Modelling the Botswana Pula/Us Dollar exchange rate using the Skewed generalized t (SGT) distributions

The economy of Botswana heavily relies on mineral exports (mainly diamond exports), which are largely dependent on the exchange rate. And, the US Dollar is one of the most important currencies in the basket of currencies to which the Botswana Pula is pegged. Therefore, this paper seeks to empirically establish the baseline characteristics of the Botswana Pula (BWP) and the US Dollar (USD) exchange rate and to identify the most plausible probability distribution from the skewed generalized t (SGT) family that can be used to model the log-returns of the daily BWP/USD exchange rates for the period January 2001 to December 2020. The SGT family is a highly versatile class of models that can capture the skewness and kleptokurticity that are inherent in financial time series. Four probability distributions are considered in this study: skewed t, skewed generalized error, generalized t and skewed generalized t. The maximum likelihood approach is used to estimate the parameters of each model. Model comparison and selection are based on the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results of the study show that the daily BWP/USD exchange rate series is nonnormal, negatively skewed heavy-tailed. It is also found that, based on the values of both the AIC and BIC, the model that gives the best fit to the data is the skewed t, which is closely followed by the skewed generalized error distribution, while the generalized t gives the worst fit. Keywords: Pula/US Dollar exchange rate, log returns, Generalized t distribution, Skewed generalized error distribution, Skewed generalized t distribution, Skewed t distribution, skewness, kurtosis, maximum likelihood

Modeling and Estimating Volatility of Day-Ahead Electricity Prices

We model day-ahead electricity prices of the UK power market using skew generalized error distribution. This distribution allows us to take into account the features of asymmetry, heavy tails, and a peak higher than in normal or Student’s t distributions. The adequacy of the estimated volatility model is verified using various tests and criteria. A correctly specified volatility model can be used for analyzing the impact of reforms or other events. We find that, after the start of the COVID-19 pandemic, price level and volatility increased.

Modeling stock market volatility in Croatia

Purpose: In this paper, the volatility of the Croatian stock market index CROBEX is investigated using the GARCH(1,1) model. Methodology: The novelty provided by this paper is the estimation of the GARCH(1,1) model by using three conditional error distributions (normal (Gaussian) distribution, Student’s-distribution with fixed degrees of freedom and generalized error distribution (GED) with fixed parameters). Results: The findings obtained in the research are in the line with previous research in this field (Erjavec & Cota, 2007; Sajter & Ćorić, 2009). The volatility of CROBEX returns is positively correlated with the volume of trade on the Zagreb Stock Exchange and movements on the main European and American stock markets. The movement of S&P 500 stock market index returns is transmitted from the previous day, providing signals for the direction of change of CROBEX index returns in the present. Conclusion: Therefore, this paper provides evidence that investors in Croatia strongly rely on the past information received from the American S&P500 stock market index. Furthermore, there seems to exist the co-movement between CROBEX and main European indexes on the same trading day.

TRIPLE PROBABILITY DENSITY DISTRIBUTION MODEL IN THE TASK OF AVIATION RISK ASSESSMENT

The probability of an airplane deviation from pre-planned trajectory is a core of aviation safety analysis. We propose to use a mixture of three probability density distribution functions it the task of aviation risk assessment. Proposed model takes into account the effect of navigation system error, flight technical error, and occurrence of rare events. Univariate Generalized Error Distribution is used as a basic component of distribution functions, that configures the error distribution model from the normal error distribution to double exponential distribution function. Statistical fitting of training sample by proposed Triple Univariate Generalized Error Distribution (TUGED) is supported by Maximum Likelihood Method. Optimal set of parameters is estimated by sequential approximation method with defined level of accuracy. The developed density model has been used in risk assessment of airplane lateral deviation from runway centreline during take-off and landing phases of flight. The efficiency of the developed model is approved by Chi-square, Akaike’s, and Bayes information criteria. The results of TUGED fitting indicate better performance in comparison with double probability density distribution model. The risk of airplane veering off the runway is considered as the probability of a rare event occurrence and is estimated as an area under the TUGED.