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Backtesting of Time Series Models
Stroukalová, Marika ; Houfková, Lucia (advisor) ; Zichová, Jitka (referee)
Title: Backtesting of Time Series Models Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Lucia Jarešová Supervisor's e-mail address: lucia.jaresova@centrum.cz Abstract: In the present work we study the basic models of financial time series (ARMA, GARCH), we focus on parameter estimation and forecasting in estimated models. We describe the means of estimating parametres and future values in the program R. In the theoretical section we also discuss the features of financial time series, define simple returns and log returns and we introduce the benefits of the log returns. We also apply the white noise model, ARMA(1,1) and GARCH(1,1) on historic time series of logarithmic returns of chosen stock exchange indices, we also backtest 1-step ahead fore- cats and 5-step ahead forecasts and we compare the results of these models. By empirical comparison of real data we also analyze how the models reac- ted on the present financial crisis and evaluate how the normal distribution assumption for the data held up. Keywords: time series, ARMA, GARCH, backtesting. 1
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Software products for financial time series analysis
Vlasáková, Romana ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The present work deals with selected methods suitable to work with financial time series. Firstly, univariate linear models ARMA are introduced, followed by the description of volatility models ARCH and their generalization to GARCH models. There are many modifications of standard GARCH models designed with respect to the nature of financial data, some of which are presented. Another part of the work dealing with multiple time series focuses on VAR models and bivariate GARCH models. The most important part of the work are practical examples of building the theoretically described models in various types of software with built-in procedures for time series analysis. We apply five different types of commercial and non-commercial software, namely EViews, Mathematica, R, S-PLUS and XploRe. The used software products are presented and compared in terms of their capabilities and the results obtained for particular methods.
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Extreme value theory: Empirical analysis of tail behaviour of GARCH models
Šiml, Jan ; Šopov, Boril (advisor) ; Kocourek, David (referee)
This thesis investigates the capability of GARCH-family models to capture the tail properties using Monte Carlo simulation in framework of Conditional Extreme Value Theory. Analysis is carried out for three different GARCH-type models: GARCH, EGARCH, GJR-GARCH using Normal and Student's t-distributed innovations on four well-known stock market indices: S&P 500, FTSE 100, DAX and Nikkei 225. After conducting 3000 simulations of every estimated model, the Hill estimate of shape parameter implied by the GARCH-type models will be calculated and the models' performance will be assessed based on histograms, descriptive statistics and Root Mean Squared Error of simulated Hill estimates. Interesting results and im- plications for further research have been identified. Firstly, we highlight the Normal distribution's inappropriate nature in this case and its inability to capture the tail properties. Furthermore, GJR-GARCHT with t-distributed innovations is identified to be the best model, closely followed by other t-distributed GARCH-type models. Finally, a pattern in all Q-Q plots forecasting the simulation study results is appar- ent, with the exception of the DAX. This anomalous behaviour therefore necessitated further analysis and a significant right tail influence was recorded. Even though Hill estimates...
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International Stock Market Co movements and the Global Financial Crisis
Poldauf, Petr ; Horváth, Roman (advisor) ; Baruník, Jozef (referee)
International Stock Market Co-movements and The Global Financial Crisis Petr Poldauf May 16, 2011 Abstract This thesis investigates development of co-movements among international equity returns at the market and industry level over the period 2000 - 2010. Emphasis is put on the influence of the Global Financial Crisis of 2008/2009. We analyze daily data from major markets in Australia, Brazil, Canada, China, Germany, Japan, Russia, South Africa, the UK, and the USA using GARCH family of models. We find that there are still weakly correlated markets and the influence of the Crisis differs from country to country. The sectoral indices, including the financial sector, were significantly less correlated than the market indices over the whole period. 1
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The Effects of Foreign Exchange Interventions in a Small Open Economy: The Case of the Czech Republic in a World Context
Timko, Jan ; Holub, Tomáš (advisor) ; Dědek, Oldřich (referee)
In this thesis we examine the effect of foreign exchange interventions in small open economy, focusing on the Czech experience. In the first part we model volatility development before and after the intervention using GARCH model. In the second part we estimate relationship between macroeconomical variables using vector autoregressive model. In this part we estimate impulse response function of exchange rate and inflation. In second part of VAR modeling we provide counterfactual analysis, which compare actual development of variables with alternative scenario in which the interventions would not happen . Our results suggest that the interventions is associated with few months delayed decrease in volatility. Base on scenario analysis the interventions increased inflation by approximately 1.5 % and without the intervention the economy would in deflation around -1 % nowadays. KEYWORDS: Vector autoregression, Volatility modelling, Monetary policy, Intervention Author's e-mail: jantimko16@gmail.com Supervisor's e-mail: tomas.holub@cnb.cz
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Value-at-risk forecasting with the ARMA-GARCH family of models during the recent financial crisis
Jánský, Ivo ; Rippel, Milan (advisor) ; Seidler, Jakub (referee)
The thesis evaluates several hundred one-day-ahead VaR forecasting models in the time period between the years 2004 and 2009 on data from six world stock indices - DJI, GSPC, IXIC, FTSE, GDAXI and N225. The models model mean using the AR and MA processes with up to two lags and variance with one of GARCH, EGARCH or TARCH processes with up to two lags. The models are estimated on the data from the in-sample period and their forecasting ac- curacy is evaluated on the out-of-sample data, which are more volatile. The main aim of the thesis is to test whether a model estimated on data with lower volatility can be used in periods with higher volatility. The evaluation is based on the conditional coverage test and is performed on each stock index sepa- rately. Unlike other works in this eld of study, the thesis does not assume the log-returns to be normally distributed and does not explicitly select a partic- ular conditional volatility process. Moreover, the thesis takes advantage of a less known conditional coverage framework for the measurement of forecasting accuracy.
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Modeling Conditional Quantiles of Central European Stock Market Returns
Burdová, Diana ; Baruník, Jozef (advisor) ; Krištoufek, Ladislav (referee)
Most of the literature on Value at Risk concentrates on the unconditional nonparametric or parametric approach to VaR estimation and much less on the direct modeling of conditional quantiles. This thesis focuses on the direct conditional VaR modeling, using the flexible quantile regression and hence imposing no restrictions on the return distribution. We apply semiparamet- ric Conditional Autoregressive Value at Risk (CAViaR) models that allow time-variation of the conditional distribution of returns and also different time-variation for different quantiles on four stock price indices: Czech PX, Hungarian BUX, German DAX and U.S. S&P 500. The objective is to inves- tigate how the introduction of dynamics impacts VaR accuracy. The main contribution lies firstly in the primary application of this approach on Cen- tral European stock market and secondly in the fact that we investigate the impact on VaR accuracy during the pre-crisis period and also the period covering the global financial crisis. Our results show that CAViaR models perform very well in describing the evolution of the quantiles, both in abso- lute terms and relative to the benchmark parametric models. Not only do they provide generally a better fit, they are also able to produce accurate forecasts. CAViaR models may be therefore used as a...
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Forecasting electricity prices in the Czech spot market
Černý, Kryštof ; Lebovič, Michal (advisor) ; Rečka, Lukáš (referee)
This master thesis is focused on analysis and forecasting of hourly and daily electricity price on the deregulated Czech daily electricity market. The methods used for estimating and forecasting hourly and daily prices are picked from the ARIMA-GARCH family of models and Neural Networks. For daily price data, the Redundant Haar Wavelet Transform decomposition of the time series is used in combination with ARIMA and Neural Networks models for forecasting. For hourly data, ARIMA and Neural Network models are considered. The forecasting results of daily data indicate that simpler models such as seasonal ARIMA outperform all other methods. Also the wavelet decomposi- tion of the daily series didn't prove useful in enhancing the forecast precision. For hourly data, the Multilayer Perceptron architecture of the neural network outperformed the ARIMA forecast. JEL Classification C20, C22, C45, C53, C65 Keywords Forecasting, Time Series, ARIMA, GARCH, Neural Net- works, Wavelet Transform Author's e-mail krystof.cerny@gmail.com Supervisor's e-mail lebovicm@gmail.com 1
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The Inflation-Output Variability Relationship in the CEE countries: A Bivariate GARCH Model
Kubovič, Jozef ; Čech, František (advisor) ; Červinka, Michal (referee)
This thesis examines the output-variability relationship and causal relationships among the inflation, the output growth and their uncertainties for the Central and Eastern European region during the period of time that covers the economic crisis of 2008. We apply the bivariate GARCH(1,1) model with the constant conditional correlation covariance matrix to obtain conditional variances that proxy the two uncertainties and use Granger causality test to determine the causal effects among four variables. We come up with a number of interesting results. First, we did not find statistical evidence neither for the inflation-output variability relationship nor for the Phillips curve. Second, we uncovered support for the positive causal effect of the inflation on its uncertainty and negative causal effect for the reverse direction. Additionally, we also found some support for the indirect negative causal effect of the inflation on the output growth. These results support the policy of low and stable inflation in the countries. Finally, we showed that crisis has a significant impact on the results, changing the behaviour of conditional variances and causal effects among the variables. Powered by TCPDF (www.tcpdf.org)
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Forecasting with neural network during covid-19 crisis
Luu Danh, Tiep ; Baruník, Jozef (advisor) ; Kukačka, Jiří (referee)
The thesis concerns the topic of forecasting using Neural Networks, particu- larly the return and volatility forecasting in the volatile period of Covid-19. The thesis uses adjusted close daily data from Jan 1, 2000, until Jan 1, 2021, of the S&P index and Prague Exchange Stock index (PX). The comparison was between the vanilla econometrical model, a neural network model, and a hybrid neural network model. Hybrid neural networks were constructed with an additional feature column of the fitted econometrical model. Additionally to comparing the prediction, a risk-return trade-o analysis of the forecasted series was conducted. The test period for all models was from Jan 1, 2020, until Jan 1, 2021, where predictions were made. During the test period, MSE be- tween predicted and true values was extracted and compared. The results are that the hybrid model outperformed both econometrical as well as only neural networks models. Furthermore, the risk-return trade-o forecast provided by the hybrid model fares better than the other ones. JEL Classification C53, C81 Keywords Financial Time Series, Forecasting, Neural Net- works, ARIMA, GARCH Title Forecasting with Neural Network during Covid- 19 Crisis Author's e-mail tiep.luud@gmail.com Supervisor's e-mail barunik@fsv.cuni.cz
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