Joint Regression and Association Models for Repeated Categorical Responses

The focus of this study is on statistical analysis of categorical responses, where the response values are dependent of each other. The most typical example of this kind of dependence is when repeated responses have been obtained from the same study unit. For example, in Paper I, the response of interest is the pneumococcal nasopharengyal carriage (yes/no) on 329 children. For each child, the carriage is measured nine times during the first 18 months of life, and thus repeated respones on each child cannot be assumed independent of each other. In the case of the above example, the interest typically lies in the carriage prevalence, and whether different risk factors affect the prevalence. Regression analysis is the established method for studying the effects of risk factors. In order to make correct inferences from the regression model, the associations between repeated responses need to be taken into account. The analysis of repeated categorical responses typically focus on regression modelling. However, further insights can also be gained by investigating the structure of the association. The central theme in this study is on the development of joint regression and association models. The analysis of repeated, or otherwise clustered, categorical responses is computationally difficult. Likelihood-based inference is often feasible only when the number of repeated responses for each study unit is small. In Paper IV, an algorithm is presented, which substantially facilitates maximum likelihood fitting, especially when the number of repeated responses increase. In addition, a notable result arising from this work is the freely available software for likelihood-based estimation of clustered categorical responses.

Generalised regression estimation for domain class frequencies

This study examines the properties of Generalised Regression (GREG) estimators for domain class frequencies and proportions. The family of GREG estimators forms the class of design-based model-assisted estimators. All GREG estimators utilise auxiliary information via modelling. The classic GREG estimator with a linear fixed effects assisting model (GREG-lin) is one example. But when estimating class frequencies, the study variable is binary or polytomous. Therefore logistic-type assisting models (e.g. logistic or probit model) should be preferred over the linear one. However, other GREG estimators than GREG-lin are rarely used, and knowledge about their properties is limited. This study examines the properties of L-GREG estimators, which are GREG estimators with fixed-effects logistic-type models. Three research questions are addressed. First, I study whether and when L-GREG estimators are more accurate than GREG-lin. Theoretical results and Monte Carlo experiments which cover both equal and unequal probability sampling designs and a wide variety of model formulations show that in standard situations, the difference between L-GREG and GREG-lin is small. But in the case of a strong assisting model, two interesting situations arise: if the domain sample size is reasonably large, L-GREG is more accurate than GREG-lin, and if the domain sample size is very small, estimation of assisting model parameters may be inaccurate, resulting in bias for L-GREG. Second, I study variance estimation for the L-GREG estimators. The standard variance estimator (S) for all GREG estimators resembles the Sen-Yates-Grundy variance estimator, but it is a double sum of prediction errors, not of the observed values of the study variable. Monte Carlo experiments show that S underestimates the variance of L-GREG especially if the domain sample size is minor, or if the assisting model is strong. Third, since the standard variance estimator S often fails for the L-GREG estimators, I propose a new augmented variance estimator (A). The difference between S and the new estimator A is that the latter takes into account the difference between the sample fit model and the census fit model. In Monte Carlo experiments, the new estimator A outperformed the standard estimator S in terms of bias, root mean square error and coverage rate. Thus the new estimator provides a good alternative to the standard estimator.

Detecting Earnings Management Using Neural Networks

Detecting Earnings Management Using Neural Networks. Trying to balance between relevant and reliable accounting data, generally accepted accounting principles (GAAP) allow, to some extent, the company management to use their judgment and to make subjective assessments when preparing financial statements. The opportunistic use of the discretion in financial reporting is called earnings management. There have been a considerable number of suggestions of methods for detecting accrual based earnings management. A majority of these methods are based on linear regression. The problem with using linear regression is that a linear relationship between the dependent variable and the independent variables must be assumed. However, previous research has shown that the relationship between accruals and some of the explanatory variables, such as company performance, is non-linear. An alternative to linear regression, which can handle non-linear relationships, is neural networks. The type of neural network used in this study is the feed-forward back-propagation neural network. Three neural network-based models are compared with four commonly used linear regression-based earnings management detection models. All seven models are based on the earnings management detection model presented by Jones (1991). The performance of the models is assessed in three steps. First, a random data set of companies is used. Second, the discretionary accruals from the random data set are ranked according to six different variables. The discretionary accruals in the highest and lowest quartiles for these six variables are then compared. Third, a data set containing simulated earnings management is used. Both expense and revenue manipulation ranging between -5% and 5% of lagged total assets is simulated. Furthermore, two neural network-based models and two linear regression-based models are used with a data set containing financial statement data from 110 failed companies. Overall, the results show that the linear regression-based models, except for the model using a piecewise linear approach, produce biased estimates of discretionary accruals. The neural network-based model with the original Jones model variables and the neural network-based model augmented with ROA as an independent variable, however, perform well in all three steps. Especially in the second step, where the highest and lowest quartiles of ranked discretionary accruals are examined, the neural network-based model augmented with ROA as an independent variable outperforms the other models.

Modeling and Forecasting Implied Volatility: Implications for Trading, Pricing, and Risk Management

Modeling and forecasting of implied volatility (IV) is important to both practitioners and academics, especially in trading, pricing, hedging, and risk management activities, all of which require an accurate volatility. However, it has become challenging since the 1987 stock market crash, as implied volatilities (IVs) recovered from stock index options present two patterns: volatility smirk(skew) and volatility term-structure, if the two are examined at the same time, presents a rich implied volatility surface (IVS). This implies that the assumptions behind the Black-Scholes (1973) model do not hold empirically, as asset prices are mostly influenced by many underlying risk factors. This thesis, consists of four essays, is modeling and forecasting implied volatility in the presence of options markets’ empirical regularities. The first essay is modeling the dynamics IVS, it extends the Dumas, Fleming and Whaley (DFW) (1998) framework; for instance, using moneyness in the implied forward price and OTM put-call options on the FTSE100 index, a nonlinear optimization is used to estimate different models and thereby produce rich, smooth IVSs. Here, the constant-volatility model fails to explain the variations in the rich IVS. Next, it is found that three factors can explain about 69-88% of the variance in the IVS. Of this, on average, 56% is explained by the level factor, 15% by the term-structure factor, and the additional 7% by the jump-fear factor. The second essay proposes a quantile regression model for modeling contemporaneous asymmetric return-volatility relationship, which is the generalization of Hibbert et al. (2008) model. The results show strong negative asymmetric return-volatility relationship at various quantiles of IV distributions, it is monotonically increasing when moving from the median quantile to the uppermost quantile (i.e., 95%); therefore, OLS underestimates this relationship at upper quantiles. Additionally, the asymmetric relationship is more pronounced with the smirk (skew) adjusted volatility index measure in comparison to the old volatility index measure. Nonetheless, the volatility indices are ranked in terms of asymmetric volatility as follows: VIX, VSTOXX, VDAX, and VXN. The third essay examines the information content of the new-VDAX volatility index to forecast daily Value-at-Risk (VaR) estimates and compares its VaR forecasts with the forecasts of the Filtered Historical Simulation and RiskMetrics. All daily VaR models are then backtested from 1992-2009 using unconditional, independence, conditional coverage, and quadratic-score tests. It is found that the VDAX subsumes almost all information required for the volatility of daily VaR forecasts for a portfolio of the DAX30 index; implied-VaR models outperform all other VaR models. The fourth essay models the risk factors driving the swaption IVs. It is found that three factors can explain 94-97% of the variation in each of the EUR, USD, and GBP swaption IVs. There are significant linkages across factors, and bi-directional causality is at work between the factors implied by EUR and USD swaption IVs. Furthermore, the factors implied by EUR and USD IVs respond to each others’ shocks; however, surprisingly, GBP does not affect them. Second, the string market model calibration results show it can efficiently reproduce (or forecast) the volatility surface for each of the swaptions markets.