The F test for comparing two normal variances: correct and incorrect calculation of the two-sided p-value?

This article illustrates that not all statistical software packages are correctly calculating a p-value for the classical F test comparison of two independent Normal variances. This is illustrated with a simple example, and the reasons why are discussed. Eight different software packages are considered.

Small time two-sided LIL behavior for Lévy processes at zero

We wish to characterize when a Lévy process X t crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of sup t→0|X t |/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that sup t→0 |X t |/b(t) = 1.

On the principal eigenvalue of a Robin problem with a large parameter

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.

Application of the direct Liapunov method to the problem of symmetric stability in the atmosphere

The problem of symmetric stability is examined within the context of the direct Liapunov method. The sufficient conditions for stability derived by Fjørtoft are shown to imply finite-amplitude, normed stability. This finite-amplitude stability theorem is then used to obtain rigorous upper bounds on the saturation amplitude of disturbances to symmetrically unstable flows.By employing a virial functional, the necessary conditions for instability implied by the stability theorem are shown to be in fact sufficient for instability. The results of Ooyama are improved upon insofar as a tight two-sided (upper and lower) estimate is obtained of the growth rate of (modal or nonmodal) symmetric instabilities.The case of moist adiabatic systems is also considered.

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

A review of growth for construction service companies in global markets

Throughout the developed world, professional services play an increasingly important part in an economy, with many countries showing a substantial positive trade balance for services. Yet, there has been relatively little research on construction services (CS) and, in particular, how well professional service companies (PSFs) perform in the international arena. The method for collecting services export information differs to the way in which goods and products exports data are gathered because of the intangible nature of services. Organisational growth of companies aims to share risks across different regions and sectors, however, the rapidly changing business environment challenges companies with the increasing foreign ownership and changes in procurement. The complexity of today’s international construction services organisations raises two questions: how the organisations can successfully manage growth and what are their motives for international trade. The research focuses on top UK consulting engineering companies to understand their organisational strategy, their export strategy, and drivers for overseas activities. The data will feed a model of professional services exports, which can help to inform the way services export data could be collected to better reflect the industry’s performance.

Back from beyond bid-ask spread: estimating liquidity in international markets

Research on the topic of liquidity has greatly benefited from the improved availability of data. Researchers have addressed questions regarding the factors that influence bid-ask spreads and the relationship between spreads and risk, return and liquidity. Intra-day data have been used to measure the effective spread and researchers have been able to refine the concepts of liquidity to include the price impact of transactions on a trade-by-trade analysis. The growth in the creation of tax-transparent securities has greatly enhanced the visibility of securitized real estate, and has naturally led to the question of whether the increased visibility of real estate has caused market liquidity to change. Although the growth in the public market for securitized real estate has occurred in international markets, it has not been accompanied by universal publication of transaction data. Therefore this paper develops an aggregate daily data-based test for liquidity and applies the test to US data in order to check for consistency with the results of prior intra-day analysis. If the two approaches produce similar results, we can apply the same technique to markets in which less detailed data are available and offer conclusions on the liquidity of a wider set of markets.

Liquidity in commercial property markets: deconstructing the transaction process

This paper draws from a wider research programme in the UK undertaken for the Investment Property Forum examining liquidity in commercial property. One aspect of liquidity is the process by which transactions occur including both how properties are selected for sale and the time taken to transact. The paper analyses data from three organisations; a property company, a major financial institution and an asset management company, formally a major public sector pension fund. The data covers three market states and includes sales completed in 1995, 2000 and 2002 in the UK. The research interviewed key individuals within the three organisations to identify any common patterns of activity within the sale process and also identified the timing of 187 actual transactions from inception of the sale to completion. The research developed a taxonomy of the transaction process. Interviews with vendors indicated that decisions to sell were a product of a combination of portfolio, specific property and market based issues. Properties were generally not kept in a “readiness for sale” state. The average time from first decision to sell the actual property to completion had a mean time of 298 days and a median of 190 days. It is concluded that this study may underestimate the true length of the time to transact for two reasons. Firstly, the pre-marketing period is rarely recorded in transaction files. Secondly, and more fundamentally, studies of sold properties may contain selection bias. The research indicated that vendors tended to sell properties which it was perceived could be sold at a ‘fair’ price in a reasonable period of time.

Can we explain the dynamics of the UK FTSE 100 stock and stock index futures markets?

If stock and stock index futures markets are functioning properly price movements in these markets should best be described by a first order vector error correction model with the error correction term being the price differential between the two markets (the basis). Recent evidence suggests that there are more dynamics present than should be in effectively functioning markets. Using self-exciting threshold autoregressive (SETAR) models, this study analyses whether such dynamics can be related to different regimes within which the basis can fluctuate in a predictable manner without triggering arbitrage. These findings reveal that the basis shows strong evidence of autoregressive behaviour when its value is between the two thresholds but that the extra dynamics disappear once the basis moves above the upper threshold and their persistence is reduced, although not eradicated, once the basis moves below the lower threshold. This suggests that once nonlinearity associated with transactions costs is accounted for, stock and stock index futures markets function more effectively than is suggested by linear models of the pricing relationship.

The dynamics of asset prices and transaction activity in illiquid markets: the case of private commercial real estate

This paper investigates the relationship between capital flows, turnover and returns for the UK private real estate market. We examine a number of possible implication of capital flows and turnover on capital returns testing for evidence of a price pressure effect, ‘return chasing’ behaviour and information revelation. The main tool of analysis is a panel vector autoregressive (VAR) regression model in which institutional capital flows, turnover and returns are specified as endogenous variables in a two equation system in which we also control for macro-economic variables. Data on flows, turnover and returns are obtained for the 10 market segments covering the main UK commercial real estate sectors. Our results do not support the widely-held belief among practitioners that capital flows have a ‘price pressure’ effect. Although there is some evidence of return chasing behaviour, the short timescales involved suggest this finding may be due to delayed recording of flows relative to returns given the difficulties of market entry. We find a significant positive relationship between lagged turnover and contemporaneous capital returns, suggesting that asset turnover provides pricing information.

Buyer–seller interaction in experimental spatial markets

We report results from experimental spatial markets with endogenous buyer location on a discrete version of Hotelling's linear city. Buyer locations favor more often the hypothesis of transportation cost minimization than that of strategic location aimed at increasing price competition between sellers. However, the latter of the two hypotheses receives systematic support too. Differentiation by seller-subjects is substantially less than the theory would predict for the specific framework used. Our results suggest that location strategies adopted by subjects can be seen as a rational process favoring conservative product design and spatial agglomeration of economic activities.

Endogenous retailer preferences in intermediate good markets

We model strategic interaction in a differentiated input market as a game among two suppliers and n retailers. Each one of the upstream firms chooses the specification of the input which it will offer.Then, retailers choose their type from a continuum of possibilities. The decisions made in these two first stages affect the degree of compatibility between each retailer's ideal input specification and that of the inputs offered by the two upstream firms. In a third stage, upstream firms compete setting input prices. Equilibrium may be of the two-vendor policy or of the technological monopoly type.

The level of compliance with the International Code of marketing of breast-milk substitutes: does it matter to stock markets?

The present paper explores, theoretically, and empirically, whether compliance with the International Code of marketing of breast-milk substitutes impacts on financial performance measured by stock markets. The empirical analysis, which considers a 20-year period, shows that stock markets are indifferent to the level of compliance by manufacturers with the International Code. Two important issues emerge from this result. Based on our finding that financial performance as measured by stock markets cannot explain the level of compliance, the first issue refers to what alternative types of mechanisms drive manufacturers who comply the least with voluntary codes such as the International Code. Conversely, from our finding that stock markets do not reward the most compliant, the second issue raised is an inherent weakness of stock markets to fully incorporate social and environmental values.

On the evolution of monopoly pricing in Internet-assisted search markets

This study examines the evolution of prices in markets with Internet price-comparison search engines. The empirical study analyzes laboratory data of prices available to informed consumers, for two industry sizes and two conditions on the sample (complete and incomplete). Distributions are typically bimodal. One of the two modes of distribution, corresponding to monopoly pricing, tends to attract such pricing strategies increasingly over time. The second one, corresponding to interior pricing, follows a decreasing trend. Monopoly pricing can serve as a means of insurance against more competitive (but riskier) behavior. In fact, experimental subjects who initially earn low profits due to interior pricing are more likely to switch to monopoly pricing than subjects who experience good returns from the start.