This dissertation consists of three essays. In the first essay, I estimate a high dimensional covariance matrix of returns for 88 individual stocks from the S&P 100 index, using daily return data for 1995-2005. This study applies the two-step estimator of the dynamic conditional correlation multivariate GARCH model, proposed by Engle (2002b) and Engle and Sheppard (2001) and applies variations of this model. This is the first study estimating variances and covariances of returns using a large number of individual stocks (e.g., Engle and Sheppard (2001) use data on various aggregate sub-indexes of stocks). This avoids errors in estimation of GARCH models with contemporaneous aggregation of stocks (e.g. Nijman and Sentana 1996; Komunjer 2001). Second, this is the first multivariate GARCH adopting a systematic general-to-specific approach to specification of lagged returns in the mean equation. Various alternatives to simple GARCH are considered in step one univariate estimation, and econometric results favour an asymmetric EGARCH extension of Engle and Sheppard’s model. In essay two, I aggregate a variance-covariance matrix of return risk (estimated using DCC-MVGARCH in essay one) to an aggregate index of return risk. This measure of risk is compared with the standard approach to measuring risk from a simple univariate GARCH model of aggregate returns. In principle the standard approach implies errors in estimation due to contemporaneous aggregation of stocks. The two measures are compared in terms of correlation and economic values: measures are not perfectly correlated, and the economic value for the improved estimate of risk as calculated here is substantial. Essay three has three parts. The major part is an empirical study of the aggregate risk return tradeoff for U.S. stocks using daily data. Recent research indicates that past risk-return studies suffer from inadequate sample size, and this suggests using daily rather than monthly data. Modeling dynamics/lags is critical in daily models, and apparently this is the first such study to model lags correctly using a general to specific approach. This is also the first risk return study to apply Wu tests for possible problems of endogeneity/measurement error for the risk variable. Results indicate a statistically significant positive relation between expected returns and risk, as is predicted by capital asset pricing models. Development of the Wu test leads naturally into a model relating aggregate risk of returns to economic variables from the risk return study. This is the first such model to include lags in variables based on a general to specific methodology and to include covariances of such variables. I also derive coefficient links between such models and risk-return models, so in theory these models are more closely related than has been realized in past literature. Empirical results for the daily model are consistent with theory and indicate that the economic and financial variables explain a substantial part of variation in daily risk of returns. The first section of this essay also investigates at a theoretical and empirical level several alternative index number approaches for aggregating multivariate risk over stocks. The empirical results indicate that these indexes are highly correlated for this data set, so only the simplest indexes are used in the remainder of the essay.

GARCH models have been widely used in finance to model volatility ever since the introduction of the ARCH model and its extension to the generalized ARCH (GARCH) model. Lately, there has been growing interest in modelling seasonal volatility, most recently with the introduction of the multiplicative seasonal GARCH models. As an application of the multiplicative seasonal GARCH model with real data, call prices from the major stock market index of India are calculated using estimated parameter values. It is shown that a multiplicative seasonal GARCH option pricing model outperforms the Black-Scholes formula and a GARCH(1,1) option pricing formula. A parametric bootstrap procedure is also employed to obtain an interval approximation of the call price. Narrower confidence intervals are obtained using the multiplicative seasonal GARCH model than the intervals provided by the GARCH(1,1) model for data that exhibits multiplicative seasonal GARCH volatility.

<p>This dissertation explores issues regarding the short-lived temporal variation of the equity risk premium. In the past decade, the equity risk premium puzzle is resolved by many competing consumption-based asset pricing models. However, before \cite{btz:vrp:rfs}, the return predictability as an outcome of such models has limited empirical support in the short-run. Nowadays, there has been a consensus of the literature that the short-run equity return's predictability is intimately linked with the variance risk premium---the difference between options-implied and actual realized variation measures.</p><p>In this work, I continue to argue the importance of the short-lived components in the equity risk premium. Specifically, I first provide simulation evidence of the strong return predictability based on the variance risk premium in the U.S. aggregate market, and document new empirical findings in the international setting. Then I attempt to use a structural macro-finance model to guide through the predictability estimation with much more efficiency gain. Finally I decompose the equity risk premium into two short-lived parts --- tail risk and diffusive risk --- and propose a semi-parametric estimation method for each part. The results are arranged in the following order.</p><p>Chapter 1 of the dissertation is co-authored with Tim Bollerslev, James Marrone and Hao Zhou. In this chapter, we demonstrate that statistical finite sample biases cannot ``explain'' this apparent predictability in U.S. market based on variance risk premium. Further corroborating the existing evidence of the U.S., we show that country specific regressions for France, Germany, Japan, Switzerland, the Netherlands, Belgium and the U.K. result in quite similar patterns. Defining a ``global'' variance risk premium, we uncover even stronger predictability and almost identical cross-country patterns through the use of panel regressions. </p><p>Chapter 2 of the dissertation is co-authored with Tim Bollerslev and Hao Zhou. In this chapter, we examine the joint predictability of return and cash flow within a present value framework, by imposing the implications from a long-run risk model that allow for both time-varying volatility and volatility uncertainty. We provide new evidences that the expected return variation and the variance risk premium positively forecast both short-horizon returns \textit{and} dividend growth rates. We also confirm that dividend yield positively forecasts long-horizon returns, but that it does not help in forecasting dividend growth rates. Our equilibrium-based ``structural'' factor GARCH model permits much more accurate inference than %the reduced form VAR and</p><p>univariate regression procedures traditionally employed in the literature. The model also allows for the direct estimation of the underlying economic mechanisms, including a new volatility leverage effect, the persistence of the latent long-run growth component and the two latent volatility factors, as well as the contemporaneous impacts of the underlying ``structural'' shocks.</p><p>In Chapter 3 of the dissertation, I develop a new semi-parametric estimation method based on an extended ICAPM dynamic model incorporating jump tails. The model allows for time-varying, asymmetric jump size distributions and a self-exciting jump intensity process while avoiding commonly used but restrictive affine assumptions on the relationship between jump intensity and volatility. The estimated model implies that the average annual jump risk premium is 6.75\%. The model-implied jump risk premium also has strong explanatory power for short-to-medium run aggregate market returns. Empirically, I present new estimates of the model based equity risk premia of so-called "Small-Big", "Value-Growth" and "Winners-Losers" portfolios. Further, I find that they are all time-varying and all crashed in the 2008 financial crisis. Additionally, both the jump and volatility components of equity risk premia are especially important for the "Winners-Losers" portfolio.</p> / Dissertation

This paper examines return co-movements and volatility spillovers between major exchange rates before and after the introduction of euro. Dynamic correlations and VAR-based spillover index results suggest significant return co-movements and volatility spillovers, however, their extend is, on average, lower in the post-euro period. Co-movements and spillovers are positively associated with extreme episodes and US dollar appreciations. The euro (Deutsche mark) is the dominant net transmitter of volatility, while the British pound the dominant net receiver of volatility in both periods. Nevertheless, cross-market volatility spillovers are bidirectional, and the highest spillovers occur between European markets. (author's abstract)

The purpose of this thesis is to identify the best volatility model for Value-at-Risk(VaR) estimations. We estimate 1 % and 5 % VaR figures for Nordic indices andstocks by using two symmetrical and two asymmetrical GARCH models underdifferent error distributions. Out-of-sample volatility forecasts are produced usinga 500 day rolling window estimation on data covering January 2007 to December2014. The VaR estimates are thereafter evaluated through Kupiec’s test andChristoffersen’s test in order to find the best model. The results suggest thatasymmetrical models perform better than symmetrical models albeit the simpleARCH is often good enough for 1 % VaR estimates.

過去文獻在探究股市報酬率波動行為時，多採用GARCH/ARCH等傳統時間序列模型，但這些模型不能解決波動度的高持續性(persistence)。本文以Gray(1996)提出的一般化狀態轉換模型(GRS-GARCH)為基礎並加入Dueker(1997)所提出的Dispersion設定，建立GRS-GARCH-K以及GRS-GRACH-DF模型來預測股市報酬率波動行為。GRS-GARCH-K模型設定最大的優點是加入Student’s t分配之自由度可隨狀態轉換，使峰態亦可隨狀態轉換，另外GRS-GRACH-DF模型除了擁有GRS-GARCH-K的特性外，還擁有均數復歸的特色。本文以單一狀態下的GARCH-N、GARCH-t模型，以及雙狀態下的GRS-GARCH、GRS-GARCH-K以及GRS-GARCH-DF模型做研究，並以台灣股價加權股價指數為研究樣本，探討並預測股價日報酬率的波動度，最後將波動度代入Black-Scholes選擇權訂價模型，探討模型之其評價效果。 研究顯示，在樣本內以AIC和SBC檢定法則下，GRS-GARCH-DF有最好的配適能力，樣本外的預測能力在MAE、MASE、MAPE三種誤差比較法下，GRS-GARCH-DF相較於GARCH-N、GARCH-t、GRS-GARCH和GRS-GARCH-K四種模型，在訂價方面與市場價格誤差最小，並以DM檢定法證實其統計上的顯著性。因此擁有均數復歸特色的GRS-GARCH-DF在波動度的估計上相較於其他模型來的優異。

Short-term traffic flow forecasting is a critical function in advanced traffic management systems (ATMS) and advanced traveler information systems (ATIS). Accurate forecasting results are useful to indicate future traffic conditions and assist traffic managers in seeking solutions to congestion problems on urban freeways and surface streets. There is new research interest in short-term traffic flow forecasting due to recent developments in ITS technologies. Previous research involves technologies in multiple areas, and a significant number of forecasting methods exist in literature. However, forecasting reliability is not properly addressed in existing studies. Most forecasting methods only focus on the expected value of traffic flow, assuming constant variance when perform forecasting. This method does not consider the volatility nature of traffic flow data. This paper demonstrated that the variance part of traffic flow data is not constant, and dependency exists. A volatility model studies the dependency among the variance part of traffic flow data and provides a prediction range to indicate the reliability of traffic flow forecasting. We proposed an ARIMA-GARCH (Autoregressive Integrated Moving Average- AutoRegressive Conditional Heteroskedasticity) model to study the volatile nature of traffic flow data. Another problem of existing studies is that most methods have limited forecasting abilities when there is missing data in historical or current traffic flow data. We developed a General Regression Neural Network(GRNN) based multivariate forecasting method to deal with this issue. This method uses upstream information to predict traffic flow at the studied site. The study results indicate that the ARIMA-GARCH model outperforms other methods in non-missing data situations, while the GRNN model performs better in missing data situations.

Abstract This thesis considers some linear and nonlinear time series models. In the linear case, the analysis of a large number of short time series generated by a first order autoregressive type model is considered. The conditional and exact maximum likelihood procedures are developed to estimate parameters. Simulation results are presented and compare the bias and the mean square errors of the parameter estimates. In Chapter 3, five important nonlinear models are considered and their time series properties are discussed. The estimating function approach for nonlinear models is developed in detail in Chapter 4 and examples are added to illustrate the theory. A simulation study is carried out to examine the finite sample behavior of these proposed estimates based on the estimating functions.

Universiẗat, Diss.--Köln, 1999. / Literaturverz. S. 168 - 193.

Master-Arbeit Univ. St. Gallen, 2006.