This thesis analyses, derives and evaluates specification tests of Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) regression models, both univariate and multivariate. Of particular interest, in the first half of the thesis, is the derivation of robust test procedures designed to assess the Constant Conditional Correlation (CCC) assumption often employed in multivariate GARCH (MGARCH) models. New asymptotically valid conditional moment tests are proposed which are simple to construct, easily implementable following the full or partial Quasi Maximum Likelihood (QML) estimation and which are robust to non-normality. In doing so, a non-normality robust version of the Tse's (2000) LM test is provided. In addition, a new and easily programmable expressions of the expected Hessian matrix associated with the QMLE is obtained. The finite sample performances of these tests are investigated in an extensive Monte Carlo study, programmed in GAUSS.In the second half of the thesis, attention is devoted to nonparametric testing of GARCH regression models. First simultaneous consistent nonparametric tests of the conditional mean and conditional variance structure of univariate GARCH models are considered. The approach is developed from the Integrated Generalized Spectral (IGS) and Projected Integrated Conditional Moment (PICM) procedures proposed recently by Escanciano (2008 and 2009, respectively) for time series models. Extending Escanciano (2008), a new and simple wild bootstrap procedure is proposed to implement these tests. A Monte Carlo study compares the performance of these nonparametric tests and four parametric tests of nonlinearity and/or asymmetry under a wide range of alternatives. Although the proposed bootstrap scheme does not strictly satisfy the asymptotic requirements, the simulation results demonstrate its ability to control the size extremely well and therefore the power comparison seems justified. Furthermore, this suggests there may exist weaker conditions under which the tests are implementable. The simulation exercise also presents the new evidence of the effect of conditional mean misspecification on various parametric tests of conditional variance. The testing procedures are also illustrated with the help of the S&P 500 data. Finally the PICM and IGS approaches are extended to the MGARCH case. The procedure is illustrated with the help of a bivariate CCC-GARCH model, but can be generalized to other MGARCH specifications. Simulation exercise shows that these tests have satisfactory size and are robust to non-normality. The marginal mean and variance tests have excellent power; however the covariance marginal tests lack power for some alternatives.

Thesis ( M.Sc.(Agricultural Economics)) --University of Limpopo, 2019. / Potato is perceived as an excellent crop in the fight against hunger and poverty. The recent high potato price in South Africa has pushed the vegetable out of reach of the poorest of the poor. The study attempts to analyse potato price volatility in South Africa and furthermore assess how various factors were responsible for the recent potato price volatility. Quarterly data for potato price, number of hectares planted, rainfall and temperature levels from 2006q1 to 2017q4 was collected from various sources and were used for analysis. The total observation of 48. The volatility in the series was determined by performing ARCH/GARCH model. GARCH model indicates an evidence of GARCH effect in the series, meaning that GARCH model influences potato price volatility in South Africa. The Johansen cointegration used both trace and eigenvalue to test the existence of a long run relationship between potato price and various variables. The cointegration results were positive indicating that there exists long run relationship amongst variables. The study further used Johansen cointegration as well as standard error to determine the number of cointegrating variables in the long run. The results indicated that the number of hectares planted and rainfall level have significant relationship with potato price. Wald tests was used to check whether the past values of number of hectares planted and rainfall level influenced the current value of potato price. The Walt test results concluded that there is no evidence of short run causality running from number of hectares planted and rainfall level to potato price. In the study, ECM model was used to forecast the potato price fluctuation in South Africa. The study recommends that farmers need to engage in contract market so as to minimize the risk of potato price volatility. The Department of Agriculture should forecast agricultural commodities price volatility and make information accessible to the farmers so that they are able to adopt strategies that will assist them to overcome crisis.

The primary purpose of this thesis was to investigate if the modern Phillips Curve is valid for ASEAN five (Indonesia, Malaysia, Thailand, Singapore and Philippines) countries using a time-varying approach in the form of an ARMA-GARCH model. The method enables us to investigate how the inflation volatility reacts to economic shocks and if its history can predict the conditional variance of inflation. This study also aimed to investigate whether financial liberalisation affects the conditional variance of inflation. Moreover, we introduce a new parameter into the Phillips Curve. We propose the inclusion of a globally decomposed financial spillover index to see how it affects the inflation dynamics. Examining the period between 1996-2020, using monthly data. We find weak results, and the Phillips Curve was only valid for Singapore. Our findings also suggest that the inflation volatility is highly time-varying, indicating the suitability of the ARMA-GARCH framework. Significant coefficients in the model allow forecasting the conditional variance of inflation. The results support the idea that financial liberalisation to be volatility augmenting in some countries, suggesting a negative relationship between the degree of financial integration and received spillover effects. The globally decomposed spillover indices demonstrated weak results. For further investigations, we, therefore, propose the usage of regionally decomposed spillover indices.

Theses deals with network traffic modeling focused on elaboration by time series analysis. The nature of network traffic is discussed above all http traffic. First three chapters are theoretical, which describes time series and basic models, linear AR, MA, ARMA, ARIMA and nonlinear ARCH. Other chapters define terms like self-similarity and long range dependence. It is demonstrated a failure of conventional models which cannot capture these specific properties of network data traffic. On the basis of study in chapter 6. is closely described the combined ARIMA/GARCH model and its parameter estimation procedure. Applied part of this theses deals with procedure of estimation and fitting the estimation model to observed network traffic. After an estimation a few future values are predicted on the basis of estimated model. These predicted values are consequently compared with real data.

This study explores Bitcoin’s volatility characteristics using different extensions of the GARCH model. The volatility characteristics of bitcoin are compared with to a gold commodity and the S&P 500 index. The purpose is to identify which model fits best for the data and to see how the volatility changes during the time period of 1st February 2017 to 1stFebruary 2022. The dataset is divided into two time periods, one prior to the pandemic which is the low uncertainty period and the other after the pandemic being the high uncertainty period. The attention for cryptocurrencies and especially bitcoin, has risen expeditiously the last couple of years, this makes the analysis appropriate and current for the market. The result showed that bitcoin’s volatility is more effected by the volatility of gold than for S&P 500. The volatility shows that bitcoin was more similar to the behavior of the gold than the S&P 500 prior to the pandemic. Further is there still no clearer explanation and bitcoins behavior cannot be stated as a commodities or financial asset. The GARCH model results showed that bitcoin’s volatility is persistent over time and can therefore be an explanation that will apply well as for the next years. The high volatility time periods of bitcoin can be explained by optimism and overestimate bias. The bias connected the overly confident investment decisions to less accurate rents. Bitcoin is still new on the financial market which makes new knowledge extremely important in order to create safer investment portfolios.

Market risk is the risk of capital loss due to unexpected changes in market prices. One risk measure used to estimate market risk is Value at Risk (VaR). The common historical simulation methodology of VaR forecasting usually does not capture the time-varying volatilities associated with financial data. Therefore, dynamic factor models (DFM) are employed to improve VaR forecasting. The paper’s main focus is to use different volatility model specifications in the DFM to evaluate which is the most appropriate for VaR forecasting. The volatility models considered are the Constant Conditional Correlation (CCC-) GARCH, the Dynamic Conditional Correlation (DCC-) GARCH, and the corrected Dynamic Conditional Correlation (cDCC-) GARCH. The method is applied to an empirical dataset consisting of Swedish large-cap stocks between 2017-2021 where two different portfolios are used, the equally- and the value-weighted portfolio. The data purposefully includes the COVID-19 pandemic such that the models can be compared during less- and more volatile periods. The method is further evaluated in a simulation study where randomized portfolio weights are used. It is found that the VaR forecasts produced by the three different model specifications are similar throughout the entire sample. Therefore the most restricted volatility model (CCC-GARCH) is recommended.

This paper explores the possibility of gold and Bitcoin acting as safe haven investments during the Corona pandemic. To answer the research question the authors use OLS-, GARCH-, and TGARCH-models. The S&P 500 stock- and S&P U.S. Aggregate bond-indexes are used as a measure of the performance on U.S. stock- and bond-market. Safe haven assets have a negative beta during turbulent times and therefore the period of 2020-01-01 to 2022-03-31 will be analyzed. A period of five years leading up to the pandemic as well as the turbulent time period will be used as an average to enable comparison between regular and trying times. The results conclude that neither Bitcoin nor gold can be viewed as safe haven assets. However, it is found that both assets can work as diversifiers in the two markets.

The world has faced tumultuous times in recent years with the COVID-19 pandemic as well as the Russian invasion of Ukraine causing the stock market to be unusually volatile. During such times investors tend to flee to alternative investment opportunities that are uncorrelated or negatively correlated with the stock market, called safe-haven assets. Traditionally, the most prominent safe-haven asset has been gold but with the rise of cryptocurrencies as a new asset class there has been much speculation if they could act as a safe-haven against the stock market. The leading cryptocurrency Bitcoin is often the main target for such research and has even been called “digital gold”. However, some studies have explored the possibility that the second largest cryptocurrency Ethereum has an even greater potential as a safe-have asset. With the stock market crash in 2020 providing the first “real” test if cryptocurrencies can behave as safe-haven assets a myriad of papers on the topic have been published. However, little research has been done taking on the perspective of a Swedish investor. This thesis aims to fill this research gap by investigating whether the two major cryptocurrencies Bitcoin and Ethereum have acted as safe-havens towards the Swedish stock index OMX30 during the COVID-19 crisis and the Russian invasion of Ukraine. For this purpose, DCC-GARCH analysis was conducted, and the results were compared with gold as benchmark of how a more traditional safe-haven asset has behaved. The findings in this study showed that neither Bitcoin or Ethereum have acted as safe-havens during the COVID-19 crisis or the Russian invasion of Ukraine. The study also finds that gold did not act as a safe-haven for the COVID-19 crisis while it did during the Russian invasion of Ukraine. These findings imply that Bitcoin and Ethereum seem to be unable to act as “digital gold” for Swedish investors in a safe-haven and hedging sense. Instead, these cryptocurrencies have only provided diversification benefits during the recent stock market turmoil.

In this thesis, we have built an optimal portfolio using five assets from the Japanese market. We have investigated the use of GARCH(1,1) when forecasting the volatility of our optimal portfolio. Different time periods have been considered for optimizing our results. An equally-weighted portfolio has been used as a benchmark. Our results show that the optimal portfolio we constructed is more efficient than the equally-weighted portfolio in all chosen situations.

In this thesis the performance of the quantile based CAV iaR models is evaluated and compared with GARCH models for predicting the Value at Risk. This is done by one step ahead out of sample prediction. The one step ahead out of sample prediction is done for the 500 observations at the end of the sample. To calculate the predictions a rolling forecast is used. This means that the sample that is used to do the one step ahead predictions is equally sized for all 500 predictions. Then tests are performed to evaluate the predictive power of the forecasts. The tests that are used to evaluate the predictions are: the dynamic quantile test, the Kupiec test and the Christoffersens test. The data that is used in the analysis are two stock indexes and one exchange rate index. What is concluded from the thesis is that the models perform good in general for the Stockholmsb ̈orsen data. For the First north data the 1% V aR produced too high risk predictions so the exceedance rate became too low. For the 5% V aR the predictions were more accurate. For the exchange rate data the predictions from the models were generally good as well.