| 1. |
- Kiss, Tamás, 1988-, et al.
(författare)
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Modelling the Relation between the US Real Economy and the Corporate Bond-Yield Spread in Bayesian VARs with non-Gaussian Disturbances
- 2021
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we analyze how skewness and heavy tails affect the estimated relationship between the real economy and the corporate bond-yield spread, a popular predictor of rea lactivity. We use quarterly US data to estimate Bayesian VAR models with stochastic volatility and various distributional assumptions regarding the disturbances. In-sample, we find that – after controlling for stochastic volatility – innovations in GDP growth can be well-described by a Gaussian distribution. In contrast, both the unemployment rate and the yield spread appear to benefit from being modelled using non-Gaussian innovations. When it comes to real-time forecasting performance, we find that the yield spread is an important predictor of GDP growth, and that accounting for stochastic volatility matters, mainly for density forecasts. Incremental improvements from non-Gaussian innovations are limited to forecasts of the unemployment rate. Our results suggest that stochastic volatility is of first order importance when modelling the relationship between yield spread and real variables; allowing for non-Gaussian innovations is less important.
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| 2. |
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| 3. |
- Kiss, Tamás, 1988-, et al.
(författare)
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Predicting returns and dividend growth - The role of non-Gaussian innovations
- 2022
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Ingår i: Finance Research Letters. - : Elsevier. - 1544-6123 .- 1544-6131. ; 46:Part A
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we assess whether flexible modelling of innovations impact the predictive performance of the dividend price ratio for returns and dividend growth. Using Bayesian vector autoregressions we allow for stochastic volatility, heavy tails and skewness in the innovations. Our results suggest that point forecasts are barely affected by these features, suggesting that workhorse models on predictability are sufficient. For density forecasts, however, we find that stochastic volatility substantially improves the forecasting performance.
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| 4. |
- Alfelt, Gustav, 1985-, et al.
(författare)
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On the mean and variance of the estimated tangency portfolio weights for small samples
- 2022
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Ingår i: Modern Stochastics: Theory and Applications. - Vilnius : VTeX. - 2351-6054 .- 2351-6046. ; 9:4, s. 453-482
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, a sample estimator of the tangency portfolio (TP) weights is con-sidered. The focus is on the situation where the number of observations is smaller than the number of assets in the portfolio and the returns are i.i.d. normally distributed. Under these as-sumptions, the sample covariance matrix follows a singular Wishart distribution and, therefore, the regular inverse cannot be taken. In the paper, bounds and approximations for the first two moments of the estimated TP weights are derived, as well as exact results are obtained when the population covariance matrix is equal to the identity matrix, employing the Moore-Penrose inverse. Moreover, exact moments based on the reflexive generalized inverse are provided. The properties of the bounds are investigated in a simulation study, where they are compared to the sample moments. The difference between the moments based on the reflexive generalized inverse and the sample moments based on the Moore-Penrose inverse is also studied.
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| 5. |
- Bauder, David, et al.
(författare)
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Bayesian inference for the tangent portfolio
- 2018
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Ingår i: International Journal of Theoretical and Applied Finance. - : World Scientific Publishing Co. Pte. Ltd.. - 0219-0249. ; 21:8
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For diffuse and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.
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| 6. |
- Bodnar, Taras, et al.
(författare)
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A test for the global minimum variance portfolio for small sample and singular covariance
- 2017
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Ingår i: AStA Advances in Statistical Analysis. - : Springer. - 1863-8171 .- 1863-818X. ; 101:3, s. 253-265
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Tidskriftsartikel (refereegranskat)abstract
- Recently, a test dealing with the linear hypothesis for the global minimum variance portfolio weights was obtained under the assumption of non-singular covariance matrix. However, the problem of potential multicollinearity and correlations of assets constitutes a limitation of the classical portfolio theory. Therefore, there is an interest in developing theory in the presence of singularities in the covariance matrix. In this paper, we extend the test by analyzing the portfolio weights in the small sample case with a singular population covariance matrix. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented.
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| 7. |
- Bodnar, Taras, et al.
(författare)
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Bayesian estimation of the global minimum variance portfolio
- 2017
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Ingår i: European Journal of Operational Research. - : Elsevier. - 0377-2217 .- 1872-6860. ; 256:1, s. 292-307
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the estimation of the weights of optimal portfolios from the Bayesian point of view under the assumption that the conditional distributions of the logarithmic returns are normal. Using the standard priors for the mean vector and the covariance matrix, we derive the posterior distributions for the weights of the global minimum variance portfolio. Moreover, we reparameterize the model to allow informative and non-informative priors directly for the weights of the global minimum variance portfolio. The posterior distributions of the portfolio weights are derived in explicit form for almost all models. The models are compared by using the coverage probabilities of credible intervals. In an empirical study we analyze the posterior densities of the weights of an international portfolio.
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| 8. |
- Bodnar, Taras, et al.
(författare)
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Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix-variate location mixture of normal distributions
- 2019
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Ingår i: Scandinavian Journal of Statistics. - : John Wiley & Sons. - 0303-6898 .- 1467-9469. ; 46:2, s. 636-660
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal distributions. The central limit theorem is derived for the product of the sample covariance matrix and the sample mean vector. Moreover, we consider the product of the inverse sample covariance matrix and the mean vector for which the central limit theorem is established as well. All results are obtained under the large-dimensional asymptotic regime where the dimension p and the sample size n approach to infinity such that p/n → c ∈ [0, +∞) when the sample covariance matrix does not need to be invertible and p/n → c ∈ [0, 1) otherwise.
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| 9. |
- Bodnar, Taras, et al.
(författare)
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Discriminant analysis in small and large dimensions
- 2020
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Ingår i: Theory of Probability and Mathematical Statistics. - Providence, Rhode Island : American Mathematical Society (AMS). - 1547-7363 .- 0094-9000. ; 100, s. 21-41
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Tidskriftsartikel (refereegranskat)abstract
- We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the discriminant function coefficients is derived, which is then used to obtain their asymptotic distribution under the high-dimensional asymptotic regime. We investigate the performance of the classification analysis based on the discriminant function in both small and large dimensions. A stochastic representation is established, which allows to compute the error rate in an efficient way. We further compare the calculated error rate with the optimal one obtained under the assumption that the covariance matrix and the two mean vectors are known. Finally, we present an analytical expression of the error rate calculated in the high-dimensional asymptotic regime. The finite-sample properties of the derived theoretical results are assessed via an extensive Monte Carlo study.
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| 10. |
- Bodnar, Taras, et al.
(författare)
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Distribution of the product of a singular Wishart matrix and a normal vector
- 2014
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Ingår i: Theory of Probability and Mathematical Statistics. - : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; :91, s. 1-15
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we derive a very useful formula for the stochastic representation of the product of a singular Wishart matrix with a normal vector. Using this result, the expressions of the density function as well as of the characteristic function are established. Moreover, the derived stochastic representation is used to generate random samples from the product which leads to a considerable improvement in the computation efficiency. Finally, we present several important properties of the singular Wishart distribution, like its characteristic function and distributional properties of the partitioned singular Wishart matrix.
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