A Hausman test for Brownian motion

New tests are proposed for the specification of the intraday price process of a risky asset, based on open, high, low, and close prices. Under the null of a Brownian process we derive two stochastically independent, unbiased volatility estimators. For a Hausman specification test we prove its equivalence with an F-test, consider its robustness against variation in drift and volatility, and analyze the power against an Ornstein–Uhlenbeck process, as well as a random walk with alternative distributions.     

Statistical consulting

The paper and the special issue focus on the activity of statistical consulting and its varieties. This includes academic consulting, consulting to and in industry as well as statistics in public media.     

Inference in hybrid Bayesian networks using dynamic discretization

We consider approximate inference in hybrid Bayesian Networks (BNs) and present a new iterative algorithm that efficiently combines dynamic discretization with robust propagation algorithms on junction trees. Our approach offers a significant extension to Bayesian Network theory and practice by offering a flexible way of modeling continuous nodes in BNs conditioned on complex configurations of evidence and intermixed with discrete nodes as both parents and children of continuous nodes. Our algorithm is implemented in a commercial Bayesian Network software package, AgenaRisk, which allows model construction and testing to be carried out easily. The results from the empirical trials clearly show how our software can deal effectively with different type of hybrid models containing elements of expert judgment as well as statistical inference. In particular, we show how the rapid convergence of the algorithm towards zones of high probability density, make robust inference analysis possible even in situations where, due to the lack of information in both prior and data, robust sampling becomes unfeasible.     

Multi-phase sampling under cost constraints

Multi-phase sampling (M-PhS) scheme is useful when the interest is in the estimation of the population mean of an expensive variable strictly connected with other cheaper (auxiliary) variables. The MSE is an accuracy measure of an estimator. Usually it decreases as the sample size increases. In practice the sample size cannot become arbitrarily large for possible cost constraints. From a practical point of view it would be useful to know the sample sizes which guarantee the best accuracy of the estimates for fixed costs. These “optimum” sample sizes can be, in some cases, computable but not admissible. In other cases, they can be neither admissible nor computable. The main goal of this paper is to propose a solution for both these situations. It will be clear that in both situations the solution is to consider a M-PhS scheme with one or more phases less.     

H-likelihood: problems and solutions

In recent issues of this journal it has been asserted in two papers that the use of h-likelihood is wrong, in the sense of giving unsatisfactory estimates of some parameters for binary data (Kuk and Cheng, 1999; Waddington and Thompson, 2004) or theoretically unsound (Kuk and Cheng, 1999). We wish to refute both these assertions.     

A direct derivation of the REML likelihood function

The original derivation of the widely cited form of the REML likelihood function for mixed linear models is difficult and indirect. This paper derives it directly using familiar operations with matrices and determinants.     

Nonconglomerative coherent conditional probabilities in statistical inference

Noteworthy connections among conglomerability, countable additivity and coherence are discussed in detail, reaching the conclusion that nonconglomerable conditional probabilities must not be doomed and play a significant role in statistical inference. Extended and updated version of a contributed paper presented at the International Conference on “Information Processing and Management of Uncertainty in knowledge-based systems”, IPMU 2004, Perugia, Italy.     

Modelling Variability in the Branching Structure of Strawberry Inflorescences

The branching structure of inflorescences of the cultivated strawberry ( Fragaria × ananassa Duch.) is very variable. This paper demonstrates that some aspects of this variability are well described by a simple stochastic model of branching that has two adjustable parameters. The model is shown to provide a good fit to data from a set of almost 700 inflorescences of the cultivar Elsanta, collected over two successive years. For one parameter the maximum likelihood estimator is a moment estimator which is fully efficient even if the detailed branching structure of the inflorescences is not recorded. This parameter provides a convenient summary of branching vigour. The maximum likelihood estimator of the second parameter must be determined iteratively and can be quite inefficient unless the full branching structure is recorded. The model demonstrates that branching structure is affected by the order in which inflorescences emerge on the plant.     

A Bootstrap Stationarity Test for Predictive Regression Invalidity

In order for predictive regression tests to deliver asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that any predictability in the variable of interest is purely attributable to the predictors under test. Violation of this assumption by the omission of relevant persistent predictors renders the predictive regression invalid, and potentially also spurious, as both the finite sample and asymptotic size of the predictability tests can be significantly inflated. In response, we propose a predictive regression invalidity test based on a stationarity testing approach. To allow for an unknown degree of persistence in the putative predictors, and for heteroscedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We demonstrate the asymptotic validity of the proposed bootstrap test by proving that the limit distribution of the bootstrap statistic, conditional on the data, is the same as the limit null distribution of the statistic computed on the original data, conditional on the predictor. This corrects a long-standing error in the bootstrap literature whereby it is incorrectly argued that for strongly persistent regressors and test statistics akin to ours the validity of the fixed regressor bootstrap obtains through equivalence to an unconditional limit distribution. Our bootstrap results are therefore of interest in their own right and are likely to have applications beyond the present context. An illustration is given by reexamining the results relating to U.S. stock returns data in Campbell and Yogo (2006 Campbell, J. Y. and Yogo, M. (2006), “Efficient Tests of Stock Return Predictability,” Journal of Financial Economics, 81, 27–60.[Crossref], [Web of Science ®] , [Google Scholar]). Supplementary materials for this article are available online.