|
on Econometric Time Series |
| By: | Timo Teräsvirta (Aarhus University and CREATES); Yukai Yang (CORE, Université catholique de Louvain and CREATES) |
| Abstract: | In this paper, we derive Lagrange multiplier and Lagrange multiplier type specification and misspecification tests for vector smooth transition models. We report results from simulation studies in which the size and power properties of the proposed tests in small samples are considered. The results show that these asymptotic tests generally suffer from size distortion. We find thatWilks’s lambda and Rao’s F statistic both have satisfactory size properties and can be recommended for empirical use. Bootstrapping the standard asymptotic LM statistic offers another solution to the problem. JEL Classification: C12, C32, C52. |
| Keywords: | Vector STAR models, Linearity test, Misspecification test, Vector nonlinear time series, Serial correlation, Parameter constancy, Residual nonlinearity test |
| Date: | 2014–06–02 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2014-04&r=ets |
| By: | Peter Tankov |
| Abstract: | We study the left tail behavior of the logarithm of the distribution function of a sum of dependent positive random variables. Asymptotics are computed under the assumption that the marginal distribution functions decay slowly at zero, meaning that the their logarithms are slowly varying functions. This includes parametric families such as log-normal, gamma, Weibull and many distributions from the financial mathematics literature. We show that the logarithmic asymptotics of the sum in question depend on a characteristic of the copula of the random variables which we term weak lower tail dependence function, and which is computed explicitly for several families of copulas in this paper. In applications, our results may be used to quantify the diversification of long-only portfolios of financial assets with respect to extreme losses. As an illustration, we compute the left tail asymptotics for a portfolio of options in the multidimensional Black-Scholes model. |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1402.4683&r=ets |
| By: | Majid Al-Sadoon |
| Abstract: | This paper develops an approach to rank testing that nests all existing rank tests and simplifies their asymptotics. The approach is based on the fact that implicit in every rank test there are estimators of the null spaces of the matrix in question. The approach yields many new insights about the behavior of rank testing statistics under the null as well as local and global alternatives in both the standard and the cointegration setting. The approach also suggests many new rank tests based on alternative estimates of the null spaces as well as the new fixed-b theory. A brief Monte Carlo study illustrates the results. |
| Keywords: | rank testing, stochastic tests, classical tests, subspace estimation, cointegration |
| JEL: | C12 C13 C30 |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:750&r=ets |
| By: | Katarzyna Lasak (VU University Amsterdam, the Netherlands); Carlos Velasco (Universidad Carlos III de Madrid, Spain) |
| Abstract: | We consider cointegration rank estimation for a p-dimensional Fractional Vector Error Correction Model. We propose a new two-step procedure which allows testing for further long-run equilibrium relations with possibly different persistence levels. The first step consists in estimating the parameters of the model under the null hypothesis of the cointegration rank r=1,2,…,p-1. This step provides consistent estimates of the order of fractional cointegration, the cointegration vectors, the speed of adjustment to the equilibrium parameters and the common trends. In the second step we carry out a sup-likelihood ratio test of no-cointegration on the estimated p-r common trends that are not cointegrated under the null. The order of fractional cointegration is re-estimated in the second step to allow for new cointegration relationships with different memory. We augment the error correction model in the second step to adapt to the representation of the common trends estimated in the first step. The critical values of the proposed tests depend only on the number of common trends under the null, p-r, and on the interval of the orders of fractional cointegration b allowed in the estimation, but not on the order of fractional cointegration of already identified relationships. Hence this reduces the set of simulations required to approximate the critical values, making this procedure convenient for practical purposes. In a Monte Carlo study we analyze the finite sample properties of our procedure and compare with alternative methods. We finally apply these methods to study the term structure of interest rates. |
| Keywords: | Error correction model; Gaussian VAR model; Likelihood ratio tests; Maximum likelihood estimation |
| JEL: | C12 C15 C32 |
| Date: | 2014–02–13 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140021&r=ets |
| By: | Korobilis, Dimitris |
| 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:pra:mprapa:53772&r=ets |
| By: | Zhu, Ke; Li, Wai Keung; Yu, Philip L.H. |
| Abstract: | This paper introduces a new model called the buffered autoregressive model with generalized autoregressive conditional heteroskedasticity (BAR-GARCH). The proposed model, as an extension of the BAR model in Li et al. (2013), can capture the buffering phenomenon of time series in both conditional mean and conditional variance. Thus, it provides us a new way to study the nonlinearity of a time series. Compared with the existing AR-GARCH and threshold AR-GARCH models, an application to several exchange rates highlights an interesting interpretation of the buffer zone determined by the fitted BAR-GARCH models. |
| Keywords: | Buffered AR model; Buffered AR-GARCH model; Exchange rate; GARCH model; Nonlinear time series; Threshold AR model. |
| JEL: | C1 C51 C52 C58 G1 |
| Date: | 2014–02–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:53874&r=ets |