Statistical methods for causal inference and financial time series analysis

Abstract

This thesis includes three important research topics focusing on statistical methods and their practical applications.

In the first part of this thesis, we aim to evaluate the effects of the "2+26" policy launched by the Chinese government to improve air quality in Beijing-Tianjin-Hebei and its surrounding region. In order to evaluate such policy interventions, we propose a new inverse difference-in-differences (IDID) framework, which can identify the average quasi causal effect under the inverse common trend condition. Using a baseline IDID regression model, we find that the "2+26" policy has a significant effect on improving the air quality, since the policy would reduce the value of Air Quality Index by 9.338 on average, if it had been implemented in the pre-treatment period.

The second part of this thesis proposes a new approach to estimate the conditional moments (CMs). The conditional variance, skewness, and kurtosis play a central role in time series analysis. These three CMs are often studied by some parametric models but with two big issues: the risk of model mis-specification and the instability of model estimation. To avoid the above two issues, this thesis proposes a novel method to estimate these three CMs by the so-called quantiled CMs (QCMs). The QCM method first adopts the idea of Cornish-Fisher expansion to construct a linear regression model, based on $n$ different estimated conditional quantiles. Next, it computes the QCMs simply and simultaneously by using the ordinary least squares estimator of this regression model, without any prior estimation of the conditional mean. Under certain conditions, the QCMs are shown to be consistent with the convergence rate $n^{-1/2}$. Simulation studies indicate that the QCMs perform well under different scenarios of Cornish-Fisher expansion errors and quantile estimation errors. In the application, the QCMs for three exchange rates demonstrate the effectiveness of financial rescue plans during the COVID-19 pandemic outbreak, suggest the unsuitability of the existing "news impact curve" functions for the conditional skewness and kurtosis, and lead to an attractive forecasting method for Value-at-Risk.

The last part of this thesis introduces a novel family of distributions called generalized Laguerred gamma (Glam) distributions that have support on the interval $[0,\infty)$. The Glam distributions are an extension of the generalized gamma distribution, incorporating the use of generalized Laguerre polynomials. We derive the moments of the Glam distributions and explore their properties, including their skewness-kurtosis frontier, modes, and hazard functions. One notable feature of the Glam distributions is their flexible ability to study multi-modality non-negative data. We discuss the estimation of Glam parameters using the maximum likelihood method and conduct a simulation study that validates the desirable properties of the maximum likelihood estimators. Furthermore, we apply the Glam distributions to two real-world datasets, integrating them into the frameworks of generalized linear models and autoregressive conditional duration models. The empirical results demonstrate the exceptional flexibility of Glam distributions in capturing the complex dynamics of real-world phenomena.