. The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly extend the nuisance parameter approach. How and why the nuisance parameter approach works and how it can be extended bears closely on recent developments in artificial neural networks. Statistical content is provided by viewing specification tests with nuisance parameters as tests of hypotheses about Banach-valued random elements and applying the Banach Central Limit Theorem and Law of Iterated Logarithm, leading to simple procedures that can be used as a guide to when computationally more elaborate procedures may be warranted. 1. Introduction In testing whether or not a parametric statistical model is correctly specified, there are a number of apparently distinct approaches one might take. T...

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: This paper develops a new test for speculative bubbles, which is applied to data for the Japanese yen, the German mark and the Canadian dollar exchange rates from 1977 to 1991. The test assumes that bubbles display a particular kind of regime-switching behaviour, which is shown to imply coefficient restrictions on a simple switching-regression model of exchange rate innovations. Test results are sensitive to the specification of exchange rate fundamentals and other factors. Evidence most consistent with the bubble hypothesis is found using an overshooting model of the Canadian dollar and a PPP model of the Japanese yen. Page 1 of 57 /home/int/vann/fm/swpfx/swfx_jae.acc 9 August 1995 13:50 Introduction This paper develops a new test for speculative bubbles in exchange rates and then applies this test to data for three bilateral exchange rates over the 1977 - 1991 period. Recent work in testing for bubbles has shifted from general tests that should detect any kind of bubble (Meese...

We consider two conditional moment tests for neglected nonlinearity in regression models and examine their finite sample performance. The two tests are the nonparametric kernel test by Li and Wang (1998) and Zheng (1996) and the neural network test of White (1989). We examine asymptotic test, naive bootstrap test, and wild bootstrap test for weakly dependent time series and independent data.

: We look for evidence of "hysteresis" in the U.S. unemployment rate --- that is, that current labor-market outcomes can affect the future equilibrium level of unemployment. We first examine (using a variety of econometric tests for unit roots) whether the unemployment rate tends to come back to a long-run average over time. On balance, our results suggest that the unemployment rate tends to return to a long-run value, ruling out the possibility of permanent hysteresis. We look for evidence of temporary hysteresis by examining whether lagged unemployment enters a standard Phillips-curve model of U.S. inflation. We find weak evidence in support of temporary hysteresis, but the effect is not very large, suggesting that hysteresis is not very important for U.S. unemployment. We are grateful to Carol Corrado, Dan Sichel, Dave Stockton, Sandy Struckmeyer, Bill Wascher, and seminar participants at the Federal Reserve Board for helpful comments. The views expressed in this paper are those of...

Abstract — Given the location of a relative maximum of the log-likelihood function, how to assess whether it is the global maximum? This paper investigates a statistical tool, which answers this question by posing it as a hypothesis testing problem. A general framework for constructing tests for global maximum is given. The characteristics of the tests are investigated for two cases: correctly specified model and model mismatch. A finite sample approximation to the power is given, which gives a tool for performance prediction and a measure for comparison between tests. The sensitivity of the tests to model mismatch is analyzed in terms of the Renyi divergence and the Kullback-Leibler distance between the true underlying distribution and the assumed parametric class and tests that are insensitive to small deviations from the model are derived. The tests are illustrated for three applications: passive localization or direction finding using an array of sensors, estimating the parameters of a Gaussian mixture model, and estimation of superimposed exponentials in noise- problems that are known to suffer from local maxima. Index Terms — Parameter estimation, maximum likelihood, global optimization, local maxima, array processing, Gaussian

Abstract. Many nonparametric estimators and tests are naturally set in infinite dimensional contexts. Prevalence is the infinite dimensional analogue of full Lebesgue measure, shyness the analogue of being a Lebesgue null set. A prevalent set of prior distributions lead to wildly inconsistent Bayesian updating when independent and identically distributed observations happen in class of infinite spaces that includes R n and N. For any rate of convergence, no matter how slow, only a shy set of target functions can be approximated by consistent nonparametric regression schemes in a class that includes series approximations, kernels and other locally weighted regressions, splines, and artificial neural networks. When the instruments allow for the existence of an instrumental regression, the regression function only exists for a shy set of dependent variables. The instruments allow for existence in a counterintuitive dense set of cases, shyness is an open question. A prevalent set of integrated conditional moment (ICM) specification tests are consistent, a dense subset of the finitely parametrized ICM tests are consistent, prevalence is an open question.

This paper develops a valuation framework for a perpetual American call option when the underlying asset return dynamic is modelled by a regime switching process. In particular, asset return dynamic is governed by a stochastic dividend process which randomly switches between two regimes that are characterized by different rates of both drift and volatility. This regime-switching characterization of dividend growth is supported by empirical works. We provide analytical results by solving the fundamental differential equation. The analysis reveals that the option value may differ between states. Our empirical application shows that these differences may be quantitatively very important.

: In this paper we provide considerable Monte Carlo evidence on the finite sample performance of several alternative forms of White's [1982] IM test. Using linear regression and probit models, we extend the range of previous analysis in a manner that reveals new patterns in the behavior of the asymptotic version of the IM test -- particularly with respect to curse of dimensionality effects. We also explore the potential of parametric and nonparametric bootstrap methods for reducing the size bias that characterizes the asymptotic IM test. The nonparametric bootstrap is of particular interest because of the weak conditions it imposes, but the results of our Monte Carlo experiments suggest that this technique is not without limitations. The parametric bootstrap demonstrates good size and power in reasonably small samples, but requires assumptions that may be auxiliary from the standpoint of a QMLE. We observe that the effects of violating one of these auxiliary assumptions has ...

ThispapershowshowtoderivethepriceofaperpetualAmericancalloptionon thepriceofastockmarketindexthatshiftsfromtimetotimebetweentwodi®erent states, each with di®erent rates of drift and volatility. Much empirical evidence supportsaregime-switchingcharacterizationofdividendgrowth. Theanalysisshows thattheoptionvaluemaydi®ergreatlybetweenstates. Ourempiricalapplication showsthatthesedi®erencesmaybequantitativelyveryimportant.