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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.

Stock and bond are the two most crucial assets for portfolio allocation and risk management. This study proposes generalized autoregressive score mixed frequency data sampling (GAS MIDAS) copula models to analyze the dynamic dependence between stock returns and bond returns. A GAS MIDAS copula decomposes their relationship into a short-term dependence and a long-term dependence. While the long-term dependence is driven by related macro-finance factors using a MIDAS regression, the short-term effect follows a GAS process. Asymmetric dependence at different quantiles is also taken into account. We find that the proposed GAS MIDAS copula models are more effective in optimal portfolio allocation and improve the accuracy in risk management compared to other alternatives.

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 gains of macro-variables in forecasting total (long run) variance by GM models are overstated (understated). Estimation of different components of volatility is crucial for designing differentiated investing strategies, risk management plans and pricing of 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.

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 characterize 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 → c ∈ (0, 1). A good performance of the theoretical findings is documented in the simulation study. In the empirical study, we apply the theoretical results to real data of the stocks included in the S&P 500 index.

The sum of a random number of independent and identically distributed random vectors has a distribution which is not analytically tractable, in the general case. The problem has been addressed by means of asymptotic approximations embedding the number of summands in a stochastically increasing sequence. Another approach relies on tting exible and tractable parametric, multivariate distributions, as for example nite mixtures. In this paper we investigate both approaches within the framework of Edgeworth expansions. We derive a general formula for the fourth-order cumulants of the random sum of independent and identically distributed random vectors and show that the above mentioned asymptotic approach does not necessarily lead to valid asymptotic normal approximations. We address the problem by means of Edgeworth expansions. Both theoretical and empirical results suggest that mixtures of two multivariate normal distributions with proportional covariance matrices satisfactorily t data generated from random sums where the counting random variable and the random summands are Poisson and multivariate skew-normal, respectively.

The APARCH model is a generalization of the GARCH model that attempts to capture asymmetric responses of returns and of volatility to positive and negative `news shocks' -the phenomenon known as the leverage effect. Despite its potential, the model's mathematical properties have not yet been fully investigated. While the capacity of the model to account for the leverage effect is clear from its defining structure, little is known how the effect is quantifed in terms of the model's parameters. The same applies to the quantifcation of heavy tails and time dependence. Here, in an attempt to fill this void, we study the model in further detail. We obtain sufficient conditions of its existence in different metrics as well as explicit forms of important characteristics: skewness, kurtosis, correlations and leverage. Utilizing these results, we analyze the roles of the parameters and discuss statistical inference. We also propose a natural extension by introducing an additional parameter and discuss how it affects the model. Through theoretical results and a Monte Carlo study we demonstrate that the model can produce heavy-tailed data. We illustrate these properties using S&P500 data as well as country indices for dominant European economies.

This paper applies the GARCH-MIDAS (Mixed Data Sampling) model to examine whether information contained in macroeconomic variables can help to predict short-term and long-term components of the return variance. A principal component analysis is used to incorporate the information contained in different variables. Our results show that including low-frequency macroeconomic information in the GARCH-MIDAS model improves the prediction ability of the model, particularly for the long-term variance component. Moreover, the GARCH-MIDAS model augmented with the first principal component outperforms all other specifications, indicating that the constructed principal component can be considered as a good proxy of the business cycle.

This paper aims to examine the role of macroeconomic variables in forecasting the return volatility of the US stock market. We apply the GARCH-MIDAS (Mixed Data Sampling) model to examine whether information contained in macroeconomic variables can help to predict shortterm and long-term components of the return variance. We investigate several alternative models and use a large group of economic variables. A principal component analysis is used toincor porate the information contained in different variables. Our results show that including low frequency macroeconomic information into the GARCH-MIDAS model improves the prediction ability of the model, particularly for the long-term variance component. Moreover, the GARCHMIDAS model augmented with the first principal component outperforms all other specifications, indicating that the constructed principal component can be considered as a good proxy of the business cycle.