Challenges of financial forecasting, such as a dearth of independent samples and non- stationary underlying process, limit the relevance of conventional machine learning towards financial forecasting. Meta-learning approaches alleviate some of these is- sues by allowing the model to generalize across unrelated or loosely related tasks with few observations per task. The neural process family achieves this by con- ditioning forecasts based on a supplied context set at test time. Despite promise, meta-learning approaches remain underutilized in finance. To our knowledge, ours is the first application of neural processes to realized volatility (RV) forecasting and financial forecasting in general. We propose a hybrid temporal convolutional network attentive neural process (ANP- TCN) for the purpose of financial forecasting. The ANP-TCN combines a conven- tional and performant financial time series embedding model (TCN) with an ANP objective. We found ANP-TCN variant models outperformed the base TCN for equity index realized volatility forecasting. In addition, when stack-ensembled with a tree- based model to forecast a trading signal, the ANP-TCN outperformed the baseline buy-and-hold strategy and base TCN model in out-of-sample performance. Across four liquid US equity indices (incl. S&P 500) tested over ∼15 years, the best long-short models (reported by median trajectory) resulted in the following out-of-sample (∼3 years) performance ranges: directional accuracy of 58.65% to 62.26%, compound an- nual growth rate (CAGR) of 0.2176 to 0.4534, and annualized Sharpe ratio of 2.1564 to 3.3375. All project code can be found at: https://github.com/kpa28-git/thesis-code.

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Various approaches for discriminant analysis of longitudinal data are investigated, with some focus on model-based approaches. The latter are typically based on the modi ed Cholesky decomposition of the covariance matrix in a Gaussian mixture; however, non-Gaussian mixtures are also considered. Where applicable, the Bayesian information criterion is used to select the number of components per class. The various approaches are demonstrated on real and simulated data. / Thesis / Master of Science (MSc)

Doctor of Philosophy / Department of Statistics / Weixin Yao / This dissertation contains two projects that are related to varying coefficient models. The traditional least squares based kernel estimates of the varying coefficient model will lose some efficiency when the error distribution is not normal. In the first project, we propose a novel adaptive estimation method that can adapt to different error distributions and provide an efficient EM algorithm to implement the proposed estimation. The asymptotic properties of the resulting estimator is established. Both simulation studies and real data examples are used to illustrate the finite sample performance of the new estimation procedure. The numerical results show that the gain of the adaptive procedure over the least squares estimation can be quite substantial for non-Gaussian errors. In the second project, we propose a unified inference for sparse and dense longitudinal data in time-varying coefficient models. The time-varying coefficient model is a special case of the varying coefficient model and is very useful in longitudinal/panel data analysis. A mixed-effects time-varying coefficient model is considered to account for the within subject correlation for longitudinal data. We show that when the kernel smoothing method is used to estimate the smooth functions in the time-varying coefficient model for sparse or dense longitudinal data, the asymptotic results of these two situations are essentially different. Therefore, a subjective choice between the sparse and dense cases may lead to wrong conclusions for statistical inference. In order to solve this problem, we establish a unified self-normalized central limit theorem, based on which a unified inference is proposed without deciding whether the data are sparse or dense. The effectiveness of the proposed unified inference is demonstrated through a simulation study and a real data application.

In longitudinal studies, outcomes are measured repeatedly over time, but in reality clinical studies are full of missing data points of monotone and non-monotone nature. Often this missingness is related to the unobserved data so that it is non-ignorable. In such context, pattern-mixture model (PMM) is one popular tool to analyze the joint distribution of outcome and missingness patterns. Then the unobserved outcomes are imputed using the distribution of observed outcomes, conditioned on missing patterns. However, the existing methods suffer from model identification issues if data is sparse in specific missing patterns, which is very likely to happen with a small sample size or a large number of repetitions. We extend the existing methods using latent class analysis (LCA) and a shared-parameter PMM. The LCA groups patterns of missingness with similar features and the shared-parameter PMM allows a subset of parameters to be different among latent classes when fitting a model, thus restoring model identifiability. A novel imputation method is also developed using the distribution of observed data conditioned on latent classes. We develop this model for continuous response data and extend it to handle ordinal rating scale data. Our model performs better than existing methods for data with small sample size. The method is applied to two datasets from a phase II clinical trial that studies the quality of life for patients with prostate cancer receiving radiation therapy, and another to study the relationship between the perceived neighborhood condition in adolescence and the drinking habit in adulthood.

Experimental infection (EI) studies, involving the intentional inoculation of animal or human subjects with an infectious agent under controlled conditions, have a long history in infectious disease research. Longitudinal infection response data often arise in EI studies designed to demonstrate vaccine efficacy, explore disease etiology, pathogenesis and transmission, or understand the host immune response to infection. Viral loads, antibody titers, symptom scores and body temperature are a few of the outcome variables commonly studied. Longitudinal EI data are inherently nonlinear, often with single-peaked response trajectories with a common pre- and post-infection baseline. Such data are frequently analyzed with statistical methods that are inefficient and arguably inappropriate, such as repeated measures analysis of variance (RM-ANOVA). Newer statistical approaches may offer substantial gains in accuracy and precision of parameter estimation and power. We propose an alternative approach to modeling single-peaked, longitudinal EI data that incorporates recent developments in nonlinear hierarchical models and Bayesian statistics. We begin by introducing a nonlinear mixed model (NLMM) for a symmetric infection response variable. We employ a standard NLMM assuming normally distributed errors and a Gaussian mean response function. The parameters of the model correspond directly to biologically meaningful properties of the infection response, including baseline, peak intensity, time to peak and spread. Through Monte Carlo simulation studies we demonstrate that the model outperforms RM-ANOVA on most measures of parameter estimation and power. Next we generalize the symmetric NLMM to allow modeling of variables with asymmetric time course. We implement the asymmetric model as a Bayesian nonlinear hierarchical model (NLHM) and discuss advantages of the Bayesian approach. Two illustrative applications are provided. Finally we consider modeling of viral load. For several reasons, a normal-errors model is not appropriate for viral load. We propose and illustrate a Bayesian NLHM with the individual responses at each time point modeled as a Poisson random variable with the means across time points related through a Tricube mean response function. We conclude with discussion of limitations and open questions, and a brief survey of broader applications of these models.