Bootstrap based probability forecasting in multiplicative error models

As evidenced by an extensive empirical literature, multiplicative error models (MEM) show good performance in capturing the stylized facts of nonnegative time series; examples include, trading volume, financial durations, and volatility. This paper develops a bootstrap based method for producing multi-step-ahead probability forecasts for a nonnegative valued time-series obeying a parametric MEM. In order to test the adequacy of the underlying parametric model, a class of bootstrap specification tests is also developed. Rigorous proofs are provided for establishing the validity of the proposed bootstrap methods. The paper also establishes the validity of a bootstrap based method for producing probability forecasts in a class of semiparametric MEMs. Monte Carlo simulations suggest that our methods perform well in finite samples. A real data example illustrates the methods

A nonparametric control chart based on the Mann-Whitney statistic

Nonparametric or distribution-free charts can be useful in statistical process control problems when there is limited or lack of knowledge about the underlying process distribution. In this paper, a phase II Shewhart-type chart is considered for location, based on reference data from phase I analysis and the well-known Mann-Whitney statistic. Control limits are computed using Lugannani-Rice-saddlepoint, Edgeworth, and other approximations along with Monte Carlo estimation. The derivations take account of estimation and the dependence from the use of a reference sample. An illustrative numerical example is presented. The in-control performance of the proposed chart is shown to be much superior to the classical Shewhart $\bar{X}$ chart. Further comparisons on the basis of some percentiles of the out-of-control conditional run length distribution and the unconditional out-of-control ARL show that the proposed chart is almost as good as the Shewhart $\bar{X}$ chart for the normal distribution, but is more powerful for a heavy-tailed distribution such as the Laplace, or for a skewed distribution such as the Gamma. Interactive software, enabling a complete implementation of the chart, is made available on a website.Comment: Published in at http://dx.doi.org/10.1214/193940307000000112 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Business Cycle Asymmetry and the Stock Market

This paper investigates whether the systematic asymmetric behaviour of the US unemployment rate can be explained by the stock market. We consider threshold models to capture the asymmetric relationship between quarterly US unemployment rate and Dow Jones Industrial Average (DJ) stock returns. We test a range of null hypotheses of equlity restrictions against inequality constraints and the composite null hypothesis involving "steepness" in business cycles.UNEMPLOYMENT ; BUSINESS CYCLES ; MODELS

Robust Terms Against Smooth Transition Autoregressive (STAR) Models.

Testing for linearity in time series models has been an active area of research [see Granger and Terasvirta (1993), Tong (1991)]. The authors consider a test for linearity against a particular regime switching model known as the smooth transition autoregressive (STAR) model.TESTING ; TIME SERIES ; ECONOMETRICS

Testing for ARCH in ARCH-in-Mean Model

An issue that arises in aspplications involving the ARCH-in-Mean (ARCH-M) model is whether or not the error variance is constant over time. A proper statistical formualtion of this as a test of hypothesis presents two difficulties. First, the model does not satisfy the standard regularity conditions because a nuisance parameter becomes unidentified under the null hypothesis and consequently the usual tests, such as the Lagrange Multiplier test, and their distribution theory require modification.MODELS ; TESTING

A Goodness-of-Fit Test for a Class of Autoregressive Conditional Duration Models

This article develops a method for testing the goodness-of-fit of a given parametric autoregressive conditional duration model against unspecified nonparametric alternatives. The test statistics are functions of the residuals corresponding to the quasi maximum likelihood estimate of the given parametric model, and are easy to compute. The limiting distributions of the test statistics are not free from nuisance parameters. Hence, critical values cannot be tabulated for general use. A bootstrap procedure is proposed to implement the tests, and its asymptotic validity is established. The finite sample performances of the proposed tests and several other competing ones in the literature, were compared using a simulation study. The tests proposed in this article performed well consistently throughout, and they were either the best or close to the best. None of the tests performed uniformly the best. The tests are illustrated using an empirical example