Fat Tails Research Articles

CircARID1A Inhibits Tail Fat Cell Differentiation in Guangling Large-Tailed Sheep by Regulating the miR-493-3p/YTHDF2 Axis.

The Guangling Large-Tailed sheep is renowned for its unique tail fat deposition, with a significant proportion of its total body fat being localized in the tail region. Fat deposition is a complex biological process regulated by various molecular mechanisms. Our previous studies have identified a large number of differentially expressed circular RNAs (circRNAs) in the tail adipose tissue of the Guangling Large-Tailed sheep. These circRNAs may play a pivotal role in the process of fat deposition. Given the potential regulatory functions of circRNAs in adipose metabolism, investigating their roles in tail fat deposition is of significant scientific importance. In this study, we identified novel circARID1A. Using various experimental methods, including lentivirus infection, RNase R treatment, actinomycin D assay, qPCR, western blotting, and dual-luciferase reporter assays, we determined that circARID1A inhibits the expression of miR-493-3p through competitive binding, thereby regulating adipocyte differentiation. Further research revealed that miR-493-3p promotes adipocyte differentiation by targeting YTH domain family 2 (YTHDF2), and this regulatory effect is also influenced by circARID1A. In conclusion, our findings suggest that circARID1A inhibits tail fat cell differentiation in the Guangling Large-Tailed sheep through the circARID1A/miR-493-3p/YTHDF2 axis, providing theoretical support for improving meat quality and fat deposition in sheep.

Strong error bounds for Trotter and strang-splittings and their implications for quantum chemistry

Efficient error estimates for the Trotter product formula are central in quantum computing, mathematical physics, and numerical simulations. However, the Trotter error's dependency on the input state and its application to unbounded operators remains unclear. Here, we present a general theory for error estimation, including higher-order product formulas, with explicit input state dependency. Our approach overcomes two limitations of the existing operator-norm estimates in the literature. First, previous bounds are too pessimistic as they quantify the worst-case scenario. Second, previous bounds become trivial for unbounded operators and cannot be applied to a wide class of Trotter scenarios, including atomic and molecular Hamiltonians. Our method enables analytical treatment of Trotter errors in chemistry simulations, illustrated through a case study on the hydrogen atom. Our findings reveal the following: (i) for states with fat-tailed energy distribution, such as low-angular-momentum states of the hydrogen atom, the Trotter error scales worse than expected (sublinearly) in the number of Trotter steps; (ii) certain states do not admit an advantage in the scaling from higher-order Trotterization and, thus, the higher-order Trotter hierarchy breaks down for these states, including the hydrogen atom's ground state; (iii) the scaling of higher-order Trotter bounds might depend on the order of the Hamiltonians in the Trotter product for states with fat-tailed energy distribution. Physically, the enlarged Trotter error is caused by the atom's ionization due to the Trotter dynamics. Mathematically, we find that certain domain conditions are not satisfied by some states so higher moments of the potential and kinetic energies diverge. Our analytical error analysis agrees with numerical simulations, indicating that we can estimate the state-dependent Trotter error scaling genuinely. Published by the American Physical Society 2024

Relationships between growth characteristics and GDF9 gene polymorphisms in Awassi sheep

ABSTRACT The Awassi sheep, a breed with a distinctive fat tail, is bred specifically in the south-eastern region in Turkey. It has proven its adaptability to the hot environment of this region, especially in the provinces of Şanlıurfa, Hatay and Gaziantep, which are close to the Syrian border. The aim of this study was to investigate the SNP polymorphisms in the GDF9 gene/exon2 using DNA sequencing. In addition, the study investigated the relationships between SNP genotypes and growth traits, in particular birth weight (BW), weaning weight (WW) and weight at the end of the grazing season (GSW), in Awassi sheep. Four different flocks with a total of 131 Awassi lambs were used. PCR was used to amplify exon2 of the GDF9 gene region, which has a length of 815 base pairs (bp), from the genomic DNA of the Awassi sheep. Thus, four new single nucleotide polymorphisms (SNPs) were identified. The results showed that although the effects of SNP2 and SNP4 on body weight (BW) were statistically significant, only SNP4 had a significant effect on weaning weight (WW) (P < 0.05). In addition, SNP1 and SNP3 were found to have no significant effect on any developmental trait in the dataset.

The Interaction of Microalgae Dietary Inclusion and Forage-to-Concentrate Ratio on the Lipid Metabolism-Related Gene Expression in Subcutaneous Adipose Tissue of Dairy Goats.

Long-chain polyunsaturated fatty acids (PUFAs) such as docosahexaenoic acid (DHA) have been shown to be effective in enhancing the quality of ruminant products, including meat and milk. However, under these dietary conditions, the de novo lipogenesis could be influenced, too. On the other hand, even if the forage-to-concentrate ratio (F:C) is also a key factor affecting lipid metabolism in small ruminants, there is scarce information about its interaction with dietary PUFA. This study investigates the potential of the F:C ratio as a lever to manipulate lipid metabolism in dairy goats under high dietary PUFA supplementation. For this purpose, twenty-two crossbred dairy goats [Alpine × Local (Greek) breeds] (BW = 50.6 ± 6.1 kg) at early lactation (70 ± 10 days in milk) during the age of 3-4 years old, were separated into two homogeneous subgroups (n = 11). In the first phase, each goat was fed 20 g Schizochytrium spp./day followed by either a high-forage (20 HF) or a high-grain (20 HG) diet, while in the second phase, each goat was fed 40 g Schizochytrium spp./day followed once again either a high-forage (40 HF) or a high-grain (40 HG) diet. The F:C ratio of a high-forage and high-grain diet was 60:40 and 40:60, respectively. Tail fat tissue samples were collected by biopsy on the 42nd day of each experimental phase (last day). Significant decreases (p < 0.05) in the gene expression of ACACA, CBR2, COX4I1, ELOVL5, ELOVL7, LEP, and SCD were presented in goats fed 40 g compared to those fed 20 g Schizochytrium spp., while the gene expression of ACACA, AGPAT2, AGPAT3, ELOVL5, ELOVL6, EPHX2, FASN, and SCD was decreased in high grain compared to high-forage diets. This study also indicated that with the aim to enrich goat products with PUFA by increasing their levels in the diet, lipid metabolism is negatively affected. However, a diet with higher forage inclusion can partially attenuate this condition.

Abstract B012: HNRNPL-mediated mRNA stability underlies metastasis triggered by resistance to radiation therapy

Abstract The high rate of locoregional/distant recurrence in triple-negative breast cancer (TNBC) is a major driver of the decreased survival observed in breast cancer patients. Radiation therapy is a reliable treatment modality to limit recurrence for many cancers, but TNBC patients have a higher chance for relapse despite receiving increased doses of radiation compared to patients with other breast cancer subtypes. This study investigated the differential pathways in radioresistant TNBC tumors that impact recurrence. We developed two radioresistant cell line models (468-RR and 4T1-RR) by administering a radiation dose of 50Gy over the course of 8 weeks to the human TNBC cell line, MDA-MB-468, and the mouse TNBC cell line, 4T1, respectively. Migration and invasion were assessed using the scratch-wound assay and transwell assay, respectively. We assessed in vivo metastasis by injecting the cells in the mammary fat pad, tail vein, or left ventricle. RNA-sequencing of the cell lines was done to identify global transcriptomic changes and regulatory pathways induced by radiation therapy. The mRNA stability of integrin b3 was assessed by inhibiting transcription using actinomycin D. Moreover, we implemented the newly developed InduroRT-mediated circRNA-sequencing (IMRT-seq) to identify the circular RNAs processed by HNRNPL that are present in radioresistant cells. We observed enhanced lung and bone metastasis, based on bioluminescent imaging, in both the spontaneous and vascular metastasis models for the radioresistant cells compared to the parental cells. Genset enrichment analysis identified mRNA stability and metabolism as upregulated pathways in radioresistant cells with HNRNPL, a ribonucleoprotein involved in mRNA stability, as one of the top genes. By knocking down HNRNPL, we observed decreased migration capacity of the radioresistant cells. Given the role of HNRNPL in integrin and extracellular matrix genes, which are key components associated with metastasis in cancer cells, we screened for these genes in our RNA-seq dataset and identified integrin b3 as a possible target. More specifically, knocking down HNRNPL decreased the mRNA stability of integrin b3 as assessed by actinomycin d treatment. By expressing integrin b3 in the HNRNPL-depleted cells, we were able to rescue the migration capacity of these cells. We believe a subset of HNRNPL-mediated circular RNAs are responsible for integrin b3 mRNA stability by sequestering miRNAs that target integrin b3. With IMRT-seq we are exploring the potential circRNA-miRNA interactions present in radioresistant TNBC responsible for its metastatic phenotype. The radioresistant cells derived from TNBC cell lines have an enhanced metastatic potential than the treatment-naive cell lines and our data suggest that RNA metabolism is pivotal to this phenotype. The upregulation of HNRNPL upon radiation by Nrf2 increases integrin b3 expression by stabilizing its transcripts and preventing its degradation. This novel mechanism of radioresistant metastasis provides a therapeutic approach to minimize TNBC recurrence. Citation Format: Ayush Kumar, Kensei Kishimoto, Christi Wisniewski, Shivam Goel, Arthur Mercurio. HNRNPL-mediated mRNA stability underlies metastasis triggered by resistance to radiation therapy [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: RNAs as Drivers, Targets, and Therapeutics in Cancer; 2024 Nov 14-17; Bellevue, Washington. Philadelphia (PA): AACR; Mol Cancer Ther 2024;23(11_Suppl):Abstract nr B012.

To Bequeath, or Not to Bequeath? On Labour Income Risk and Top Wealth Concentration

Abstract Recent theoretical advances suggest that capital income risk, rather than earnings uncertainty, is the key determinant of fat-tailed behavior of stationary wealth distributions. I provide novel insights into this issue by studying an incomplete market model with general time and state separable preferences, where parental altruism and unobservable idiosyncratic shocks engender non-linear bequest rules. I analytically pin down conditions on the preference structure and other model’s primitives under which optimal bequest behavior hinders intergenerational wealth transmission for any degree of capital income risk, causing the dynamics of wealth to converge to a unique (stationary) distribution with thin tails. These results imply, in particular, that (i) the stochastic properties of labour income risk (as shaped by, e.g. fiscal policies) may play a role in defining the structure of the upper tail of the limiting distribution of wealth, and that (ii) matching empirically documented fat tails with choice theoretic frameworks of wealth dynamics requires joint restrictions on preferences and calibrated earnings processes to be met.

Foundational Aspects for Incorporating Dependencies in Copula-Based Bayesian Networks Using Structured Expert Judgments, Exemplified by the Ice Sheet-Sea Level Rise Elicitation.

The work presented here marks a further advance in expert uncertainty quantification. In a recent probabilistic evaluation of ice sheet process contributions to sea level rise, tail dependence was elicited and propagated through an uncertainty analysis for the first time. The elicited correlations and tail dependencies concerned pairings of three processes: Accumulation, Discharge and Run-off, which operate on major ice sheets in the West and East Antarctic and in Greenland. The elicitation enumerated dependencies between these processes under selected global temperature change scenarios over different future time horizons. These expert judgments allowed us to populate a Paired Copula Bayesian network model to obtain the estimated contributions of these ice sheets for future sea level rise. Including positive central tendency dependence and tail dependence increases the fatness of the upper tails of projected sea level rise distributions, an amplification important for designing and evaluating possible mitigation strategies. Detailing and jointly computing distributional dependencies and tail dependencies can be crucial components of good practice for assessing the influence of uncertainties on extreme values when modelling stochastic multifactorial processes.

Asian Rainbow Option Pricing Problem Based on Uncertain Fractional Differential Equations

Option pricing is a core issue in option trading, which directly affects investors’ trading decisions and risk management. With the growing maturity of uncertainty theory, the research on option pricing problems based upon uncertainty theory has been gradually deepened. However, the volatility of stock price is not only related to the price at the current moment, but also related to all the previous stock price changes. Uncertain fractional differential equations can well portray the memory and history dependence of financial markets. Its nonlocal nature can more accurately describe the long-term memory effect and the phenomenon of spiky fat tails of stock market fluctuations. Thus, this paper mainly explores the pricing of Asian rainbow option in uncertain financial environments, where the underlying asset price is viewed as uncertain fractional processes. First, two models are presented for discussing the price of Asian rainbow option in two-asset cases, respectively. Then the pricing problems of different types of Asian rainbow options under [Formula: see text]-assets case are further discussed. Finally, empirical analysis is conducted on the proposed models with real stock data to verify the validity of the pricing formulas.

Lipidomics analysis of adipose depots at differently aged Sunit sheep

The objective of this study was to optimize the utilization of deposited fat in Sunit sheep, with a focus on dietary nutrition. This study also elucidated variations in lipid metabolism among subcutaneous fat (SF), perirenal fat (PF), and tail fat (TF) in sheep of different ages using non-targeted lipidomic techniques. In total, 173 different lipids were identified, of which triacylglycerol (TG) and phosphatidylcholine (PC) were prominent. The relative intensity of TG was highest at 6 months of age in three adipose depots. Glycerophospholipids (PLs) were expressed at peak levels in TF and SF at 18 months of age. Pathway analysis revealed that biosynthesis of unsaturated fatty acids, linoleic acid metabolism, glycerophospholipid metabolism, and fatty acid biosynthesis were the main pathways involved in the metabolism of adipose depots. These findings provide a comprehensive reference for the metabolic characteristics and pathways of adipose tissue in sheep and the utilization of its by-products.

Modeling the distribution of jet fuel price returns based on fat-tail stable Paretian distribution.

Jet fuel plays a crucial role as an essential energy source in aerospace and aviation operations. The recent increase in fuel prices has presented airlines with the new challenge of managing jet fuel costs to ensure consistent cash flow and minimize operational uncertainties. The conventional risk prediction models used by airlines often assume that risks are normally distributed according to the classical Central Limit Theorem, which can lead to under-hedging. This paper proposes an innovative approach using the stable Paretian model to analyze the price return of jet fuel in large samples. It comprehensively compares the fitting effect of the stable Paretian distribution with that of the normal distribution based on specific criteria and non-parametric significance tests. Furthermore, it investigates the accuracy of risk measures such as Value at Risk (VaR) and Conditional Value at Risk (CVaR) predicted by both models. In addition to comparing differences in VaR between predicted values and actual values, this paper provides a more comprehensive comparison of risk measures under rolling window forecast situation. Results suggest that despite indistinguishable results in VaR backtest, the stable Paretian distribution has a overall better fitting effect as well as a less biased predicted CVaR based on the AIC of -14099.46, BIC of -14110.98, p = 0.58 in Kolmogorov-Smirnov test and p = 0.46(0.92) in the 0.01(0.05) significance level of Expected Shortfall Regression Test. This might be explained by its ability to capture asset return dynamics while maintaining shape stability with few parameters. This research can provide valuable insights for guiding airlines' risk management decisions. its ability to capture asset return dynamics while maintaining shape stability with few parameters. This research can provide valuable insights for guiding airlines' risk management decisions.

Escape from a metastable state in non-Markovian population dynamics.

We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modeled as a stochastic process with a fat-tailed nonexponential distribution of waiting times, mimicking long-term memory. We focus on three prototypical examples: genetic switching, population establishment, and population extinction, all with nonexponential production rates. The system is studied in two regimes. In the first, the distribution of waiting times has a finite mean. Here, the system approaches a (quasi)stationary steady state at long times, and we develop a general Wentzel-Kramers-Brillouin approach for these non-Markovian systems. We derive explicit results for the mean population size and mean escape time from the metastable state of the stochastic dynamics. In this realm, we reveal that for sufficiently strong memory, a memory-induced (meta)stable state can emerge in the system. In the second regime, the waiting time distribution is assumed to have an infinite mean. Here, for bistable systems we find two distinct scaling regimes, separated by an exponentially long time which may strongly depend on the initial conditions of the system.

Ethereum futures and the efficiency of cryptocurrency spot markets

This paper examines the impact of the introduction of Ethereum futures contracts on the market efficiency of major cryptocurrency (Bitcoin, Ethereum, Ripple, Litecoin, and Dogecoin) spot prices. Using a multifractality-based approach and daily data from September 4, 2017 to February 16, 2024, the main results show a slight improvement in market efficiency. Specifically, the degree of multifractality persistence decreases, implying reduced market inefficiencies in major cryptocurrencies. The temporal linear correlation effect and thick tail effect are less pronounced post-launch. The asymmetry of the generalized Hurst exponent increases after the launch of Ethereum futures, with a higher persistence under the downward trend of cryptocurrencies noted. This downward trend emerges after the launch of Ethereum futures, coinciding with the final stage of the COVID-19 pandemic. Additional analysis shows that fat tails and temporal linear correlations are the main sources of multifractality. The results highlight the influence of introducing financial derivatives into the relatively new and volatile cryptocurrency area, which should concern traders, hedgers, investors, and regulators.

The Conditional Autoregressive F-Riesz Model for Realized Covariance Matrices

Abstract We introduce a new model for the dynamics of fat-tailed (realized) covariance-matrix-valued time-series using the F-Riesz distribution. The model allows for heterogeneous tail behavior across the coordinates of the covariance matrix via two vector-valued degrees of freedom parameters, thus generalizing the familiar Wishart and matrix-F distributions. We show that the filter implied by the new model is invertible and that a two-step targeted maximum likelihood estimator is consistent. Applying the new F-Riesz model to U.S. stocks, both tail heterogeneity and tail fatness turn out to be empirically relevant: they produce significant in-sample and out-of-sample likelihood increases, ex-post portfolio standard deviations that are in the global minimum variance model confidence set, and economic differences that are either in favor of the new model or competitive with a range of benchmark models.

Asymptotic limits of transient patterns in a continuous-space interacting particle system

We study a discrete-time interacting particle system with continuous state space, which is motivated by a mathematical model for turnover through branching in actin filament networks. It gives rise to transient clusters reminiscent of actin filament assemblies in the cortex of living cells. We reformulate the process in terms of the inter-particle distances and characterize their marginal and joint distributions. We construct a recurrence relation for the associated characteristic functions and pass to the large population limit, reminiscent of the Fleming–Viot super processes. The precise characterization of all marginal distributions established in this work opens the way to a detailed analysis of cluster dynamics. We also obtain a recurrence relation that enables us to compute the moments of the asymptotic single particle distribution characterizing the transient aggregates. Our results indicate that aggregates have a fat-tailed distribution.

Polymorphisms of PRKAA1 and FABP4 genes and their association with feed efficiency in Hu sheep

Feed efficiency (FE) is an important economic trait in the sheep industry, influenced by biological processes such as digestion and metabolism. PRKAA1 gene participates in the synthesis and oxidation of fatty acids; the FABP4 gene is closely associated with intracellular fatty acid regulation. In this study, we use Sanger sequencing, KASPar genotyping, and qRT-PCR to investigate the association between variations in PRKAA1 and FABP4 genes and feed efficiency in Hu sheep, the expression patterns of PRKAA1 and FABP4 genes in different tissues, as well as the differences in expression of different genotypes in tail fat. The association analysis results indicated that PRKAA1 gene g.35431965 C > T locus and FABP4 gene g.62829807 C > T locus were significantly associated with the feed conversion ratio (FCR) of Hu sheep aged 80–180 days, with the dominant genotypes being CC and CC, respectively. Simultaneously, there existed notable disparities among various genotype combinations. The qRT-PCR results showed PRKAA1 and FABP4 genes were widely expressed in ten tissues, of which the PRKAA1 gene was lower expression level in rumen and lung, FABP4 gene was significantly highest expression in the tail fat than the other tissues; the expression of two different genotypes in tail fat also exhibits significant differences (P ≤ 0.05). Therefore, these findings suggested that the variation of PRKAA1 and FABP4 genes might be used as novel genetic marker for improving feed efficiency in sheep.

CEREBRAL MICROVASCULATURE IN AN EXCLUSIVELY FAT DIET MODEL

The microcirculation system plays a major role in the process of food intake and assimilation by the body. It ensures the distribution of oxygen and nutrients among neurons, taking into account their functional activity. The capillaries of the villi in the choroid plexus of cerebral ventricles remain the main source of cerebrospinal fluid production, which determines most physiological functions of the body. The aim of the study is to identify the peculiarities of remodeling of the microvasculature and vascular plexus of the third cerebral ventricle in rats kept exclusively on a fat diet. Materials and Methods. The work was performed on 20 white mongrel male rats (200–250 g.), divided into control and experimental groups. Animals of the control group were on a regular diet. Rats of the experimental group were fed exclusively with fatty food (sheep tail fat). On the 15th and 30th days, the animals were withdrawn from the experiment. A study of biochemical blood parameters (cholesterol, glucose, and protein) was carried out. After decapitation, the brain was fixed in formalin, brain sections were stained with hematoxylin and eosin (Van Gieson stain). The authors conducted light microscopy and morphometry on an Olympus B×40 microscope (Japan). Results. The animals showed a significant increase in the levels of cholesterol, glucose and albumin in the blood serum under an exclusively fat diet. By the 30th day of the experiment, the smooth muscles of the cerebral arteries undergo paresis, proteolysis, vacuolar dystrophy, hypoplasia with a sharp expansion of the vessel lumen. Signs of myoelastofibrosis are observed in the adventitia. Vein walls are thinned, the lumen is dilated, intravascular thrombi are observed. In the choroid plexus of the 3rd cerebral ventricle, a deficit of plasma flow through the sinusoidal capillaries with compensatory ependymocyte hyperfunction is noted. Conclusion. An exclusively fat diet leads to remodeling of the cerebral microvasculature, including the capillaries of the villi of the choroid plexus of the 3rd ventricle. All changes are compensatory and adaptive in nature. However, by the 30th day of the experiment, some of them become irreversible.

Mergers, firm size, and volatility in a granular economy

We study the firm dynamics associated with mergers and acquisitions (M&A) and their implications at the micro and macro levels. Our paper presents three main findings: (i) mergers generate a more fat-tailed firm-size distribution, thereby amplifying granular fluctuations and increasing aggregate volatility; (ii) the impact of mergers depends on strategic market power and endogenous markups; and (iii) under endogenous markups, we provide a novel characterization of the firm size-volatility relationship in which volatility declines disproportionately with size. We build a quantitative model of domestic horizontal mergers and find a sizeable impact of mergers on aggregate volatility using counterfactual analysis.

Whole-genome sequencing identifies functional genes for environmental adaptation in Chinese sheep

Sheep (Ovis aries), among the first domesticated species, are now globally widespread and exhibit remarkable adaptability to diverse environments. In this study, we perform whole-genome sequencing of 266 animals from 18 distinct Chinese sheep populations, each displaying unique phenotypes indicative of adaptation to varying environmental conditions. Integrating 131 environmental factors with single nucleotide polymorphism variations, we conduct a comprehensive genetic-environmental association analysis. This analysis identifies 35 key genes likely integral to the environmental adaptation of sheep. The functions of these genes include fat tail formation (HOXA10, HOXA11, JAZF1), wool characteristics (FER, FGF5, MITF, PDE4B), horn phenotypes (RXFP2), reproduction (HIBADH, TRIM71, C6H4orf22), and growth traits (ADGRL3, TRHDE). Notably, we observe a significant correlation between the frequency of missense mutations in the PAPSS2 and RXFP2 genes and variations in altitude. Our study reveals candidate genes for adaptive variation in sheep and demonstrates the diversity in the ways sheep adapt to their environment.

Housing ownership constraint and spatial sorting

The paper proposes a new theoretical explanation for the spatial sorting that the skill distribution has fatter tails in big cities. The ownership of the house make people face the constraint of house’s minimum area when purchasing it, therefore, and finally induces the spatial sorting. The new theory could distinguish buying and renting houses, and identify public services attached to housing ownership and enjoyed by all people no matter who buy or rent houses. The policy implications are also different from those in previous theories: when land supply is reduced in big cities, it predicted a decrease in the number of low-skilled workers in previous theories, whereas it predicts an increase in the theory of housing ownership constraints. In big cities, public services attached to housing ownership would attract more high-skilled workers and decrease low-skilled workers, while public services enjoyed by all people would attract both of them.

Multivariate Stochastic Volatility with Co-Heteroscedasticity

Abstract A new methodology that decomposes shocks into homoscedastic and heteroscedastic components is developed. This specification implies there exist linear combinations of heteroscedastic variables that eliminate heteroscedasticity; a property known as co-heteroscedasticity. The heteroscedastic part of the model uses a multivariate stochastic volatility inverse Wishart process. The resulting model is invariant to the ordering of the variables, which is shown to be important for volatility estimation. By incorporating testable co-heteroscedasticity restrictions, the specification allows estimation in moderately high-dimensions. The computational strategy uses a novel particle filter algorithm, a reparameterization that substantially improves algorithmic convergence and an alternating-order particle Gibbs that reduces the amount of particles needed for accurate estimation. An empirical application to a large Vector Autoregression (VAR) is provided, finding strong evidence for co-heteroscedasticity and that the new method outperforms some previously proposed methods in terms of forecasting at all horizons. It is also found that the structural monetary shock is 98.8 % homoscedastic, and that investment and the SP 500 index are nearly 100 % determined by fat tail heteroscedastic shocks. A Monte Carlo experiment illustrates that the new method estimates well the characteristics of approximate factor models with heteroscedastic errors.