To Örebro University

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 fitting flexible and tractable parametric, multivariate distributions, as for example finite mixtures. Both approaches are investigated within the framework of Edgeworth expansions. A general formula for the fourth-order cumulants of the random sum of independent and identically distributed random vectors is derived and it is shown that the above mentioned asymptotic approach does not necessarily lead to valid asymptotic normal approximations. The problem is addressed by means of Edgeworth expansions. Both theoretical and empirical results suggest that mixtures of two multivariate normal distributions with proportional covariance matrices satisfactorily fit data generated from random sums where the counting random variable and the random summands are Poisson and multivariate skew-normal, respectively.

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.

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.

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.

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.

The spillover risk and systemic risk of the troubled banking sectors of Greece, Ireland, Italy, Portugal and Spain (GIIPS) for the rest of the European and the US banking sector are investigated using the conditional value-at-risk (CoVaR) framework. Our results show that the CoVaR estimates are sensitive to the choice of static and dynamic parametrization of volatility and pairwise-correlations. Nevertheless, even the conservative estimates for CoVaR and changes in it display that the magnitude of these risks, originating from GIIPS countries, is large. These risks affect banking of large European and the US banking sectors more than the rest.

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.

Proper mapping and classification of Forest cover types are integral in understanding the processes governing the interaction mechanism of the surface with the atmosphere. In the presence of massive satellite and aerial measurements, a proper manual categorization has become a tedious job. In this study, we implement three different modest machine learning classifiers along with three statistical feature selectors to classify different cover types from cartographic variables. Our results showed that, among the chosen classifiers, the standard Random Forest Classifier together with Principal Components performs exceptionally well, not only in overall assessment but across all seven categories. Our results are found to be significantly better than existing studies involving more complex Deep Learning models.