Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions

In this paper, we propose exact inference procedures for asset pricing models that can be formulated in the framework of a multivariate linear regression (CAPM), allowing for stable error distributions. The normality assumption on the distribution of stock returns is usually rejected in empirical studies, due to excess kurtosis and asymmetry. To model such data, we propose a comprehensive statistical approach which allows for alternative - possibly asymmetric - heavy tailed distributions without the use of large-sample approximations. The methods suggested are based on Monte Carlo test techniques. Goodness-of-fit tests are formally incorporated to ensure that the error distributions considered are empirically sustainable, from which exact confidence sets for the unknown tail area and asymmetry parameters of the stable error distribution are derived. Tests for the efficiency of the market portfolio (zero intercepts) which explicitly allow for the presence of (unknown) nuisance parameter in the stable error distribution are derived. The methods proposed are applied to monthly returns on 12 portfolios of the New York Stock Exchange over the period 1926-1995 (5 year subperiods). We find that stable possibly skewed distributions provide statistically significant improvement in goodness-of-fit and lead to fewer rejections of the efficiency hypothesis.

Geometric Stable Laws Through Series Representations

Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study the asymptotic behavior of the partial sum process SN (t) = ⅀( i=1 ... [N t] ) Xi , and derive series representations of the limiting geometric stable process and the corresponding stochastic integral. We also obtain strong invariance principles for stable and geometric stable laws.

Simulation-Based Finite-Sample Tests for Heteroskedasticity and ARCH Effects.

A wide range of tests for heteroskedasticity have been proposed in the econometric and statistics literature. Although a few exact homoskedasticity tests are available, the commonly employed procedures are quite generally based on asymptotic approximations which may not provide good size control in finite samples. There has been a number of recent studies that seek to improve the reliability of common heteroskedasticity tests using Edgeworth, Bartlett, jackknife and bootstrap methods. Yet the latter remain approximate. In this paper, we describe a solution to the problem of controlling the size of homoskedasticity tests in linear regression contexts. We study procedures based on the standard test statistics [e.g., the Goldfeld-Quandt, Glejser, Bartlett, Cochran, Hartley, Breusch-Pagan-Godfrey, White and Szroeter criteria] as well as tests for autoregressive conditional heteroskedasticity (ARCH-type models). We also suggest several extensions of the existing procedures (sup-type of combined test statistics) to allow for unknown breakpoints in the error variance. We exploit the technique of Monte Carlo tests to obtain provably exact p-values, for both the standard and the new tests suggested. We show that the MC test procedure conveniently solves the intractable null distribution problem, in particular those raised by the sup-type and combined test statistics as well as (when relevant) unidentified nuisance parameter problems under the null hypothesis. The method proposed works in exactly the same way with both Gaussian and non-Gaussian disturbance distributions [such as heavy-tailed or stable distributions]. The performance of the procedures is examined by simulation. The Monte Carlo experiments conducted focus on : (1) ARCH, GARCH, and ARCH-in-mean alternatives; (2) the case where the variance increases monotonically with : (i) one exogenous variable, and (ii) the mean of the dependent variable; (3) grouped heteroskedasticity; (4) breaks in variance at unknown points. We find that the proposed tests achieve perfect size control and have good power.

Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared to simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experi-ment. Finally, the tests are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995.

Efficient estimation using the characteristic function : theory and applications with high frequency data

The attached file is created with Scientific Workplace Latex

Self-affinity in financial asset returns

We test for departures from normal and independent and identically distributed (NIID) log returns, for log returns under the alternative hypothesis that are self-affine and either long-range dependent, or drawn randomly from an L-stable distribution with infinite higher-order moments. The finite sample performance of estimators of the two forms of self-affinity is explored in a simulation study. In contrast to rescaled range analysis and other conventional estimation methods, the variant of fluctuation analysis that considers finite sample moments only is able to identify both forms of self-affinity. When log returns are self-affine and long-range dependent under the alternative hypothesis, however, rescaled range analysis has higher power than fluctuation analysis. The techniques are illustrated by means of an analysis of the daily log returns for the indices of 11 stock markets of developed countries. Several of the smaller stock markets by capitalization exhibit evidence of long-range dependence in log returns. © 2012 Elsevier Inc. All rights reserved.

Distribution of the Bari-I transposable element in stable hybrid strains between Drosophila melanogaster and Drosophila simulans and in Brazilian populations of these species

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stable isotope record and lithic fragments distribution in sediments of MIS9-14 of the North Atlantic

Stable isotope and ice-rafted debris records from three core sites in the mid-latitude North Atlantic (IODP Site U1313, MD01-2446, MD03-2699) are combined with records of ODP Sites 1056/1058 and 980 to reconstruct hydrographic conditions during the middle Pleistocene spanning Marine Isotope Stages (MIS) 9-14 (300-540 ka). Core MD03-2699 is the first high-resolution mid-Brunhes record from the North Atlantic's eastern boundary upwelling system covering the complete MIS 11c interval and MIS 13. The array of sites reflect western and eastern basin boundary current as well as north to south transect sampling of subpolar and transitional water masses and allow the reconstruction of transport pathways in the upper limb of the North Atlantic's circulation. Hydrographic conditions in the surface and deep ocean during peak interglacial MIS 9 and 11 were similar among all the sites with relative stable conditions and confirm prolonged warmth during MIS 11c also for the mid-latitudes. Sea surface temperature (SST) reconstructions further reveal that in the mid-latitude North Atlantic MIS 11c is associated with two plateaus, the younger one of which is slightly warmer. Enhanced subsurface northward heat transport in the eastern boundary current system, especially during early MIS 11c, is denoted by the presence of tropical planktic foraminifer species and raises the question how strongly it impacted the Portuguese upwelling system. Deep water ventilation at the onset of MIS 11c significantly preceded surface water ventilation. Although MIS 13 was generally colder and more variable than the younger interglacials the surface water circulation scheme was the same. The greatest differences between the sites existed during the glacial inceptions and glacials. Then a north - south trending hydrographic front separated the nearshore and offshore waters off Portugal. While offshore waters originated from the North Atlantic Current as indicated by the similarities between the records of IODP Site U1313, ODP Site 980 and MD01-2446, nearshore waters as recorded in core MD03-2699 derived from the Azores Current and thus the subtropical gyre. Except for MIS 12, Azores Current influence seems to be related to eastern boundary system dynamics and not to changes in the Atlantic overturning circulation.

Biomarkers, stable carbon isotope record and pollen distribution of the soutwest African continental margin

This is part 2 of a study examining southwest African continental margin sediments from nine sites on a north-south transect from the Congo Fan (4°S) to the Cape Basin (30°S) representing two glacial (MIS 2 and 6a) and two interglacial stages (MIS 1 and 5e). Contents, distribution patterns, and molecular stable carbon isotope signatures of long-chain n-alkanes (C27-C33) and n-alkanols (C22-C32) as indicators of land plant vegetation of different biosynthetic types were correlated with concentrations and distributions of pollen taxa in sediments of the same time horizons. Selected single pollen type data reveal details of vegetation changes, but the overall picture is best illustrated by summing pollen known to predominantly derive from C4 plants or C4 plus CAM plants. The C4 plant signals in the biomarkers are recorded in the delta13C data and in the abundances of C31 and C33 n-alkanes, and the C32 n-alkanol. Calculated clusters of wind trajectories for austral summer and winter situations for the Holocene and the Last Glacial Maximum afford information on the source areas for the lipids and pollen and their transport pathways to the ocean. This multidisciplinary approach provides clear evidence of latitudinal differences in leaf wax lipid and pollen composition, with the Holocene sedimentary data paralleling the current major phytogeographic zonations. The northern sites (Congo Fan area and northern Angola Basin) get most of their terrestrial material from the Congo Basin and the Angolan highlands dominated by C3 plants. Airborne particulates derived from the western and central South African hinterland dominated by deserts, semideserts, and savannah regions are rich in organic matter from C4 plants. As can be expected from the present and glacial positions of the phytogeographic zones, the carbon isotopic signatures of n-alkanes and n-alkanols both become isotopically more enriched in 13C from north to south. In the northern part of the transect the relative importance of C4 plant indicators is higher during the glacials than in the interglacials, indicating a northward extension of arid zones favoring grass vegetation. In the south, where grass-rich vegetation merges into semidesert and desert, the difference in C4 plant indicators is small.

(Table 1) n-alkane distribution, and stable carbon and deuterium isotope ratios of DSDP Hole 10-94

Hydrology, source region, and timing of precipitation are important controls on the climate of the Great Plains of North America and the composition of terrestrial ecosystems. Moisture delivered to the Great Plains varies seasonally and predominately derives from the Gulf of Mexico/Atlantic Ocean with minor contributions from the Pacific Ocean and Arctic region. For this work, we evaluate long-term relationships for the past ~ 35 million years between North American hydrology, climate, and floral change, using isotopic records and average carbon chain lengths of higher plant n-alkanes from Gulf of Mexico sediments (DSDP Site 94). We find that carbon isotope values (d13C) of n-alkanes, corrected for variations in the d13C value of atmospheric CO2, provide minor evidence for contributions of C4 plants prior to the Middle Miocene. A sharp spike in C4 input is identified during the Middle Miocene Climatic Optimum, and the influence of C4 plants steadily increased during the Late Miocene into the Pleistocene - consistent with other North American records. Chain-length distributions of n-alkanes, indicative of the composition of higher plant communities, remained remarkably constant from 33 to 4 Ma. However, a trend toward longer chain lengths occurred during the past 4 million years, concurrent with an increase in d13C values, indicating increased C4 plant influence and potentially aridity. The hydrogen isotope values (dD) of n-alkanes are relatively invariant between 33 and 9 Ma, and then become substantially more negative (75 per mil) from 9 to 2 Ma. Changes in the plant community and temperature of precipitation can solely account for the observed variations in dD from 33 to 5 Ma, but cannot account for Plio-Pleistocene dD variations and imply substantial changes in the source region of precipitation and seasonality of moisture delivery. We posit that hydrological changes were linked to tectonic and oceanographic processes including the shoaling and closure of the Panamanian Seaway, amplification of North Atlantic Deep Water Production and an associated increase of meridional winds. The southerly movement of the Intertropical Convergence Zone near 4 Ma allowed for the development of a near-modern pressure/storm track system, driving increased aridity and changes in seasonality within the North American interior.

Stable isotope record and distribution of foraminifera in sediment core GeoB3004-1

Fluctuations in the abundance of selected foraminiferal indicator species and diversity allowed the reconstruction of changes in deepwater oxygenation and monsoon-driven organic matter fluxes in the deep western Arabian Sea during the last 190 kyr. Times of maximum surface production coincide with periods of intensified SW monsoon as shown by the abundance of Globigerina bulloides and enhanced carbonate corrosion. Benthic ecosystem variability in the deep Arabian Sea is not exclusively driven by variations in monsoonal upwelling and related organic matter supply to the seafloor but also by changes in deepwater ventilation. Deepening of the base of the oxygen minimum zone (OMZ) below 1800 m water depth is strongly coherent on the precessional band but lags proxies of SW monsoon strength by 4 to 6 kyr. The "out-of-phase" relationship between OMZ deepening and maximum SW monsoon strength is explained by temporal changes in the advection of oxygen-rich deepwater masses of North Atlantic and Antarctic origin. This process affected the remineralization and burial efficiency of organic matter in the deep Arabian Sea, resulting in the observed phase lag between maximum monsoon strength and organic carbon preservation.

Distribution and stable isotopic compositions of hydrogen and carbon of plant-wax derived n-C29 and -C31 alkanes in terrestrial, coastal and offshore surface sediments

Reconstructing terrestrial water budgets is of prime importance for understanding past climate and environment. To shed more light on how plant-wax derived n-alkanes may be used for this purpose we investigated the distribution and stable isotopic compositions of hydrogen (dD) and carbon (d13C) of plant-wax derived n-C29 and -C31 alkanes in terrestrial, coastal and offshore surface sediments in relation to hydrology along a NW-SE transect east of the Italian Apennines from the Po River to the Eastern Gulf of Taranto. The plant wax average chain length increases southward and may relate to increasing temperature and/or aridity. The plant wax dD of the terrestrial and coastal samples also increases southward and mainly reflects changes in the dD of precipitation. The d13C of plant waxes is primarily interpreted in terms of C3 vegetation changes rather than varying contributions by C4 plants. The plant wax d13C-dD composition of the Po River and Apennine rivers differs considerably from that in southern Italy, and suggests a mainly southern source for plant waxes in marine sediments of the Gulf of Taranto. This calibration provides a basis for the reconstruction of past changes in the Italian water balance and n-alkane source areas.

Sedimentology, planktonic foraminifera distribution and stable isotope composition during marine isotope stage 3 of ODP Site 172-1060 in the West Atlantic

We have studied Ocean Drilling Program Site 1060 on the Blake Outer Ridge, which lies beneath the Gulf Stream. We focus on marine isotope stage 3, 60-25 thousand years before present (ka). Sea surface temperatures (SSTs) inferred both from foraminiferal fauna and alkenone ratios, as well as counts of iceberg melt-out debris and benthic stable isotope analyses, enable our record to be interpreted in terms of regional hydrographic changes as well as changing thermohaline circulation (THC). The observed SST record is consistent with the air temperature record from the Greenland ice cores. However, Site 1060 exhibits important differences in detail compared with the ice core record, and when compared to other sites within the North Atlantic, significant longitudinal differences emerge. At Site 1060 in the western Atlantic, all Greenland stadials (GS) whether associated with Heinrich events (HEs) or not, show a similar small amplitude of cooling; mean faunal-based SSTaug during GS is only 1.5°C colder than during Greenland interstadials (GIS). In addition, during GS the coldest SSTs are limited to apparently brief events. This is in contrast to several eastern Atlantic sites where HE stadials exhibit coolings that are enhanced by 2°C compared to other GS and where cold conditions are not restricted to cold pulses but cover 2 ka-long intervals. Furthermore, Site 1060 SSTs remained warm right through each interstadial, in contrast to the sustained and uniform cooling trend through interstadials that is consistently observed in Greenland, indicated by measurements of delta18O in ice.