Bootstrapping I(1) Data

A functional law for an I(1) sample data version of the continuous-path block bootstrap of Paparoditis and Politis (2001) is given. The results provide an alternative demonstration that continuous-path block bootstrap unit root tests are consistent under the null.Asymptotic theory, Block bootstrap, Bootstrap, Brownian motion, Continuous path bootstrap, Embedding, Unit root

The Mysteries of Trend

Trends are ubiquitous in economic discourse, play a role in much economic theory, and have been intensively studied in econometrics over the last three decades. Yet the empirical economist, forecaster, and policy maker have little guidance from theory about the source and nature of trend behavior, even less guidance about practical formulations, and are heavily reliant on a limited class of stochastic trend, deterministic drift, and structural break models to use in applications. A vast econometric literature has emerged but the nature of trend remains elusive. In spite of being the dominant characteristic in much economic data, having a role in policy assessment that is often vital, and attracting intense academic and popular interest that extends well beyond the subject of economics, trends are little understood. This essay discusses some implications of these limitations, mentions some research opportunities, and briefly illustrates the extent of the difficulties in learning about trend phenomena even when the time series are far longer than those that are available in economics.Climate change, Etymology of trend, Paleoclimatology, Policy, Stochastic trend

A specification test for nonlinear nonstationary models

We provide a limit theory for a general class of kernel smoothed U-statistics that may be used for specification testing in time series regression with nonstationary data. The test framework allows for linear and nonlinear models with endogenous regressors that have autoregressive unit roots or near unit roots. The limit theory for the specification test depends on the self-intersection local time of a Gaussian process. A new weak convergence result is developed for certain partial sums of functions involving nonstationary time series that converges to the intersection local time process. This result is of independent interest and is useful in other applications. Simulations examine the finite sample performance of the test.Comment: Published in at http://dx.doi.org/10.1214/12-AOS975 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Exact local Whittle estimation of fractional integration

An exact form of the local Whittle likelihood is studied with the intent of developing a general-purpose estimation procedure for the memory parameter (d) that does not rely on tapering or differencing prefilters. The resulting exact local Whittle estimator is shown to be consistent and to have the same N(0,{1/4}) limit distribution for all values of d if the optimization covers an interval of width less than {9/2} and the initial value of the process is known.Comment: Published at http://dx.doi.org/10.1214/009053605000000309 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Local Whittle estimation in nonstationary and unit root cases

Asymptotic properties of the local Whittle estimator in the nonstationary case (d>{1/2}) are explored. For {1/2}<d\leq 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of d. For d=1, the limit distribution is mixed normal. For d>1 and when the process has a polynomial trend of order \alpha >{1/2}, the estimator is shown to be inconsistent and to converge in probability to unity

A Conversation with Eric Ghysels

Published in Econometric Theory, 2012, https://doi.org/10.1017/S026646661100017X</p

Jeffreys Prior Analysis of the Simultaneous Equations Model in the Case with n+1 Endogenous Variables

This paper analyzes the behavior of posterior distributions under the Jeffreys prior in a simultaneous equations model. The case under study is that of a general limited information setup with n + 1 endogenous variables. The Jeffreys prior is shown to give rise to a marginal posterior density which has Cauchy-like tails similar to that exhibited by the exact finite sample distribution of the corresponding LIML estimator. A stronger correspondence is established in the special case of a just-identified orthonormal canonical model, where the posterior density under the Jeffreys prior is shown to have the same functional form as the density of the finite sample distribution of the LIML estimator. The work here generalizes that of Chao and Phillips (1997), which gives analogous results for the special case of two endogenous variables.Cauchy tails, exact finite sample distributions, Jeffreys prior, just identification, limited information, posterior density, simultaneous equations model

Simulation-based Estimation of Contingent-claims Prices

A new methodology is proposed to estimate theortical prices of financial contingent-claims whose values are dependent on some other underlying financial assets. In the literature the preferred choice of estimator is usually maximum likelihood (ML). ML has strong asymptotic justification but is not necessarily the best method in finite samples. The present paper proposes instead a simulation-based method that improves the finite sample performance of the ML estimator while maintaining its good asymptotic properties. The methods are implemented and evaluated here in the Black-Scholes option pricing model and in the Vasicek bond pricing model, but have wider applicability. Monte Carlo studies show that the proposed procedures achieve bias reductions overML estimation in pricing contingent claims. The bias reductions are sometimes accompanied by reductions in variance, leading to significant overall gains in mean squared estimation error. Empirical applications to US treasure bills highlight the differences between the bond prices implied by the simulation-based approach and those delivered by ML and the consequences on the statistical tesing of contingent-claim pricing models.Bias Reduction, Bond Pricing, Indirect Inference, Option Pricing, Simulation-based Estimation

Dating the Timeline of Financial Bubbles during the Subprime Crisis

A new recursive regression methodology is introduced to analyze the bubble characteristics of various financial time series during the subprime crisis. The methods modify a technique proposed in Phillips, Wu and Yu (2010) and provide a technology for identifying bubble behavior and consistent dating of their origination and collapse. The tests also serve as an early warning diagnostic of bubble activity. Seven relevant financial series are investigated, including three financial assets (the Nasdaq index, home price index and asset-backed commercial paper), two commodities (the crude oil price and platinum price), one bond rate (Baa), and one exchange rate (Pound/USD). Statistically significant bubble characteristics are found in all of these series. The empirical estimates of the origination and collapse dates suggest an interesting migration mechanism among the financial variables: a bubble first emerged in the equity market during mid-1995 lasting to the end of 2000, followed by a bubble in the real estate market between January 2001 and July 2007 and in the mortgage market between November 2005 and August 2007. After the subprime crisis erupted, the phenomenon migrated selectively into the commodity market and the foreign exchange market, creating bubbles which subsequently burst at the end of 2008, just as the effects on the real economy and economic growth became manifest. Our empirical estimates of the origination and collapse dates match well with the general datetimes of this crisis put forward in a recent study by Caballero, Farhi and Gourinchas (2008).Financial bubbles, Crashes, Date stamping, Explosive behavior, Mildly explosive process, Subprime crisis, Timeline