Bruce E. Hansen
Boston College
A distribution theory is developed for least squares estimates of the threshold in threshold autoregressive (TAR) models. We find that if we let the threshold effect (the difference in slopes between the two regimes) get small as the sample size increases, then the asymptotic distribution of the threshold estimator is free of nuisance parameters (up to scale). Similarly, the likelihood ratio statistic for testing hypotheses concerning the unknown threshold is asymptotically free of nuisance parameters. These asymptotic distributions are non-standard, but are available in closed form so critical values are readily available. To illustrate this theory, we report an application to the U.S. unemployment rate. We find statistically significant threshold effects.
Investigating Cyclical Asymmetries
Randal Verbrugge
VPI&SU
This paper accomplishes two goals: First, it introduces a powerful nonparametric test of asymmetry to the economics literature, the triples test of Randles et al. (1980). Second, it documents the presence of two specific kinds of asymmetry in US macroeconomic time series. Depth, asymmetry in the distribution of a (detrended) series, is a feature of numerous economic time series; steepness, asymmetry in the distribution of first differences, is a feature of hours, employment, and the unemployment rate, but is absent from real GDP and aggregate industrial production. The pattern of asymmetries found provides guidelines for restricting the set of alternative nonlinear models from which to select in modeling these time series.
Technical Trading Rules and the Size of the Risk Premium in Security Returns
Ramazan Gencay
U. of Windsor
Thanasis Stengos
U. of Guelph
Among analysts, technical trading rules are widely used for forecasting security returns. Recent literature provides evidence that these rules may provide positive profits after accounting for transaction costs. This would be contrary to the theory of the efficient market hypothesis which states that security prices cannot be forecasted from their past values or other past variables. This paper uses the daily Dow Jones Industrial Average Index from 1963 to 1988 to examine the linear and nonlinear predictability of stock market returns with simple technical trading rules, by using the nearest neighbors and the feedforward network regressions. Evidence of nonlinear predictability is found in the stock market returns by using the past returns and the buy and sell signals of the moving average rules.
Finite Sample Properties of the Efficient Method of Moments
R—mulo A. Chumacero
University of Chile
Gallant and Tauchen (1996) describe an estimation technique, known as Efficient Method of Moments (EMM), that uses numerical methods to estimate parameters of a structural model by using as matching conditions (moments in the GMM jargon) the gradients of an auxiliary model that fits a subset of variables that may be simulated from the structural model.
This paper presents three Monte Carlo experiments to asses the finite sample properties of EMM. The first one compares it with a fully efficient procedure (Maximum Likelihood) by estimating an invertible MA process. The second and third experiments, compare the finite sample properties of the EMM estimators with those of GMM by using stochastic volatility models and consumption-based asset pricing models. The experiments show that the gains in efficiency are impressive; however, given that both EMM and GMM share the same type of objective function, finite sample inference based on asymptotic theory continues to lead, in some cases, to "over rejections" even though they are not as significant as in GMM.
A Fast Algorithm for the BDS Statistic
Blake LeBaron
University of Wisconsin
The BDS statistic has proved to be one of several useful nonlinear diagnostics. It has been shown to have good power against many nonlinear alternatives, and its asymptotic properties as a residual diagnostic are well understood. Furthermore, extensive monte-carlo results have proved it useful in relatively small samples. However, the BDS test is not trivial to calculate, and is even more difficult to deal with if one wants the speed necessary to make bootstrap resampling feasable. This short paper presents a fast algorithm for the BDS statistic, and outlines how these speed improvements are achieved. Source code in the c programming language is included.