Empirical finance has growingly relied on statistical methods to draw inferences. Such finance applications require tailoring the methods to particular problems, especially when the underlying assumptions are violated in the data. This dissertation studies the development and application of statistical methodologies to address empirical problems in the contexts of empirical asset pricing, household finance and investments.

The dissertation consists of four chapters. The first chapter gives an overview of the empirical problems and associated statistical issues for three different finance settings: stock return predictability, house price comovement and mutual fund performance. It also briefly outlines the main contribution of this dissertation in each setting. The second chapter develops a robust methodology of unit root testing and statistical inference for autoregressive processes when the errors are heteroscedastic and heavy-tailed. Applications of the robust test demonstrate that some commonly used financial ratios for stock return predictability are highly persistent with unit roots. The third chapter introduces a new nonparametric framework for estimating and testing comovements among U.S. regional home prices. Comovements are found to be strong in housing prices of four U.S. states, but there is little empirical support for asymmetric tail dependence. The fourth chapter comprehensively studies the bootstrap inference problem in fund performance evaluation. It shows the inadequate size and power properties of two existing bootstrap tests and develops the theory for a valid bootstrap Hotelling’s T-squared test. The new bootstrap test, applied in a sequential testing procedure, identifies a small set of skilled funds. Skilled funds are more engaged in active management and hold stocks with higher expected anomalous returns.