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Can Lognormal, Weibull or Gamma Distributions Improve the EWS-GARCH Value-at-Risk Forecasts?

100%
Chlebus M.
Przegląd Statystyczny
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2016
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vol. 63
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issue 3
329-350
PL
W badaniu analizie poddane zostały dwustopniowe modele EWS-GARCH służące do prognozowania wartości narażonej na ryzyko. W ramach analizy rozpatrywane były modele EWS-GARCH zakładające rozkłady lognormalny, Weibulla oraz Gamma w stanie turbulencji oraz modele GARCH(1,1) i GARCH(1,1) z poprawką na rozkład empiryczny w stanie spokoju. Ocena jakości prognoz Value-at-Risk uzyskanych na podstawie wspomnianych modeli została przeprowadzona na podstawie miar adekwatności (wskaźnik przekroczeń, test Kupca, test Christoffersena, test asymptotyczny bezwarunkowego pokrycia oraz kryteria backtestingu określone przez Komitet Bazylejski) oraz analizy funkcji strat (kwadratowa funkcja straty Lopeza, absolutna funkcja straty Abad i Benito, 3 wersja funkcji straty Caporina oraz funkcja nadmiernych kosztów). Uzyskane wyniki wskazują, że modele EWS-GARCH z rozkładem lognormalnym, Weibulla lub Gamma mogą konkurować z modelami EWS-GARCH z rozkładem wykładniczym lub empirycznym. Modele EWS-GARCH z rozkładem lognormalnym, Weibulla lub Gamma są nieco mniej konserwatywne, jednocześnie jednak koszt ich stosowania jest mniejszy niż modeli EWS-GARCH z rozkładem wykładniczym lub empirycznym.
EN
In the study, two-step EWS-GARCH models to forecast Value-at-Risk are analysed. The following models were considered: the EWS-GARCH models with lognormal, Weibull or Gamma distributions as a distributions in a state of turbulence, and with GARCH(1,1) or GARCH(1,1) with the amendment to empirical distribution of random error models as models used in a state of tranquillity. The evaluation of the quality of the Value-at-Risk forecasts was based on the Value-at-Risk forecasts adequacy (the excess ratio, the Kupiec test, the Christoffersen test, the asymptotic test of unconditional coverage and the backtesting criteria defined by the Basel Committee) and the analysis of loss functions (the Lopez quadratic loss function, the Abad & Benito absolute loss function, the 3rd version of Caporin loss function and the function of excessive costs). Obtained results show that the EWSGARCH models with lognormal, Weibull or Gamma distributions may compete with EWS-GARCH models with exponential and empirical distributions. The EWS-GARCH model with lognormal, Weibull or Gamma distributions are relatively less conservative, but using them is less expensive than using the other EWS-GARCH models.
2
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One-day-ahead forecast of state of turbulence based on today's economic situation

100%
Chlebus M.
Equilibrium. Quarterly Journal of Economics and Economic Policy
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2018
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vol. 13
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issue 3
357-389
EN
Research background: In the literature little discussion was made about predicting state of time series in daily manner. The ability to recognize the state of a time series gives, for example, an opportunity to measure the level of risk in a state of tranquility and a state of turbulence independently, which can provide more accurate measurements of the market risk in a financial institution. Purpose of the article: The aim of article is to find an appropriate tools to predict, based on today's economic situation, the state, in which time series of financial data will be tomorrow. Methods: This paper proposes an approach to predict states (states of tranquillity and turbulence) for a current portfolio in a one-day horizon. The prediction is made using 3 different models for a binary variable (Logit, Probit, Cloglog), 4 definitions of a dependent variable (1%, 5%, 10%, 20% of worst realization of returns), 3 sets of independent variables (un-transformed data, PCA analysis and factor analysis). Additionally, an optimal cut-off point analysis is performed. The evaluation of the models was based on the LR test, Hosmer-Lemeshow test, Gini coefficient analysis and CROC criterion based on the ROC curve. The analyses were performed for 43 individual shares and 5 portfolios of shares quoted on the Warsaw Stock Exchange. The study has been conducted for the period from 1 January 2006 to 31 January 2012. Findings & Value added: Six combinations of assumptions have been chosen as appropriate (any model for a binary variable, the dependent variable defined as 5% or 10% of worst realization of returns, untransformed data, 5% or 10% cut-off point respectively). Models built on these assumptions meet all the formal requirements and have a high predictive and discriminant ability to one-day-ahead forecast of state of turbulence based on today's economic situation.
3
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Prognozowanie stanu turbulencji dla instrumentu finansowego w perspektywie dziennej na podstawie modeli dla binarnej zmiennej zależnej

100%
Chlebus M.
Ekonomia. Rynek, Gospodarka, Społeczeństwo
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2014
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issue 37
127-147
PL
W artykule przedstawiono propozycję modeli prognozowania stanów dla instrumentu finansowego w horyzoncie jednodniowym. W badaniu poddano analizie modele zakładające: jeden z trzech modeli dla zmiennej binarnej (logitowy, probitowy oraz cloglog), cztery definicje zmiennej zależnej (20%, 10%, 5% oraz 1% najgorszych realizacji stopy zwrotu) oraz trzy różne zbiory zmiennych niezależnych (dane nieprzekształcone, główne składowe z analizy PCA oraz czynniki z analizy czynnikowej). Ponadto w badaniu przeprowadzono analizę wyboru optymalnego punktu odcięcia. Ocena modeli została wykonana na podstawie testów LR i Hosmera-Lemeshowa oraz analizy parametru GINI i kryterium KROC. Na podstawie wyników badania empirycznego ustalono dziewięć kombinacji założeń, dla których modele stanu turbulencji spełniają określone w badaniu wymogi formalne oraz charakteryzują się wysoką zdolnością prognostyczną i dyskryminacyjną.
EN
This paper proposes an approach to predict states (states of tranquillity and turbulence) for a financial instrument in a one-day horizon. The prediction is made using 3 different models for a binary variable (LOGIT, PROBIT, CLOGLOG), 4 definitions of a dependent variable (1%, 5%, 10%, 20% of worst realization of returns), 3 sets of independent variables (untransformed data, PCA analysis and factor analysis). Additionally an optimal cut-off point analysis is performed. The evaluation of the models was based on the LR test, Hosmer-Lemeshow test, GINI coefficient analysis and KROC criterion based on the ROC curve. Nine combinations of assumptions have been chosen as appropriate (any model for a binary variable, the dependent variable defined as 1%, 5% or 10% of worst realization of returns, untransformed data, 1%, 5% or 10% cut-off point respectively). Models built on these assumptions meet all the formal requirements and have a high predictive and discriminant ability.
4
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Combining forecasts? Keep it simple

63%
Lis S., Chlebus M.
Central European Economic Journal
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2023
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vol. 10
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issue 57
343-370
EN
This study contrasts GARCH models with diverse combined forecast techniques for Commodities Value at Risk (VaR)modeling, aiming to enhance accuracy and provide novel insights. Employing daily returns data from 2000 to 2020 forgold, silver, oil, gas, and copper, various combination methods are evaluated using the Model Confidence Set (MCS) procedure. Results show individual models excel in forecasting VaR at a 0.975 confidence level, while combined methods outperform at 0.99 confidence. Especially during high uncertainty, as during COVID-19, combined forecasts prove more effective. Surprisingly, simple methods such as mean or lowest VaR yield optimal results, highlighting their efficacy. This study contributes by offering a broad comparison of forecasting methods, covering a substantial period, and dissecting crisis and prosperity phases. This advances understanding in financial forecasting, benefiting both academia and practitioners.
5
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Nvidia's Stock Returns Prediction Using Machine Learning Techniques for Time Series Forecasting Problem

51%
Chlebus M., Dyczko M., Woźniak M.
Central European Economic Journal
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2021
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vol. 8
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issue 55
EN
Statistical learning models have profoundly changed the rules of trading on the stock exchange. Quantitative analysts try to utilise them predict potential profits and risks in a better manner. However, the available studies are mostly focused on testing the increasingly complex machine learning models on a selected sample of stocks, indexes etc. without a thorough understanding and consideration of their economic environment. Therefore, the goal of the article is to create an effective forecasting machine learning model of daily stock returns for a preselected company characterised by a wide portfolio of strategic branches influencing its valuation. We use Nvidia Corporation stock covering the period from 07/2012 to 12/2018 and apply various econometric and machine learning models, considering a diverse group of exogenous features, to analyse the research problem. The results suggest that it is possible to develop predictive machine learning models of Nvidia stock returns (based on many independent environmental variables) which outperform both simple naïve and econometric models. Our contribution to literature is twofold. First, we provide an added value to the strand of literature on the choice of model class to the stock returns prediction problem. Second, our study contributes to the thread of selecting exogenous variables and the need for their stationarity in the case of time series models.
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