Three Essays on Financial Econometrics

This dissertation develops several econometric techniques to address three issues in financial economics, namely, constructing a real estate price index, estimating structural break points, and estimating integrated variance in the presence of market microstructure noise and the corresponding microstructure noise function.

Chapter 2 develops a new methodology for constructing a real estate price index that utilizes all transaction price information, encompassing both single-sales and repeat-sales. The method is less susceptible to specification error than standard hedonic methods and is not subject to the sample selection bias involved in indexes that rely only on repeat sales. The methodology employs a model design that uses a sale pairing process based on the individual building level, rather than the individual house level as is used in the repeat-sales method. The approach extends ideas from repeat-sales methodology in a way that accommodates much wider datasets. In an empirical analysis of the methodology, we fit the model to the private residential property market in Singapore between Q1 1995 and Q2 2014, covering several periods of major price fluctuation and changes in government macroprudential policy. The index is found to perform much better in out-of-sample prediction exercises than either the S&P/Case-Shiller index or the index based on standard hedonic methods. In a further empirical application, the recursive dating method of Phillips, Shi and Yu (2015a, 2015b) is used to detect explosive behavior in the Singapore real estate market. Explosive behavior in the new index is found to arise two quarters earlier than in the other indices.

Chapter 3, based on the Girsanov theorem, obtains the exact finite sample distribution of the maximum likelihood estimator of structural break points in a continuous time model. The exact finite sample theory suggests that, in empirically realistic situations, there is a strong finite sample bias in the estimator of structural break points. This property is shared by least squares estimator of both the absolute structural break point and the fractional structural break point in discrete time models. A simulation-based method based on the indirect estimation approach is proposed to reduce the bias both in continuous time and discrete time models. Monte Carlo studies show that the indirect estimation method achieves substantial bias reductions. However, since the binding function has a slope less than one, the variance of the indirect estimator is larger than that of the original estimator.

Chapter 4 develops a novel panel data approach to estimating integrated variance and testing microstructure noise using high frequency data. Under weak conditions on the underlying efficient price process and the nature of high frequency noise contamination, we employ nonparametric kernel methods to estimate a model that accommodates a very general formulation of the effects of microstructure noise. The methodology pools information in the data across different days, leading to a panel model form that enhances efficiency in estimation and produces a convenient approach to testing the linear noise effect that is conventional in existing procedures. Asymptotic theory is developed for the nonparametric estimates and test statistics.