| 1. |
- Alfelt, Gustav, et al.
(författare)
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Goodness-of-fit tests for centralized Wishart processes
- 2020
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Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 49:20, s. 5060-5090
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present several goodness-of-fit tests for the centralized Wishart process, a popular matrix-variate time series model used to capture the stochastic properties of realized covariance matrices. The new test procedures are based on the extended Bartlett decomposition derived from the properties of the Wishart distribution and allows to obtain sets of independently and standard normally distributed random variables under the null hypothesis. Several tests for normality and independence are then applied to these variables in order to support or to reject the underlying assumption of a centralized Wishart process. In order to investigate the influence of estimated parameters on the suggested testing procedures in the finite-sample case, a simulation study is conducted. Finally, the new test methods are applied to real data consisting of realized covariance matrices computed for the returns on six assets traded on the New York Stock Exchange.
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| 2. |
- Alfelt, Gustav
(författare)
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Modeling Realized Covariance of Asset Returns
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, which consists of two papers, we consider the modeling of positive definitive symmetric matrices, in particular covariance matrices of financial asset returns. The return covariance matrix describes the magnitude in which prices of financial assets tend to change over time, and how price changes between different assets are related. It is an instrumental quantity in many financial applications, and furthermore, an important component in understanding the dynamics present prior to and during times of financial turbulence, such as the 2008 financial crisis.In the first paper, we provide several goodness-of-fit tests applicable to models driven by a centralized Wishart process. To apply such a distributional assumption has become a popular way of modeling the stochastic properties of time-series of realized covariance matrices for asset returns. The paper includes a simulation study that aims to investigate how the tests perform under model uncertainty stemming from parameter estimation. In addition, the presented methods are used to evaluate the fit of a typical model of realized covariance adapted to real data on six stocks traded on the New York Stock Exchange.The second paper considers positive definite and symmetric random matrices of the exponential family. Under certain conditions for this class of distributions, we derive the Stein-Haff identity. Furthermore, we determine this identity in the case of the matrix-variate gamma distribution and apply it in order to present an estimator that outperforms the maximum likelihood estimator in terms of Stein's loss function. Finally, a small simulation study is conducted to support the theoretical results.
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| 3. |
- Alfelt, Gustav, 1985-
(författare)
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Modeling the covariance matrix of financial asset returns
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The covariance matrix of asset returns, which describes the fluctuation of asset prices, plays a crucial role in understanding and predicting financial markets and economic systems. In recent years, the concept of realized covariance measures has become a popular way to accurately estimate return covariance matrices using high-frequency data. This thesis contains five research papers that study time series of realized covariance matrices, estimators for related random matrix distributions, and cases where the sample size is smaller than the number of assets considered.Paper I provides several goodness-of-fit tests for discrete realized covariance matrix time series models that are driven by an underlying Wishart process. The test methodology is based on an extended version of Bartlett's decomposition, allowing to obtain independent and standard normally distributed random variables under the null hypothesis. The paper includes a simulation study that investigates the tests' performance under parameter uncertainty, as well as an empirical application of the popular conditional autoregressive Wishart model fitted to data on six stocks traded over eight and a half years.Paper II derives the Stein-Haff identity for exponential random matrix distributions, a class which for example contains the Wishart distribution. It furthermore applies the derived identity to the matrix-variate gamma distribution, providing an estimator that dominates the maximum likelihood estimator in terms of Stein's loss function. Finally, the theoretical results are supported by a simulation study.Paper III supplies a novel closed-form estimator for the parameters of the matrix-variate gamma distribution. The estimator appears to have several benefits over the typically applied maximum likelihood estimator, as revealed in a simulation study. Applying the proposed estimator as a start value for the numerical optimization procedure required to find the maximum likelihood estimate is also shown to reduce computation time drastically, when compared to applying arbitrary start values.Paper IV introduces a new model for discrete time series of realized covariance matrices that obtain as singular. This case occur when the matrix dimension is larger than the number of high frequency returns available for each trading day. As the model naturally appears when a large number of assets are considered, the paper also focuses on maintaining estimation feasibility in high dimensions. The model is fitted to 20 years of high frequency data on 50 stocks, and is evaluated by out-of-sample forecast accuracy, where it outperforms the typically considered GARCH model with high statistical significance.Paper V is concerned with estimation of the tangency portfolio vector in the case where the number of assets is larger than the available sample size. The estimator contains the Moore-Penrose inverse of a Wishart distributed matrix, an object for which the mean and dispersion matrix are yet to be derived. Although no exact results exist, the paper extends the knowledge of statistical properties in portfolio theory by providing bounds and approximations for the moments of this estimator as well as exact results in special cases. Finally, the properties of the bounds and approximations are investigated through simulations.
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| 4. |
- Alfelt, Gustav, 1985-, et al.
(författare)
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Singular Conditional Autoregressive Wishart Model for Realized Covariance Matrices
- 2022
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Ingår i: Journal of business & economic statistics. - : Taylor & Francis Group. - 0735-0015 .- 1537-2707. ; 41:3, s. 833-845
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Tidskriftsartikel (refereegranskat)abstract
- Realized covariance matrices are often constructed under the assumption that richness of intra-day return data is greater than the portfolio size, resulting in nonsingular matrix measures. However, when for example the portfolio size is large, assets suffer from illiquidity issues, or market microstructure noise deters sampling on very high frequencies, this relation is not guaranteed. Under these common conditions, realized covariance matrices may obtain as singular by construction. Motivated by this situation, we introduce the Singular Conditional Autoregressive Wishart (SCAW) model to capture the temporal dynamics of time series of singular realized covariance matrices, extending the rich literature on econometric Wishart time series models to the singular case. This model is furthermore developed by covariance targeting adapted to matrices and a sector wise BEKK-specification, allowing excellent scalability to large and extremely large portfolio sizes. Finally, the model is estimated to a 20-year long time series containing 50 stocks and to a 10-year long time series containing 300 stocks, and evaluated using out-of-sample forecast accuracy. It outperforms the benchmark models with high statistical significance and the parsimonious specifications perform better than the baseline SCAW model, while using considerably less parameters.
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| 5. |
- Battistin, Claudia, et al.
(författare)
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Belief propagation and replicas for inference and learning in a kinetic Ising model with hidden spins
- 2015
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Ingår i: Journal of Statistical Mechanics. - 1742-5468 .- 1742-5468.
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Tidskriftsartikel (refereegranskat)abstract
- We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief propagation (BP) and susceptibility propagation (SusP) can then be used to infer the states of hidden variables and to learn the couplings. We study the convergence and performance of this algorithm for networks with both Gaussian-distributed and binary bonds. We also study how the algorithm behaves as the fraction of hidden nodes and the amount of data are changed, showing that it outperforms the Thouless-Anderson-Palmer (TAP) equations for reconstructing the connections.
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| 6. |
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| 7. |
- Bodnar, Taras, et al.
(författare)
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Quantile-based optimal portfolio selection
- 2021
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Ingår i: Computational Management Science. - : Springer Science and Business Media LLC. - 1619-697X .- 1619-6988. ; :18, s. 299-324
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Tidskriftsartikel (refereegranskat)abstract
- In this paper the concept of quantile-based optimal portfolio selection is introduced and a specific portfolio connected to it, the conditional value-of-return (CVoR) portfolio, is proposed. The CVoR is defined as the mean excess return or the conditional value-at-risk (CVaR) of the return distribution. The portfolio selection consists solely of quantile-based risk and return measures. Financial institutions that work in the context of Basel 4 use CVaR as a risk measure. In this regulatory framework sufficient and necessary conditions for optimality of the CVoR portfolio are provided under a general distributional assumption. Moreover, it is shown that the CVoR portfolio is mean-variance efficient when the returns are assumed to follow an elliptically contoured distribution. Under this assumption the closed-form expression for the weights and characteristics of the CVoR portfolio are obtained. Finally, the introduced methods are illustrated in an empirical study based on monthly data of returns on stocks included in the S&P index. It is shown that the new portfolio selection strategy outperforms several alternatives in terms of the final investor wealth.
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| 8. |
- Bodnar, Taras, et al.
(författare)
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Tangency portfolio weights for singular covariance matrix in small and large dimensions : estimation and test theory
- 2019
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Ingår i: Journal of Statistical Planning and Inference. - : Elsevier. - 0378-3758 .- 1873-1171. ; 201, s. 40-57
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we derive the finite-sample distribution of the estimated weights of the tangency portfolio when both the population and the sample covariance matrices are singular. These results are used in the derivation of a statistical test on the weights of the tangency portfolio where the distribution of the test statistic is obtained under both the null and the alternative hypotheses. Moreover, we establish the high-dimensional asymptotic distribution of the estimated weights of the tangency portfolio when both the portfolio dimension and the sample size increase to infinity. The theoretical findings are implemented in an empirical application dealing with the returns on the stocks included into the S&P 500 index.
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| 9. |
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| 10. |
- Hertz, John A., et al.
(författare)
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Ising model for inferring network structure from spike data
- 2013
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Ingår i: Principle of Neural Coding. - Boca/Raton : CRC Press. - 9781439853306 - 9781439853313 ; , s. 527-546
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Bokkapitel (refereegranskat)abstract
- Now that spike trains from many neurons can be recorded simultaneously, there is a need for methods to decode these data to learn about the networks that these neurons are part of. One approach to this problem is to adjust the parameters of a simple model network to make its spike trains resemble the data as much as possible. The connections in the model network can then give us an idea of how the real neurons that generated the data are connected and how they influence each other. In this chapter we describe how to do this for the simplest kind of model: an Ising network. We derive algorithms for finding the best model connection strengths for fitting a given data set, as well as faster approximate algorithms based on mean field theory. We test the performance of these algorithms on data from model networks and experiments.
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