| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- Hertz, John, et al.
(författare)
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Stochastic activation in a genetic switch model
- 2018
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Ingår i: Physical review. E. - 2470-0045 .- 2470-0053. ; 98:5
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Tidskriftsartikel (refereegranskat)abstract
- We study a biological autoregulation process, involving a protein that enhances its own transcription, in a parameter region where bistability would be present in the absence of fluctuations. We calculate the rate of fluctuation-induced rare transitions between locally stable states using a path integral formulation and Master and Chapman-Kolmogorov equations. As in simpler models for rare transitions, the rate has the form of the exponential of a quantity S-0 (a barrier) multiplied by a prefactor eta. We calculate S-0 and eta first in the bursting limit (where the ratio gamma of the protein and mRNA lifetimes is very large). In this limit, the calculation can be done almost entirely analytically, and the results are in good agreement with simulations. For finite gamma numerical calculations are generally required. However, S-0 can be calculated analytically to first order in 1/gamma, and the result agrees well with the full numerical calculation for all gamma > 1. Employing a method used previously on other problems, we find we can account qualitatively for the way the prefactor eta varies with gamma, but its value is 15-20% higher than that inferred from simulations.
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