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In this paper, we investigate the distributional properties of the estimated tangency portfolio (TP) weights assuming that the asset returns follow a matrix variate closed skew-normal distribution. We establish a stochastic representation of the linear combination of the estimated TP weights that fully characterizes its distribution. Using the stochastic representation we derive the mean and variance of the estimated weights of TP which are of key importance in portfolio analysis. Furthermore, we provide the asymptotic distribution of the linear combination of the estimated TP weights under the high-dimensional asymptotic regime, i.e., the dimension of the portfolio p and the sample size n tend to infinity such that p/n & RARR;c & ISIN;(0,1). A good performance of the theoretical findings is documented in the simulation study. In an empirical study, we apply the theoretical results to real data of the stocks included in the S & P 500 index.

Multivariate random sums appear in many scientic fields, most notably in actuarial science, where they model both the number of claims and their sizes. Unfortunately, they pose severe inferential problems. For example, their density function is analytically intractable, in the general case, thus preventing likelihood inference. In this paper, we address the problem by the method of moments, under the assumption that the claim size and the claim number have a multivariate skew-normal and a Poisson distribution, respectively. In doing so, we also derive closed-form expressions for some fundamental measures of multivariate kurtosis and highlight some limitations of both projection pursuit and invariant coordinate selection.

We employ a battery of model evaluation tests for a broad set of GARCH-MIDAS models and account for data snooping bias. We document that inferences based on standard tests for GM variance components can be misleading. Our data mining free results show that the gain of macro-variables in forecasting total (long-run) variance by GM models is overstated (understated). Estimation of different components of volatility is crucial for designing differentiated investing strategies, risk management plans and pricing derivative securities. Therefore, researchers and practitioners should be wary of data-mining bias, which may contaminate a forecast that may appear statistically validated using robust evaluation tests.

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.

The fourth cumulant for the random sum of random vectors is considered. A formula is presented for the general case when the aggregating variable is independent of the random vectors. Two important special cases are considered. In the first one, multivariate skew-normal random vectors are considered that are aggregated by a Poisson variable. The second case deals with multivariatea symmetric generalized Laplace random vectors and aggregation is made by a negative binomial variable. There is a well-established relation between asymmetric Laplace motion and negative binomial process that corresponds to the invariance principle of the random sum of random vectors for the generalized asymmetric Laplace distribution. We explore this relation and provide a multivariate continuous time version of the results.

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.

The nowcasting performance of autoregressive models for GDP growth are analysed in a setting where the error term is allowed to be characterized both by conditional heteroscedasticity and non-Gaussianity. Standard, publicly available, quarterly data on GDP growth from 1979 to 2019 for six countries are employed: Australia, Canada, France, Japan, the United Kingdom and the United States. In-sample analysis suggests that when homoscedasticity is assumed, support is provided for non-Gaussian error terms; the estimated degrees of freedom of the t-distribution lie between two and seven for all countries. However, allowing for both conditional heteroscedasticity and t-distributed innovations, results indicate that conditional heteroscedasticity captures the fat-tailed behaviour of the data to a large extent. Results from out-of-sample analysis show that point nowcasts are hardly affected by taking conditional heteroscedasticity and/or non-Gaussianity into account. For the density nowcasts, it is found that accounting for conditional heteroscedasticity leads to improvements for Australia, Canada, Japan, the United Kingdom and the United States; allowing for non-Gaussianity seems less important though. This result is robust to which measure is used for assessing density nowcasting performance.

Deep learning methods allow computational models involving multiple processing layers to discover intricate structures in data sets. Classifying an image is one such problem where these methods are found to be very useful. Although different approaches have been proposed in the literature, this paper illustrates a successful implementation of the Bayesian Convolution Neural Networks (BCNN)-based classification procedure to classify microscopic images of blood samples (lymphocyte cells) without involving manual feature extractions. The data set contains 260 microscopic images of cancerous and noncancerous lymphocyte cells. We experiment with different network structures and obtain the model that returns the lowest error rate in classifying the images. Our developed models not only produce high accuracy in classifying cancerous and noncancerous lymphocyte cells but also provide useful information regarding uncertainty in predictions., Funding agency:Internal research grants at Örebro University

In this paper, we consider the estimated weights of the tangency portfolio. We derive analytical expressions for the higher order non-central and central moments of these weights when the returns are assumed to be independently and multivariate normally distributed. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed forms. Later, we complement our results with a simulation study where data from the multivariate normal and t-distributions are simulated, and the first four moments of estimated weights are computed by using the Monte Carlo experiment. It is noteworthy to mention that the distributional assumption of returns is found to be important, especially for the first two moments. Finally, through an empirical illustration utilizing returns of four financial indices listed in NASDAQ stock exchange, we observe the presence of time dynamics in higher moments., Funding Agency:Örebro University