Papers by Stelios Arvanitis
Social Science Research Network, 2018
We investigate the degree to which cryptocurrencies provide diversification benefits to an invest... more We investigate the degree to which cryptocurrencies provide diversification benefits to an investor. We use a stochastic spanning methodology to construct optimal portfolios with and without cryptocurrencies, evaluating their comparative performance both in-and out-of-sample. Empirical analysis seems to indicate that the expanded investment universe with cryptocurrencies dominates the traditional one with stocks, bonds and cash, yielding potential diversification benefits and providing better investment opportunities for some risk averse investors. We further explain our results by documenting that cryptocurrency markets are segmented from the equity and bond markets.
Social Science Research Network, 2022
Social Science Research Network, 2024
Statistics & Probability Letters, Jul 1, 2017
We are occupied with the limit theory of the OLSE and of a subsequent Dickey-Fuller test when the... more We are occupied with the limit theory of the OLSE and of a subsequent Dickey-Fuller test when the unit root process has heavy tailed and dependent innovations that do not possess moments of order α for some α ∈ (0, 2]. The innovation process has the form of a ''martingale-type'' transform constructed as a pointwise product between an iid sequence in the domain of attraction of an α stable distribution with a non existing α moment, for some α ∈ (0, 2], and a positive scaling mixing sequence that has a slowly varying at infinity truncated α moment. We derive a functional limit theorem with complex rates and limits that depend on Levy α-stable processes. The OLSE remains superconsistent with rate n, and the limiting distribution is a functional of the previous process. When α = 2 we recover the standard Dickey-Fuller distribution.
Communications in Statistics, Sep 8, 2017
ABSTRACT We are occupied with an example concerning the limit theory of the ordinary least square... more ABSTRACT We are occupied with an example concerning the limit theory of the ordinary least squares estimator (OLSE) when the innovation process of the regression has the form of a martingale transform the iid part of which lies in the domain of attraction of an α-stable distribution, the scaling sequence has a potentially diverging truncated α-moment, and the regressor process has a potentially divergent truncated second moment. We obtain matrix rates that reflect the stability parameter as well as the slow variations present in the aforementioned sequences, and stable limits. We also derive asymptotic exactness, consistency, and local asymptotic unbiasedness under appropriate local alternatives for a heteroskedasticity robust Wald test based on subsampling. The results could be useful for inference on the factor loadings in an instance of the APT model.
European Journal of Operational Research, Nov 1, 2021
Abstract We investigate whether cryptocurrencies provide diversification benefits to risk averter... more Abstract We investigate whether cryptocurrencies provide diversification benefits to risk averters via a stochastic spanning methodology. We avoid the conceptual and statistical problems of non-stationary returns by providing a modification of the second order stochastic dominance relation and of the related notion of stochastic spanning. These are compatible with a mildly explosive framework for the logarithm prices, along with conditions for asymptotic negligibility of bubbles. In the empirical application, we construct optimal portfolios, both with and without cryptocurrencies, and evaluate their comparative performance both in- and out-of-sample. A conservative modification of a t-test is presented to test the null hypothesis of non-dominance of an optimal portfolio that includes cryptocurrencies over the traditional portfolio of only stocks, bonds and cash. The augmented portfolio is found to be a good diversification option for some risk averse investors in the full sample period and in a sub-period of high cryptocurrency returns.
International Journal of Forecasting, Jul 1, 2019
A methodology is developed for constructing robust forecast combinations which improve upon a giv... more A methodology is developed for constructing robust forecast combinations which improve upon a given benchmark specication for all symmetric and convex loss functions. The optimal forecast combination asymptotically almost surely dominates the benchmark and, in addition, minimizes the expected loss function, under standard regularity conditions. The optimum in a given sample can be found by solving a large Convex Optimization problem. An application to forecasting of changes of the S&P 500 Volatility Index shows that robust optimized combinations improve signicantly upon the out-of-sample forecasting accuracy of simple averaging and unrestricted optimization.
Social Science Research Network, 2017
We derive a limit theorem for appropriately centered and scaled martingale transforms ∑ =1 to mix... more We derive a limit theorem for appropriately centered and scaled martingale transforms ∑ =1 to mixed-stable limits when () is an iid sequence in the domain of attraction of an-stable distribution where ∈ (0, 2]. Using the Principle of Conditioning we recover and extend known results in the literature while imposing weaker conditions. The results are particularly useful in determining the limit theory of the Gaussian QMLE in conditionally heteroskedastic models when the squared innovations are heavy-tailed. We provide the framework for the QMLE limit theory which in the ergodic case is based on the stochastic recurrence approach used in the relevant literature and we furthermore allow for the parameter vector to lie on the boundary of the parameter space. Then we show that the QMLE weakly converges to an-stable distribution when ∈ [1, 2] and is inconsistent when < 1. We relax the assumption on ergodicity and provide analogous results for the QMLE in the non-stationary GARCH(1,1) case. We investigate the limit theory of the usual Wald statistic and provide with the asymptotic exactness and consistency of the relevant testing procedure based on subsampling. In the context of the stationary GARCH(1,1) we construct a testing procedure for weak stationarity and derive its asymptotic properties and numerically evaluate its performance.
Social Science Research Network, 2019
This supplementary Technical Appendix contains formal proofs of the propositions which are stated... more This supplementary Technical Appendix contains formal proofs of the propositions which are stated in Anyfantaki, S., S. Arvanitis, S., Th. Post, Th. and N. Topaloglou, 2019, 'Stochastic Bounds for Portfolio Analysis', available at SSRN:https://ssrn.com/abstract=3181869 or http://dx.doi.org/10.2139/ssrn.3181869, together with additional results and references.
Communications in Statistics, Apr 1, 2015
We examine the asymptotic properties of the QMLE for the GQARCH (1,1) model. Under suitable condi... more We examine the asymptotic properties of the QMLE for the GQARCH (1,1) model. Under suitable conditions, we establish that the asymptotic distribution of for θ0 the true parameter, is the one of the unique minimizer of a quadratic form over a closed and convex subset of . This form is the squared distance (w.r.t. a p.d. matrix) to a random vector that follows a normal distribution when a = 2 or is a linear transformation of an a-stable random vector when a ∈ (1, 2). This implies that we have distributional convergence to this random vector when θ0 is an interior point. Hence, we describe cases in which non normal limit distributions are obtained either due to convergence of the estimator on the boundary of the parameter space, and/or due to the non existence of high order moments for random elements involved in this framework. Possible extensions concern the establishment of analogous results for indirect estimators based on the QMLE which could have desirable first order asymptotic properties.
Management Science, Dec 1, 2021
A stochastic bound is a portfolio that stochastically dominates all alternatives in a reference p... more A stochastic bound is a portfolio that stochastically dominates all alternatives in a reference portfolio set instead of a single alternative portfolio. An approximate bound is a portfolio that comes as close as possible to this ideal. To identify and analyze exact or approximate bounds, feasible approaches to numerical optimization and statistical inference are developed based on linear programming and subsampling. The use of reference sets and stochastic bounds is shown to improve investment performance in representative applications to enhanced benchmarking using equity industry rotation and equity index options combinations. This paper was accepted by Kay Giesecke, finance.
Journal of The Korean Statistical Society, Feb 24, 2023
We derive non-asymptotic concentration inequalities for the uniform deviation between a multivari... more We derive non-asymptotic concentration inequalities for the uniform deviation between a multivariate density function and its non-parametric kernel density estimator in stationary and uniform mixing time series framework. We derive analogous inequalities for their (first) Wasserstein distance, as well as for the deviations between integrals of bounded functions w.r.t. them. They can be used for the construction of confidence regions, the estimation of the finite sample probabilities of decision errors, etc. We employ the concentration results to the derivation of statistical guarantees and oracle inequalities in regularized prediction problems with Lipschitz and strongly convex costs.
Social Science Research Network, 2022
Social Science Research Network, 2017
We derive the limit theory of the Gaussian QMLE in a non-stationary Asymmetric GARCH(1,1) model w... more We derive the limit theory of the Gaussian QMLE in a non-stationary Asymmetric GARCH(1,1) model when the squared innovation process lies in the domain of attraction of a stable law. When the stability parameter lies in (1, 2], we find regularly varying rates and stable limits for the QMLE of the asymmetry and GARCH parameters. When it is less than one we derive total inconsistency.
Social Science Research Network, 2018
Abstract A nonparametric method for comparing multiple forecast models is developed and implement... more Abstract A nonparametric method for comparing multiple forecast models is developed and implemented. The hypothesis of Optimal Predictive Ability generalizes the Superior Predictive Ability hypothesis from a single given loss function to an entire class of loss functions. Distinction is drawn between General Loss functions, Convex Loss functions and Symmetric Convex Loss functions. The research hypothesis is formulated in terms of moment inequality conditions. The empirical moment conditions are reduced to an exact and finite system of linear inequalities based on piecewise-linear loss functions. The hypothesis can be tested in a statistically consistent way using a blockwise Empirical Likelihood Ratio test statistic. A computationally feasible test procedure computes the test statistic using Convex Optimization methods, and estimates conservative, data-dependent critical values using a majorizing chi-square limit distribution and a moment selection method. An empirical application to inflation forecasting reveals that a very large majority of thousands of forecast models are redundant, leaving predominantly Phillips Curve type models, when convexity and symmetry are assumed.
Social Science Research Network, 2018
Concepts and methods are introduced for analyzing whether a given possibility set contains some p... more Concepts and methods are introduced for analyzing whether a given possibility set contains some portfolio which dominates all portfolios in another set for all risk-averse investors. A Kolmogorov-Smirnov type measure for violations of`stochastic bounding' is introduced. The statistical limit theory is developed for the empirical counterpart together with a critical value estimation method based on subsampling and a computational strategy based on Linear Programming. The application section considers various applications of the proposed concepts and methodology in asset pricing and portfolio analysis.
Social Science Research Network, 2017
We develop and apply a portfolio optimization framework based on the Stochastic Dominance (SD) de... more We develop and apply a portfolio optimization framework based on the Stochastic Dominance (SD) decision criterion and the Empirical Likelihood (EL) estimation method. SD and EL share a distribution-free assumption structure that allows for dynamic and non-Gaussian return distributions. The combination of SD and EL can be implemented with standard convex optimization and Linear Programming methods. We apply the SD/EL framework to a range of equity industry momentum strategies. Our moment conditions are based on stylized facts about common risk factors in the stock market. SD/EL yields important ex-ante performance improvements relative to heuristic diversification and optimization based on the Mean-Variance criterion and/or plug-in estimates. Relative to the CRSP all-share index, SD/EL improves average out-of-sample return by more than eight percentage points per annum, with less downside risk, semi-annual rebalancing and no short sales.
Management Science
Concepts are introduced and applied for analyzing and selecting arbitrage portfolios in the face ... more Concepts are introduced and applied for analyzing and selecting arbitrage portfolios in the face of uncertainty about initial positions and risk preferences. A stochastic arbitrage opportunity is defined as a zero-cost investment portfolio that enhances every feasible host portfolio for all admissible utility functions. The alternative to the existence of such investment opportunities is the existence of a solution to a dual system of asset pricing restrictions based on a class of stochastic discount factors. Feasible approaches to numerical optimization and statistical inference are discussed. Empirical results suggest that equity factor investing is appealing for all risk-averse stock investors with a wide range of initial position and sufficiently low transactions costs by mixing multiple factor portfolios with high after-cost appraisal ratios, low mutual correlation, and negative exposures to the relevant host portfolios. These findings weaken the case for risk-based explanation...
Journal of the Korean Statistical Society
We derive non-asymptotic concentration inequalities for the uniform deviation between a multivari... more We derive non-asymptotic concentration inequalities for the uniform deviation between a multivariate density function and its non-parametric kernel density estimator in stationary and uniform mixing time series framework. We derive analogous inequalities for their (first) Wasserstein distance, as well as for the deviations between integrals of bounded functions w.r.t. them. They can be used for the construction of confidence regions, the estimation of the finite sample probabilities of decision errors, etc. We employ the concentration results to the derivation of statistical guarantees and oracle inequalities in regularized prediction problems with Lipschitz and strongly convex costs.
Journal of Econometrics, 2018
We develop and apply a portfolio optimization framework based on the Stochastic Dominance (SD) de... more We develop and apply a portfolio optimization framework based on the Stochastic Dominance (SD) decision criterion and the Empirical Likelihood (EL) estimation method. SD and EL share a distribution-free assumption structure that allows for dynamic and non-Gaussian return distributions. The combination of SD and EL can be implemented with standard convex optimization and Linear Programming methods. We apply the SD/EL framework to a range of equity industry momentum strategies. Our moment conditions are based on stylized facts about common risk factors in the stock market. SD/EL yields important ex-ante performance improvements relative to heuristic diversification and optimization based on the Mean-Variance criterion and/or plug-in estimates. Relative to the CRSP all-share index, SD/EL improves average out-of-sample return by more than eight percentage points per annum, with less downside risk, semi-annual rebalancing and no short sales.
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Papers by Stelios Arvanitis