Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence

This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures converge to functionals of fractional Ornstein--Uhlenbeck processes. We use fractional integrated noise as an example to illustrate the important ideas. In this case, the functionals bear only formal analogy to those in the classical framework with uncorrelated innovations, with Wiener processes being replaced by fractional Brownian motions. It is also shown that limit theorems for the functionals involve nonstandard scaling and nonstandard limiting distributions. Results of this paper shed light on the asymptotic behavior of nearly unstable long-memory processes.This research was supported in part by HKSAR-RGC Grants CUHK400305 and CUHK400306

Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence

This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures converge to functionals of fractional Ornstein--Uhlenbeck processes. We use fractional integrated noise as an example to illustrate the important ideas. In this case, the functionals bear only formal analogy to those in the classical framework with uncorrelated innovations, with Wiener processes being replaced by fractional Brownian motions. It is also shown that limit theorems for the functionals involve nonstandard scaling and nonstandard limiting distributions. Results of this paper shed light on the asymptotic behavior of nearly unstable long-memory processes.Comment: Published in at http://dx.doi.org/10.1214/009053607000000136 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fractional constant elasticity of variance model

This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model is developed. European option pricing formula similar to that of the classical CEV model is obtained and a volatility skew pattern is revealed.Comment: Published at http://dx.doi.org/10.1214/074921706000001012 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Decoding the consumer’s brain: Neural representations of consumer experience

Understanding consumer experience – what consumers think about brands, how they feel about services, whether they like certain products – is crucial to marketing practitioners. ‘Neuromarketing’, as the application of neuroscience in marketing research is called, has generated excitement with the promise of understanding consumers’ minds by probing their brains directly. Recent advances in neuroimaging analysis leverage machine learning and pattern classification techniques to uncover patterns from neuroimaging data that can be associated with thoughts and feelings. In this dissertation, I measure brain responses of consumers by functional magnetic resonance imaging (fMRI) in order to ‘decode’ their mind. In three different studies, I have demonstrated how different aspects of consumer experience can be studied with fMRI recordings. First, I study how consumers think about brand image by comparing their brain responses during passive viewing of visual templates (photos depicting various social scenarios) to those during active visualizing of a brand’s image. Second, I use brain responses during viewing of affective pictures to decode emotional responses during watching of movie-trailers. Lastly, I examine whether marketing videos that evoke s

The Clinical Utility of Zinc Transporter 8 Autoantibody Measurement in Diabetes

Maturity onset diabetes of the young (MODY) is caused by single gene mutations that are of autosomal dominant inheritance. Mutations are highly penetrant, and patients often develop a phenotype similar to type 1 or type 2 diabetes. Glucokinase, Hepatic nuclear factor 1a and 4a mutations consists of 80% of MODY cases. Approximately 1% of patients with diabetes have MODY, and it is often misdiagnosed. Diagnosis is important as patients with MODY often have a good prognosis and glycaemic control if they are treated appropriately. The aim of this thesis was to explore the use of islet autoantibodies, in particular a new autoantibody against Zinc Transporter 8, as biomarkers to identify MODY. A literature review of MODY and its important subtypes are discussed. It highlights the major mutation that cause MODY and the management of patients with MODY is also explored. Islet autoantibodies will also be reviewed in the same chapter, with a discussion on established autoantibodies and ZnT8 autoantibodies in relation to type 1 diabetes. Chapter 1 aims to investigate whether ZnT8 autoantibodies are similar to established autoantibodies against GAD and IA-2 as a biomarker in differentiating T1D patients from MODY patients. The prevalence of ZnT8 autoantibodies in MODY patients and the effect of disease duration on antibody prevalence and discriminative power would also be investigated. In Chapter 2, a study was performed to investigate whether islet autoantibodies are useful in the MODY referral setting in ruling out patients for genetic testing. This is a way to rationalise genetic testing at the Exeter molecular genetics referral service. Additionally, other biomarkers will also be investigated, namely C-peptide levels and Type 1 Diabetes Genetic Risk score. Results from the study will have implications to how MODY is diagnosed at the referral service. A discussion of the findings of each chapter, implications and plans for future research will be explored in chapter 3