The asymptotic structure of nearly unstable non-negative integer-valued AR(1) models

This paper considers non-negative integer-valued autoregressive processes where the autoregression parameter is close to unity. We consider the asymptotics of this `near unit root' situation. The local asymptotic structure of the likelihood ratios of the model is obtained, showing that the limit experiment is Poissonian. To illustrate the statistical consequences we discuss efficient estimation of the autoregression parameter and efficient testing for a unit root.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ153 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Efficient Estimation in Semiparametric Time Series: the ACD Model

In this paper we consider efficient estimation in semiparametric ACD models. We consider a suite of model specifications that impose less and less structure. We calculate the corresponding efficiency bounds, discuss the construction of efficient estimators in each case, and study tvide a simulation study that shows the practical gain from using the proposed semiparametric procedures. We find that, although one does not gain as much as theory suggests, these semiparametric procedures definitely outperform more classical procedures. We apply the procedures to model semiparametrically durations observed on the Paris Bourse for the Alcatel stock in July and August 1996.

On quadratic expansions of log likelihoods and a general asymptotic linearity result

Irrespective of the statistical model under study, the derivation of limits, in the Le Cam sense, of sequences of local experiments (see [7]-[10]) often follows along very similar lines, essentially involving differentiability in quadratic mean of square roots of (conditional) densities. This chapter establishes two abstract and very general results providing sufficient and nearly necessary conditions for (i) the existence of a quadratic expansion, and (ii) the asymptotic linearity of local log-likelihood ratios (asymptotic linearity is needed, for instance, when unspecified model parameters are to be replaced, in some statistic of interest, with some preliminary estimator). Such results have been established, for locally asymptotically normal (LAN) models involving independent and identically distributed observations, by, e.g., [1], [11] and [12]. Similar results are provided here for models exhibiting serial dependencies which, so far, have been treated on a case-by-case basis (see [4] and [5] for typical examples) and, in general, under stronger regularity assumptions. Unlike their i.i.d. counterparts, our results extend beyond the context of LAN experiments, so that non-stationary unit-root time series and cointegration models, for instance, also can be handled (see [6])

Semiparametrically Point-Optimal Hybrid Rank Tests for Unit Roots

We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limit experiment associated to the unit root model. The invariance structures naturally suggest tests that are based on the ranks of the increments of the observations, their average, and an assumed reference density for the innovations. The tests are semiparametric in the sense that they are valid, i.e., have the correct (asymptotic) size, irrespective of the true innovation density. For a correctly specified reference density, our test is point-optimal and nearly efficient. For arbitrary reference densities, we establish a Chernoff-Savage type result, i.e., our test performs as well as commonly used tests under Gaussian innovations but has improved power under other, e.g., fat-tailed or skewed, innovation distributions. To avoid nonparametric estimation, we propose a simplified version of our test that exhibits the same asymptotic properties, except for the Chernoff-Savage result that we are only able to demonstrate by means of simulations

Arbitrage pricing theory for idiosyncratic variance factors

We develop an Arbitrage Pricing Theory framework extension to study the pricing of squared returns/volatilities. We analyze the interplay between factors at the return level and those in idiosyncratic variances. We confirm the presence of a common idiosyncratic variance fac- tor, but do not find evidence that this represents a missing risk factor at the (linear) return level. Thereby, we consistently identify idiosyncratic returns. The price of the idiosyncratic variance factor identified by squared returns is small relative to the price of market variance risk. The quadratic pricing kernels induced by our model are in line with standard economic intuition

De Meerwaarde van Risicodeling met Toekomstige Generaties Nader Bezien

Rapportage van bevindingen van een Netspar werkgroep waar onderzoek is gedaan naar de welvaartswinst van risicodeling met toekomstige generaties. Risicodeling met toekomstige generaties vindt plaats doordat toekomstige deelnemers ook al (deels) worden blootgesteld aan financiële mee- en tegenvallers uit het heden

Semiparametrically Efficient Inference Based on Signs and Ranks for Median Restricted Models

Since the pioneering work of Koenker and Bassett (1978), econometric models involving median and quantile rather than the classical mean or conditional mean concepts have attracted much interest.Contrary to the traditional models where the noise is assumed to have mean zero, median-restricted models enjoy a rich group-invariance structure.In this paper, we exploit this invariance structure in order to obtain semiparametrically efficient inference procedures for these models.These procedures are based on residual signs and ranks, and therefore insensitive to possible misspecification of the underlying innovation density, yet semiparametrically efficient at correctly specified densities.This latter combination is a definite advantage of these procedures over classical quasi-likelihood methods.The techniques we propose can be applied, without additional technical difficulties, to both cross-sectional and time-series models.They do not require any explicit tangent space calculation nor any projections on these.