Conditional heteroskedasticity is often encountered in economic and financial time series. Since the introduction of autoregressive conditional heteroskedasticity (ARCH) by Engle in 1982, modelling volatility has received much attention in financial econometrics. Conditional heteroskedasticity also causes many asymptotic tests in time series models not to be valid. For example, tests for autocorrelation typically assume independent and identically distributed errors. The wild bootstrap provides a solution to the problem with inference under conditional heteroskedasticity. This thesis consists of an introduction and four papers dealing with conditional heteroskedasticity in multivariate time series models. The first paper studies wild bootstrap tests for autocorrelation in vector autoregressive (VAR) models with conditional heteroskedasticity. The second paper is an empirical study of tests for cointegration in Chinese stock price data in the presence of conditional heteroskedasticity. The third paper proposes and studies a new Lagrange multiplier test for testing the adequacy of an estimated constant conditional correlation generalized ARCH model. The fourth paper studies tests for ARCH in VAR models.

Topics in Spatial Econometrics — With Applications to House Prices Spatial effects in data occur when geographical closeness of observations influences the relation between the observations. When two points on a map are close to each other, the observed values on a variable at those points tend to be similar. The further away the two points are from each other, the less similar the observed values tend to be. Recent technical developments, geographical information systems (GIS) and global positioning systems (GPS) have brought about a renewed interest in spatial matters. For instance, it is possible to observe the exact location of an observation and combine it with other characteristics. Spatial econometrics integrates spatial aspects into econometric models and analysis. The thesis concentrates mainly on methodological issues, but the findings are illustrated by empirical studies on house price data. The thesis consists of an introductory chapter and four essays. The introductory chapter presents an overview of topics and problems in spatial econometrics. It discusses spatial effects, spatial weights matrices, especially k-nearest neighbours weights matrices, and various spatial econometric models, as well as estimation methods and inference. Further, the problem of omitted variables, a few computational and empirical aspects, the bootstrap procedure and the spatial J-test are presented. In addition, a discussion on hedonic house price models is included. In the first essay a comparison is made between spatial econometrics and time series analysis. By restricting the attention to unilateral spatial autoregressive processes, it is shown that a unilateral spatial autoregression, which enjoys similar properties as an autoregression with time series, can be defined. By an empirical study on house price data the second essay shows that it is possible to form coordinate-based, spatially autoregressive variables, which are at least to some extent able to replace the spatial structure in a spatial econometric model. In the third essay a strategy for specifying a k-nearest neighbours weights matrix by applying the spatial J-test is suggested, studied and demonstrated. In the final fourth essay the properties of the asymptotic spatial J-test are further examined. A simulation study shows that the spatial J-test can be used for distinguishing between general spatial models with different k-nearest neighbours weights matrices. A bootstrap spatial J-test is suggested to correct the size of the asymptotic test in small samples.