This thesis aims to fit and compare different time series models namely the ARIMA-model, conditional heteroscedastic models and lastly a dynamic regression model with ARIMA error to Bitcoin closing price data that spans over 5 consecutive years. The purpose is to evaluate if the sanction on Russia had any effect on the cryptocurrency Bitcoin. After giving a very brief introduction to time series models and the nature of the error term, we describe the models that we want to compare. Quite early in on, autocorrelation was detected and that the time series were nonstationary. Additionally, as we are dealing with financial data, we found that the best alternative was to transform the data into logarithmic return and we then took the first difference. As we then detected a very large outlier, we decided to replace the extreme value with the mean of the two adjacent observations as we suspected it would affect the forecast interval. The dataset with first differenced log-returns was used in the ARIMA model but it turned out that there was no autocorrelation which indicated that returns in financial assets are uncorrelated across time and therefore unpredictable. The conditional heteroscedastic models, the ARCH and the GARCH models turned out to be best suitable for our data, as there was an ARCH-effect present. We could conclude that the GARCH(1,1) model using student t-distribution had the best fit, which had the lowest AIC and the highest log likelihood. In order to study the effect of the sanctions on Bitcoin volatility a dynamic regression model was used by allowing the error term to contain autocorrelation and include an independent dummy variable. The model showed that the Russian invasion of Ukraine did not, surprisingly, have any effect on the Bitcoin closing price.

This paper investigates the diversification characteristics of commodities in relation to the Swedish equity index OMXSPI. Much of the previous literature concludes that gold and oil possess diversification or hedging properties against the US equity markets. The findings from literature investigating other markets or commodities are less conclusive. We apply a DCC-GARCH model on monthly data between 1996 and 2022 and analyze the dynamic conditional correlations between eight commodities, Swedish inflation and OMXSPI. We focus our analysis on three well-known crises and find large variations in the correlation among the assets and between the different crises. We also construct three portfolios, a minimum variance-, maximum Sharpe- and equally weighted portfolio, to investigate if commodities lower the variance of a portfolio based on OMXSPI. We find that aluminum, cocoa, silver and soybeans display diversification characteristics while copper, platinum and rubber are deemed less capable diversifiers. The model returned no significant results between the commodities and inflation. We conclude this could be because of the stable nature of Sweden’s inflation or the low contribution commodities seem to have to the GDP.

The global energy sector is experiencing an transition towards renewable energy, a transition that is mainly driven by issues related to climate change and energy security. In this paper, we investigate the time-varying volatility and risk measures of renewable energy and traditional energy firms. Further, we examine how uncertainty and potential drivers connected to energy security affect the volatilities and returns of renewable energy stocks. By applying the MS- GARCH (1,1) and MS-GJR-GARCH (1,1) approach we calculate the Value at Risk (VaR) and Conditional Value-at Risk (CvaR). We estimate a fixed effects model to determine the impact of the uncertainty variables on the estimated conditional volatility and returns. We contribute to the existing literature by providing a microeconomic perspective on the effects of the transition and by examining the influence of green metal prices. Contrary to previous research our findings indicate that economic policy uncertainty has a positive impact on the returns of renewable stocks. Possibly marking a shift caused by increased engagement towards a renewable transition where the attention from both governments and financial institutions mitigates the negative effects of the uncertainty that previously affected the energy sector. However, the prices of crucial green metals were found to have a negative impact on renewable stocks suggesting that the transition to renewable energy might impose implications regarding energy security if not managed correctly. The main policy implications are that beneficial policies aimed at the green sector should be continued and consistent in order to assist renewable firms during their vulnerable development phase, encourage investment into the sector and speed up the ongoing transition. Further, policies aimed toward ensuring sustainable extraction of green metals and diversifying the sources are needed in order to mitigate the new challenges regarding energy security that the transition might impose.

The purpose of this master’s thesis is to investigate to what extent ESG assets and traditional benchmarks affect one another. Since sustainable investment is a growing segment of the financial market, investors need to be informed about how it may affect their portfolios, and by extension if it can be used for portfolio diversification. By using an AR(1)-GARCH(p,q) model and a Diebold-Yilmaz spillover approach, we can measure the spillover effects between ESG indices and other benchmark indices for both return and volatility. We find that country-level ESG indices are more integrated with other country-level ESG indices than other assets, and that country-level ESG indices transmit more to the MSCI world ESG index, MSCI world equity index, Crude oil, Gold, and our currency index EUR/USD. These findings hold true for both return and volatility spillover. Thus, our policy implications are that including country-level ESG assets in the portfolio can decrease portfolio risk and help minimize the contagious effects of shocks on the portfolio.

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Covid19 hit the world’s financial markets by surprise in March 2020 and ensuing volatility marked an end to the prior low-volatility environment. This Black Swan engendered numerous publications establishing how the equity market responded to the exogenous shock. However, there is no applicable comparison to Nasdaq100 regarding how models perform during extreme conditions such as ante, amid and post Covid19. Furthermore, goodness of fit together with forecasting accuracy are further examined in the light of new intra-day data from Oxford Man Institute covering this time-period. This thesis presents a comparison of volatility models incorporating economic intuition, sentiment, historical values of volatility and stochastics. By exploiting intra-day at 5 min interval the trade-off between noise and loss of valuable information effectively kept at a minimum yielding considerable robustness to the thesis’ result. Linear ARCH-models, Implied Volatility and HARRV applied with the addition of several different combinations of hold-out periods enable multiple vantagepoints for evaluation. This thesis finds HARRV’s series of one-step ahead prediction of future conditional volatility to be superior throughout all hold-out periods. I am able to present empirical evidence supporting the idea that HARRV’s additive cascades of volatility is superior to sentiment-driven implied volatility and ARCH-models pertaining to Nasdaq100.

The global economy has been severely impacted during the Covid-19 period. The U.S. stock market has also experienced greater volatility. Based on data from January 2020 to June 2021, this paper studies the volatility of daily returns on the stock market in the United States. The Standard and Poor's 500 (SPX) index and eight companies traded on major exchanges such as the New York Stock Exchange and the Nasdaq are used to calculate volatility. Combining the statistical analysis methods GARCH, GARCH-M, and TARCH, the time series of each security is modeled. It is demonstrated that the conditional heteroskedasticity of stock returns depends not only on the observed historical volatility (ARCH term) but also on the conditional heteroskedasticity of prior periods (GARCH term). As expected for financial markets, the COVID-19 outbreak increased the volatility of U.S. stock market returns. After the COVID-19 outbreak, the volatility of the U.S. stock market rose dramatically. It reached an extremely high level for the first quarter of 2020 and continued to move downwards in the following quarters. The significant heteroskedasticity in the return volatility indicates that external variables significantly affect the stock. Furthermore, this study combines the Capital Asset Pricing Model (CAPM) and the research of Engle et al. (1987), which provides a way to quantify the liquidity premium. However, with the results of the GARCH-M model, this study does not find a significant liquidity premium over time. Additionally, The TARCH model reveals a significant asymmetry in stock market returns during this epidemic, suggesting that negative news has a more substantial impact on U.S. financial markets. For investors and financial institutions, this research helps identify potential volatility in the face of similar risk events. It is helpful for investors to comprehensively consider various factors when investing in special periods or consider other investment portfolios to reduce investment risks in specific periods based on research results.

Forecasting financial time series is one of the most challenging problems in economics and business. Markets are highly complex due to non-linear factors in data and uncertainty. It moves up and down without any pattern. Based on historical univariate close prices from the S\&P 500, SSE, and FTSE 100 indexes, this thesis forecasts future values using two different approaches: one using a classical method, a Seasonal ARIMA model, and a hybrid ARIMA-GARCH model, while the other uses an LSTM neural network. Each method is used to perform at different forecast horizons. Experimental results have proven that the LSTM and Hybrid ARIMA-GARCH model performs better than the SARIMA model. To measure the model performance we used the Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE).

We propose new estimation methods for the factor loading matrix in modeling multivariate volatility processes. The key step of the methods is based on the weighted scatter estimators, which does not involve optimizing any objective function and was embedded with robust estimation properties. The method can therefore be easily applied to high-dimensional systems without running into computational problems. The estimation is proved to be consistent and the asymptotic distribution is derived. We compare the performance with other estimation methods and demonstrate its superiority when using both simulated data as well as real-world case studies. / Statistics

No / We examine the short-term price reaction of 424 UK stocks to large one-day price changes. Using the GJR-GARCH(1,1), we find no statistical difference amongst the cumulative abnormal returns (CARs) of the Single Index, the Fama–French and the Carhart–Fama–French models. Shocks ⩾5% are followed by a significant one-day CAR of 1% for all the models. Whilst shocks ⩽−5% are followed by a significant one-day CAR of −0.43% for the Single Index, the CARs are around −0.34% for the other two models. Positive shocks of all sizes and negative shocks ⩽−5% are followed by return continuations, whilst the market is efficient following larger negative shocks. The price reaction to shocks is unaffected when we estimate the CARs using the conditional covariances of the pricing variables.