This paper proposes the PROMETHEE II based multicriteria approach for cryptocurrency portfolio selection. Such an approach allows considering a number of variables important for cryptocurrencies rather than limiting them to the commonly employed return and risk. The proposed multiobjective decision making model gives the best cryptocurrency portfolio considering the daily return, standard deviation, value-at-risk, conditional value-at-risk, volume, market capitalization and attractiveness of nine cryptocurrencies from January 2017 to February 2020. The optimal portfolios are calculated at the first of each month by taking the previous 6 months of daily data for the calculations yielding with 32 optimal portfolios in 32 successive months. The out-of-sample performances of the proposed model are compared with five commonly used optimal portfolio models, i.e., naïve portfolio, two mean-variance models (in the middle and at the end of the efficient frontier), maximum Sharpe ratio and the middle of the mean-CVaR (conditional value-at-risk) efficient frontier, based on the average return, standard deviation and VaR (value-at-risk) of the returns in the next 30 days and the return in the next trading day for all portfolios on 32 dates. The proposed model wins against all other models according to all observed indicators, with the winnings spanning from 50% up to 94%, proving the benefits of employing more criteria and the appropriate multicriteria approach in the cryptocurrency portfolio selection process.

Neural networks (NNs) are appropriate to use in time series analysis under conditions of unfulfilled assumptions, i.e., non-normality and nonlinearity. The aim of this paper is to propose means of addressing identified shortcomings with the objective of identifying the NN structure for inflation forecasting. The research is based on a theoretical model that includes the characteristics of demand-pull and cost-push inflation; i.e., it uses the labor market, financial and external factors, and lagged inflation variables. It is conducted at the aggregate level of euro area countries from January 1999 to January 2017.Based on the estimated 90 feedforward NNs (FNNs) and 450 Jordan NNs (JNNs), which differ in variable parameters (number of iterations, learning rate, initial weight value intervals, number of hidden neurons, and weight value of the context unit), the mean square error (MSE), and the Akaike Information Criterion (AIC) are calculated for two periods: in-the-sample and outof-sample. Ranking NNs simultaneously on both periods according to either MSE or AIC does not lead to the selection of the 'best' NN because the optimal NN in-the-sample, based on MSE and/or AIC criteria, often has high out-ofsample values of both indicators. To achieve the best compromise solution, i.e., to select an optimal NN, the preference ranking organization method for enrichment of evaluations (PROMETHEE) is used. Comparing the optimal FNN and JNN, i.e., FNN(4,5,1) and JNN(4,3,1), it is concluded that under approximately equal conditions, fewer hidden layer neurons are required in JNN than in FNN, confirming that JNN is parsimonious compared to FNN.Moreover, JNN has a better forecasting performance than FNN.

In times of pronounced nonlinearity of macroeconomic variables and in situations when variables are not normally distributed, i.e. when the assumption of i.i.d. is not fulfilled, neural networks (NNs) should be used for forecasting. In this paper, Jordan neural network (JNN), a special type of NNs is examined, because of its advantages in time series forecasting suitable for inflation forecasting. The variables used as inputs include labour market variable, financial variable, external factor and lagged inflation, i.e. the most commonly used variables in previous researches. The research is conducted at the aggregate level of euro area countries in the period from January 1999 to January 2017. Based on 250 estimated JNNs, which differ in selected variables, sample breaking point and varying parameters (number of hidden neurons, weight value of the context unit), the model adequacy indicators for each JNN are calculated for two periods: in-the-sample and out-of-sample. Finally, the optimal JNN for inflation forecasting is obtained as the best compromise solution between low mean squared error inthe-sample and out-of-sample and low number of parameters to estimate. This paper contributes to existing literature in using JNN for inflation forecasting since it is rarely used for macroeconomic time series prediction in general. Moreover, this paper defines which set of variables contributes to the best inflation forecast. Additionally, JNN is examined thoroughly by fixing certain parameters of the model and alternating other parameters to contribute to the JNN literature, i.e. finding the optimal JNN.

This paper investigates whether a specific type of a recurrent neural network, in particular Jordan neural network (JNN), captures the expected inflation better than commonly used feedforward neural networks and traditional parametric time-series models. It also considers competing survey-based and model-based expected inflation towards ex-post actual inflation to find whose predictions are more accurate; predictions from survey respondents or forecasting modelers. Further, it proposes neural network modelling strategy when dealing with nonstationary time-series which exhibit long-memory property and nonlinear dependence with respect to lagged inputs and exogenous inputs as well. Following this strategy, overfitting problem was reduced until no improvement in forecasting accuracy of expected inflation is achieved. The main finding is that JNN predicts inflation in euro zone quite accurately within forecasting horizon of 2 years. Regarding rational expectation principle we have found a set of demand-pull and cost-push inflation characteristics as exogenous inputs which helps in reducing overfitting problem of recurrent neural network even more. The sample includes euro zone aggregated monthly observations from January 2000 to December 2019. The results also confirm that inflation expectations obtained from JNN are consistent with Survey of professional forecasters (SPF), and thus, monetary policy makers can use JNN as a complementary tool in shortcomings of other inflation expectations measures.

Moments of future prices and returns are not observable, but it is possible to measure them indirectly. A set of option prices with the same maturity but with different exercise prices are used to extract implied probability distribution of the underlying asset at the expiration date. The aim is to obtain market expectations from options and to investigate which non-structural model for estimating implied probability distribution gives the best fit. Nonstructural models assume that only dynamics in prices is known. Mixture of two log-normals (MLN), Edgeworth expansions and Shimko's model (representatives of parametric, semiparametric and nonparametric approaches respectively) are compared. Previous researches are inconclusive about the superiority of one approach over the others. This article contributes to finding which approach dominates. The best fit model is used to describe moments of the implied probability distribution. The sample covers one-year data for DAX index options. The results are compared through models and maturities. All models give better short-term forecasts. In pairwise comparison, MLN is superior to other approaches according to mean squared errors and Diebold-Mariano test in the observed period for DAX index options.

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Rising inequalities between countries are widely investigated. Since they involve different aspects, in this paper they are examined through the distribution of countries’ growth and development, inclusion and intergenerational equity and sustainability. These aspects involve variables that are not normally distributed so different probability density functions (PDFs) have been proposed, tested and compared through literature. This paper compares different PDFs that are considered successful in describing distribution of the variables involved, as Weibull, gamma, lognormal, normal, loglogistic, Pareto, Burr and exponential. They are usually compared using diff erent goodness-of-fit measures including the log-likelihood, sum of squared errors, sum of absolute errors and chi-square statistics which can sometimes lead to divergent conclusions. This paper adds up to these goodness-of-fit measures and includes the Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling statistics, the mean absolute and squared deviation between theoretical and empirical PDF, the mean absolute and squared deviation between theoretical and empirical cumulative distribution function, AIC and BIC as well as the deviation in skewness and kurtosis. Since diff erent distributions can be considered as alternatives and goodness-of-fit measures as conflicting criteria, the problem of finding the appropriate PDF can be viewed as multiple criteria decision making problem which can be solved using PROMETHEE method. However, diff erent preference parameters, lead to different ranking, so the final decision is obtained using PROMETHEE Group Decision Support System (GDSS) method. This paper therefore contributes to the existing literature on inequalities between countries and statistics in general by proposing a new approach for distribution modelling and selection.