An Empirical Comparison of Linear and Nonlinear Volatility Models for Nordic Stock Returns

This paper examines how volatility in financial markets can preferable be modeled. The examination investigates how good the models for the volatility, both linear and nonlinear, are in absorbing skewness and kurtosis. The examination is done on the Nordic stock markets, including Finland, Sweden, Norway and Denmark. Different linear and nonlinear models are applied, and the results indicates that a linear model can almost always be used for modeling the series under investigation, even though nonlinear models performs slightly better in some cases. These results indicate that the markets under study are exposed to asymmetric patterns only to a certain degree. Negative shocks generally have a more prominent effect on the markets, but these effects are not really strong. However, in terms of absorbing skewness and kurtosis, nonlinear models outperform linear ones.

Modeling Nonlinearities and Asymmetries in Asset Pricing

Financial time series tend to behave in a manner that is not directly drawn from a normal distribution. Asymmetries and nonlinearities are usually seen and these characteristics need to be taken into account. To make forecasts and predictions of future return and risk is rather complicated. The existing models for predicting risk are of help to a certain degree, but the complexity in financial time series data makes it difficult. The introduction of nonlinearities and asymmetries for the purpose of better models and forecasts regarding both mean and variance is supported by the essays in this dissertation. Linear and nonlinear models are consequently introduced in this dissertation. The advantages of nonlinear models are that they can take into account asymmetries. Asymmetric patterns usually mean that large negative returns appear more often than positive returns of the same magnitude. This goes hand in hand with the fact that negative returns are associated with higher risk than in the case where positive returns of the same magnitude are observed. The reason why these models are of high importance lies in the ability to make the best possible estimations and predictions of future returns and for predicting risk.

Monetary policy rules and estimated reaction functions for the European Central Bank

This thesis studies the interest-rate policy of the ECB by estimating monetary policy rules using real-time data and central bank forecasts. The aim of the estimations is to try to characterize a decade of common monetary policy and to look at how different models perform at this task.The estimated rules include: contemporary Taylor rules, forward-looking Taylor rules, nonlinearrules and forecast-based rules. The nonlinear models allow for the possibility of zone-like preferences and an asymmetric response to key variables. The models therefore encompass the most popular sub-group of simple models used for policy analysis as well as the more unusual non-linear approach. In addition to the empirical work, this thesis also contains a more general discussion of monetary policy rules mostly from a New Keynesian perspective. This discussion includes an overview of some notable related studies, optimal policy, policy gradualism and several other related subjects. The regression estimations are performed with either least squares or the generalized method of moments depending on the requirements of the estimations. The estimations use data from both the Euro Area Real-Time Database and the central bank forecasts published in ECB Monthly Bulletins. These data sources represent some of the best data that is available for this kind of analysis. The main results of this thesis are that forward-looking behavior appears highly prevalent, but that standard forward-looking Taylor rules offer only ambivalent results with regard to inflation. Nonlinear models are shown to work, but on the other hand do not have a strong rationale over a simpler linear formulation. However, the forecasts appear to be highly useful in characterizing policy and may offer the most accurate depiction of a predominantly forward-looking central bank. In particular the inflation response appears much stronger while the output response becomes highly forward-looking as well.

Diagnostic Tests Based on Quantile Residuals for Nonlinear Time Series Models

This thesis studies quantile residuals and uses different methodologies to develop test statistics that are applicable in evaluating linear and nonlinear time series models based on continuous distributions. Models based on mixtures of distributions are of special interest because it turns out that for those models traditional residuals, often referred to as Pearson's residuals, are not appropriate. As such models have become more and more popular in practice, especially with financial time series data there is a need for reliable diagnostic tools that can be used to evaluate them. The aim of the thesis is to show how such diagnostic tools can be obtained and used in model evaluation. The quantile residuals considered here are defined in such a way that, when the model is correctly specified and its parameters are consistently estimated, they are approximately independent with standard normal distribution. All the tests derived in the thesis are pure significance type tests and are theoretically sound in that they properly take the uncertainty caused by parameter estimation into account. -- In Chapter 2 a general framework based on the likelihood function and smooth functions of univariate quantile residuals is derived that can be used to obtain misspecification tests for various purposes. Three easy-to-use tests aimed at detecting non-normality, autocorrelation, and conditional heteroscedasticity in quantile residuals are formulated. It also turns out that these tests can be interpreted as Lagrange Multiplier or score tests so that they are asymptotically optimal against local alternatives. Chapter 3 extends the concept of quantile residuals to multivariate models. The framework of Chapter 2 is generalized and tests aimed at detecting non-normality, serial correlation, and conditional heteroscedasticity in multivariate quantile residuals are derived based on it. Score test interpretations are obtained for the serial correlation and conditional heteroscedasticity tests and in a rather restricted special case for the normality test. In Chapter 4 the tests are constructed using the empirical distribution function of quantile residuals. So-called Khmaladze s martingale transformation is applied in order to eliminate the uncertainty caused by parameter estimation. Various test statistics are considered so that critical bounds for histogram type plots as well as Quantile-Quantile and Probability-Probability type plots of quantile residuals are obtained. Chapters 2, 3, and 4 contain simulations and empirical examples which illustrate the finite sample size and power properties of the derived tests and also how the tests and related graphical tools based on residuals are applied in practice.

Nonlinear mixture autoregressive model: economic applications

The aim of this dissertation is to model economic variables by a mixture autoregressive (MAR) model. The MAR model is a generalization of linear autoregressive (AR) model. The MAR -model consists of K linear autoregressive components. At any given point of time one of these autoregressive components is randomly selected to generate a new observation for the time series. The mixture probability can be constant over time or a direct function of a some observable variable. Many economic time series contain properties which cannot be described by linear and stationary time series models. A nonlinear autoregressive model such as MAR model can a plausible alternative in the case of these time series. In this dissertation the MAR model is used to model stock market bubbles and a relationship between inflation and the interest rate. In the case of the inflation rate we arrived at the MAR model where inflation process is less mean reverting in the case of high inflation than in the case of normal inflation. The interest rate move one-for-one with expected inflation. We use the data from the Livingston survey as a proxy for inflation expectations. We have found that survey inflation expectations are not perfectly rational. According to our results information stickiness play an important role in the expectation formation. We also found that survey participants have a tendency to underestimate inflation. A MAR model has also used to model stock market bubbles and crashes. This model has two regimes: the bubble regime and the error correction regime. In the error correction regime price depends on a fundamental factor, the price-dividend ratio, and in the bubble regime, price is independent of fundamentals. In this model a stock market crash is usually caused by a regime switch from a bubble regime to an error-correction regime. According to our empirical results bubbles are related to a low inflation. Our model also imply that bubbles have influences investment return distribution in both short and long run.