|
on Econometric Time Series |
| By: | M. Hashem Pesaran (Cambridge University and IZA Bonn); Allan Timmermann (University of California, San Diego) |
| Abstract: | The contingency table literature on tests for dependence among discrete multi-category variables is extensive. Existing tests assume, however, that draws are independent, and there are no tests that account for serial dependencies - a problem that is particularly important in economics and finance. This paper proposes a new test of independence based on the maximum canonical correlation between pairs of discrete variables. We also propose a trace canonical correlation test using dynamically augmented reduced rank regressions or an iterated weighting method in order to account for serial dependence. Such tests are useful, for example, when testing for predictability of one sequence of discrete random variables by means of another sequence of discrete random variables as in tests of market timing skills or business cycle analysis. The proposed tests allow for an arbitrary number of categories, are robust in the presence of serial dependencies and are simple to implement using multivariate regression methods. Monte Carlo experiments show that the proposed tests have good finite sample properties. An empirical application to survey data on forecasts of GDP growth demonstrates the importance of correcting for serial dependencies in predictability tests. |
| Keywords: | contingency tables, canonical correlations, serial dependence, tests of predictability |
| JEL: | C12 C22 C42 C52 |
| Date: | 2006–07 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp2196&r=ets |
| By: | Jae Kim; Param Silvapulle; Rob J. Hyndman |
| Abstract: | The half-life is defined as the number of periods required for the impulse response to a unit shock to a time series to dissipate by half. It is widely used as a measure of persistence, especially in international economics to quantify the degree of mean reversion of the deviation from an international parity condition. Several studies have proposed bias-corrected point and interval estimation methods. However, they have found that the confidence intervals are rather uninformative with their upper bound being either extremely large or infinite. This is largely due to the distribution of the half-life estimator being heavily skewed and multi-modal. In this paper, we propose a bias-corrected bootstrap procedure for the estimation of half-life, adopting the highest density region (HDR) approach to point and interval estimation. Our Monte Carlo simulation results reveal that the bias-corrected bootstrap HDR method provides an accurate point estimator, as well as tight confidence intervals with superior coverage properties to those of its alternatives. As an application, the proposed method is employed for half-life estimation of the real exchange rates of seventeen industrialized countries. The results indicate much faster rates of mean-reversion than those reported in previous studies. |
| Keywords: | Autoregressive Model, Bias-correction, Bootstrapping, Confidence interval, Half-life, Highest density region. |
| JEL: | C15 C22 F37 |
| Date: | 2006–06 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2006-11&r=ets |
| By: | D. S. Poskitt |
| Abstract: | In this paper we will investigate the consequences of applying the sieve bootstrap under regularity conditions that are sufficiently general to encompass both fractionally integrated and non-invertible processes. The sieve bootstrap is obtained by approximating the data generating process by an autoregression whose order h increases with the sample size T. The sieve bootstrap may be particularly useful in the analysis of fractionally integrated processes since the statistics of interest can often be non-pivotal with distributions that depend on the fractional index d. The validity of the sieve bootstrap is established and it is shown that when the sieve bootstrap is used to approximate the distribution of a general class of statistics admitting an Edgeworth expansion then the error rate achieved is of order <em>O</em>(<em>T</em><sup> β+d-1</sup>), for any β > 0. Practical implementation of the sieve bootstrap is considered and the results are illustrated using a canonical example. |
| Keywords: | Autoregressive approximation, fractional process, non-invertibility, rate of convergence, sieve bootstrap. |
| JEL: | C15 C22 |
| Date: | 2006–07 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2006-12&r=ets |
| By: | S. D. Grose; D. S. Poskitt |
| Abstract: | This paper investigates the empirical properties of autoregressive approximations to two classes of process for which the usual regularity conditions do not apply; namely the non-invertible and fractionally integrated processes considered in Poskitt (2006). In that paper the theoretical consequences of fitting long autoregressions under regularity conditions that allow for these two situations was considered, and convergence rates for the sample autocovariances and autoregressive coefficients established. We now consider the finite-sample properties of alternative estimators of the AR parameters of the approximating AR(h) process and corresponding estimates of the optimal approximating order h. The estimators considered include the Yule-Walker, Least Squares, and Burg estimators. |
| Keywords: | Autoregression, autoregressive approximation, fractional process, |
| JEL: | C14 C22 C53 |
| Date: | 2006–06 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2006-15&r=ets |
| By: | Jonathan Hill (Department of Economics, Florida International University) |
| Abstract: | In this paper we establish functional central limit theorems for a broad class of dependent, heterogeneous processes that includes popularly studied tail arrays {X_(n,t)} in the extreme-value literature. We assume sup_t(E|X_(n,t)|^r)^(1/r)=O(n^(-a(r))) for some r>=2 and some function 0<a(r)<=1/2 capturing extremal exceedances, tail empirical processes and tail empirical quantile processes. We trim dependence assumptions down to a minimum by constructing an extremal version of the near-epoch-dependence property to hold exclusively in the extreme support of the distribution. Our theory can be used to characterize the functional limit distributions of a popular tail index estimator, the tail quantile function, and multivariate extremal dependence measures under substantially general conditions. |
| Keywords: | Funct ional central limit theorem, extremal processes, tail empirical process, cadlag space, mixingale, near-epoch-dependence, regular variation, Hill estimator, tail dependence |
| JEL: | C19 C22 |
| Date: | 2006–07 |
| URL: | http://d.repec.org/n?u=RePEc:fiu:wpaper:0607&r=ets |
| By: | Jonathan Hill (Department of Economics, Florida International University) |
| Abstract: | We develop a consistent conditional moment test of Lp-best predictor functional form, 1<p<=2. Our main result is a reduction of the nuisance parameter space to the set of integers which greatly simplifies asymptotic theory, and allows for removal of the nuisance parameter in a mechanical fashion. Our results provide a fresh vantage into why Bierens’ (1990) moment condition works, and uncovers a new class of weights which sharply contrasts with Stinchcombe and White’s (1997) weight classification (real analytic and non-polynomial). The computation of a weighted-Average CM statistic is easy and asymptotically nuisance parameter free be cause it incorporate s all possible nuisance paramete r values. Our test serves as a consistent model check in Lp-regression environments. Finally, we provide a simple nuisance parameter free series expansion of the best Lp-predictor. |
| Keywords: | nonlinear regression models, consistent conditional moment test, nuisance parameter-free test, Lp-best predictor |
| JEL: | C12 C45 C52 |
| Date: | 2006–07 |
| URL: | http://d.repec.org/n?u=RePEc:fiu:wpaper:0608&r=ets |
| By: | Saadet Kirbas Kasman (Department of Economics, Faculty of Business, Dokuz Eylül University); Adnan Kasman (Department of Economics, Faculty of Business, Dokuz Eylül University); Evrim Turgutlu (Department of Economics, Faculty of Business, Dokuz Eylül University) |
| Abstract: | This paper investigates the validity of the Fisher hypothesis using data from 33 developed and developing countries. Conventional cointegration tests do not provide strong evidence on the relationship between nominal interest rates and inflation. Therefore, we use fractional cointegration analysis to test the long-run relationship between the two variables. The results indicate that the long-run relationship between nominal interest rates and inflation do not exist for most countries in the sample when conventional cointegration test is employed. However, fractional cointegration between the two variables is found for a large majority of countries, implying the validity of the Fisher hypothesis. The results also indicate that the equilibrium errors display long memory. |
| Keywords: | Fisher hypothesis, interest rates, fractional cointegration, long memory |
| JEL: | E43 C22 |
| Date: | 2005–11–23 |
| URL: | http://d.repec.org/n?u=RePEc:deu:dpaper:0504&r=ets |