), “Principal Volatility Component Analysis”. The key issues are considered, and are also related to existing conditional covariance and correlation models. Some caveats are given about multivariate models of time-varying conditional covariance and correlation models. |
| Keywords: | Principal Component Analysis, Principal Volatility Component Analysis, Vector time-varying conditional heteroskedasticity, BEKK, DCC, asymptotic properties |
| JEL: | C32 C58 F37 |
| Date: | 2014–02–23 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:14/09&r=ets |
| By: | Diego Fresoli; Esther Ruiz |
| Abstract: | When forecasting conditional correlations that evolve according to a Dynamic Conditional Correlation (DCC) model, only point forecasts can be obtained at each moment of time. In this paper, we analyze the finite sample properties of a bootstrap procedure to approximate the density of these forecasts that also allows obtaining conditional densities for future returns and volatilities. The procedure is illustrated by obtaining conditional forecast intervals and regions of returns, volatilities andcorrelations in the context of a system of daily exchange rates returns of the Euro, Japanese Yen and Australian Dollar against the US Dollar |
| Keywords: | Bootstrap forecast intervals, Forecast regions, Dynamic Conditional Correlation, Exchange rates, Realized correlation, Resampling methods |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws140202&r=ets |
| By: | Igor Kheifets (New Economic School, Moscow) |
| Abstract: | We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any setup where parametric conditional distribution of the data is specified, in particular to models involving conditional volatility, conditional higher moments, conditional quantiles, asymmetry, Value at Risk models, duration models, diffusion models, etc. Compared to other tests, the new test properly controls the nonlinear dynamic behavior in conditional distribution and does not rely on smoothing techniques which require a choice of several tuning parameters. The test is based on a new kind of multivariate empirical process of contemporaneous and lagged probability integral transforms. We establish weak convergence of the process under parameter uncertainty and local alternatives. We justify a parametric bootstrap approximation that accounts for parameter estimation effects often ignored in practice. Monte Carlo experiments show that the test has good finite-sample size and power properties. Using the new test and graphical tools we check adequacy of various popular heteroscedastic models for stock exchange index data. |
| Keywords: | Conditional distribution, Time series, Goodness-of-fit, Empirical process, Weak convergence, Parameter uncertainty, Probability integral transform |
| JEL: | C12 C22 C52 |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1937&r=ets |
| By: | Eric Eisenstat; Joshua C.C. Chan; Rodney W. Strachan |
| Abstract: | This article develops a new econometric methodology for performing stochastic model specification search (SMSS) in the vast model space of time-varying parameter VARs with stochastic volatility and correlated state transitions. This is motivated by the concern of over-fitting and the typically imprecise inference in these highly parameterized models. For each VAR coefficient, this new method automatically decides whether it is constant or time-varying. Moreover, it can be used to shrink an otherwise unrestricted timevarying parameter VAR to a stationary VAR, thus providing an easy way to (probabilistically) impose stationarity in time-varying parameter models. We demonstrate the effectiveness of the approach with a topical application, where we investigate the dynamic effects of structural shocks in government spending on U.S. taxes and GDP during a period of very low interest rates. |
| Keywords: | Bayesian Lasso, shrinkage, fiscal policy |
| JEL: | C11 C52 E37 E47 |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2014-23&r=ets |
| By: | N. Fawcett; G. Kapetanios; J. Mitchell; S. Price |
| Abstract: | Density forecast combinations are becoming increasingly popular as a means of improving forecast `accuracy’, as measured by a scoring rule. In this paper we generalise this literature by letting the combination weights follow more general schemes. Sieve estimation is used to optimise the score of the generalised density combination where the combination weights depend on the variable one is trying to forecast. Specific attention is paid to the use of piecewise linear weight functions that let the weights vary by region of the density. We analyse these schemes theoretically, in Monte Carlo experiments and in an empirical study. Our results show that the generalised combinations outperform their linear counterparts. |
| Keywords: | Density Forecasting, Model Combination, Scoring Rules |
| JEL: | C53 |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2014-24&r=ets |
| By: | Dimitris Korobilis |
| Abstract: | This paper proposes full-Bayes priors for time-varying parameter vector autoregressions (TVP-VARs) which are more robust and objective than existing choices proposed in the literature. We formulate the priors in a way that they allow for straightforward posterior computation, they require minimal input by the user, and they result in shrinkage posterior representations, thus, making them appropriate for models of large dimensions. A comprehensive forecasting exercise involving TVP-VARs of different dimensions establishes the usefulness of the proposed approach. |
| Keywords: | TVP-VAR, shrinkage, data-based prior, forecasting |
| JEL: | C11 C22 C32 C52 C53 C63 E17 E58 |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:gla:glaewp:2014_04&r=ets |
| By: | Kunst, Robert M. (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria and University of Vienna) |
| Abstract: | Nonparametric unit-root tests are a useful addendum to the tool-box of time-series analysis. They tend to trade off power for enhanced robustness features. We consider combinations of the RURS (seasonal range unit roots) test statistic and a variant of the level-crossings count. This combination exploits two main characteristics of seasonal unit-root models, the range expansion typical of integrated processes and the low frequency of changes among main seasonal shapes. The combination succeeds in achieving power gains over the component tests. Simulations explore the finite-sample behavior relative to traditional parametric tests. |
| Keywords: | Seasonality, nonparametric tests, visualization, time series |
| JEL: | C12 C14 C22 |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:303&r=ets |
| By: | D.S. Poskitt; Gael M. Martin; Simone D. Grose |
| Abstract: | This paper investigates the use of bootstrap-based bias correction of semi-parametric estimators of the long memory parameter in fractionally integrated processes. The re-sampling method involves the application of the sieve boot-strap to data pre-filtered by a preliminary semi-parametric estimate of the long memory parameter. Theoretical justification for using the bootstrap techniques to bias adjust log-periodogram and semi-parametric local Whittle estimators of the memory parameter is provided. Simulation evidence comparing the performance of the bootstrap bias correction with analytical bias correction techniques is also presented. The bootstrap method is shown to produce notable bias reductions, in particular when applied to an estimator for which analytical adjustments have already been used. The empirical coverage of confidence intervals based on the bias-adjusted estimators is very close to the nominal, for a reasonably large sample size, more so than for the comparable analytically adjusted estimators. The precision of inferences (as measured by interval length) is also greater when the bootstrap is used to bias correct rather than analytical adjustments. |
| Keywords: | nd phrases: Bias adjustment, bootstrap-based inference, fractional process, log-periodogram regression, local Whittle estimator |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2014-10&r=ets |
| By: | Chaohua Dong; Jiti Gao; Dag Tjostheim |
| Abstract: | Estimation in two classes of popular models, single-index models and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link function in the models and a profile approach is used to derive the estimators. The findings include dual convergence rates of the estimators for the single-index models and a trio of convergence rates for the partially linear single-index models. More precisely, the estimators for single-index model converge along the direction of the true parameter vector at rate of n^(-1/4), while at rate of n^(-3/4) along all directions orthogonal to the true parameter vector; on the other hand, the estimators of the index vector for the partially single-index model retain the dual convergence rates as in the single-index model but the estimators of the coefficients in the linear part of the model possess rate n^(-1). Monte Carlo simulation verifies these theoretical results. An empirical study on the dataset of aggregate disposable income, consumption, investment and real interest rate in the United States between 1960:1-2009:3 furnishes an application of the proposed estimation procedures in practice. |
| Keywords: | onstationarity, orthogonal series expansion, single-index models, partially linear single-index models, dual convergence rates, a trio of convergence rates. |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2014-7&r=ets |
| By: | Chaohua Dong; Jiti Gao; Dag Tjostheim; Jiying Yin |
| Abstract: | This paper considers a general model specification test for nonlinear multivariate cointegrating regressions where the regressor consists of a univariate integrated time series and a vector of stationary time series. The regressors and the errors are generated from the same innovations, so that the model accommodates endogeniety. A new and simple test is proposed and the resulting asymptotic theory is established. The test statistic is constructed based on a natural distance function between a nonparametric estimate and a smoothed parametric counterpart. The asymptotic distribution of the test statistic under the parametric specification is proportional to that of a local-time random variable with a known distribution. In addition, the finite sample performance of the proposed test is evaluated through using both simulated and real data examples. |
| Keywords: | ointegration, endogeneity, nonparametric kernel estimation, parametric model speci-fication, time series. |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2014-8&r=ets |
| By: | Francq, Christian; Zakoian, Jean-Michel |
| Abstract: | A new approach is proposed to estimate a large class of multivariate volatility models. The method is based on estimating equation-by-equation the volatility parameters of the individual returns by quasi-maximum likelihood in a first step, and estimating the correlations based on volatility-standardized returns in a second step. Instead of estimating a $d$-multivariate volatility model we thus estimate $d$ univariate GARCH-type equations plus a correlation matrix, which is generally much simpler and numerically efficient. The strong consistency and asymptotic normality of the first-step estimator is established in a very general framework. For generalized constant conditional correlation models, and also for some time-varying conditional correlation models, we obtain the asymptotic properties of the two-step estimator. Our estimator can also be used to test the restrictions imposed by a particular MGARCH specification. An application to financial series illustrates the interest of the approach. |
| Keywords: | Constant conditional correlation; Dynamic conditional correlation; Markov switching models; Multivariate GARCH; Quasi maximum likelihood estimation |
| JEL: | C01 C13 C32 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:54250&r=ets |