Common Features in Vector Nonlinear Time Series Models

This thesis consists of four manuscripts in the area of nonlinear time series econometrics on topics of testing, modeling and forecasting nonlinear common features. The aim of this thesis is to develop new econometric contributions for hypothesis testing and forecasting in these area. Both stationary and nonstationary time series are concerned. A definition of common features is proposed in an appropriate way to each class. Based on the definition, a vector nonlinear time series model with common features is set up for testing for common features. The proposed models are available for forecasting as well after being well specified. The first paper addresses a testing procedure on nonstationary time series. A class of nonlinear cointegration, smooth-transition (ST) cointegration, is examined. The ST cointegration nests the previously developed linear and threshold cointegration. An Ftypetest for examining the ST cointegration is derived when stationary transition variables are imposed rather than nonstationary variables. Later ones drive the test standard, while the former ones make the test nonstandard. This has important implications for empirical work. It is crucial to distinguish between the cases with stationary and nonstationary transition variables so that the correct test can be used. The second and the fourth papers develop testing approaches for stationary time series. In particular, the vector ST autoregressive (VSTAR) model is extended to allow for common nonlinear features (CNFs). These two papers propose a modeling procedure and derive tests for the presence of CNFs. Including model specification using the testing contributions above, the third paper considers forecasting with vector nonlinear time series models and extends the procedures available for univariate nonlinear models. The VSTAR model with CNFs and the ST cointegration model in the previous papers are exemplified in detail,and thereafter illustrated within two corresponding macroeconomic data sets.

First-principle data-driven models for assessment of motor disorders in Parkinson’s disease

Parkinson’s disease (PD) is an increasing neurological disorder in an aging society. The motor and non-motor symptoms of PD advance with the disease progression and occur in varying frequency and duration. In order to affirm the full extent of a patient’s condition, repeated assessments are necessary to adjust medical prescription. In clinical studies, symptoms are assessed using the unified Parkinson’s disease rating scale (UPDRS). On one hand, the subjective rating using UPDRS relies on clinical expertise. On the other hand, it requires the physical presence of patients in clinics which implies high logistical costs. Another limitation of clinical assessment is that the observation in hospital may not accurately represent a patient’s situation at home. For such reasons, the practical frequency of tracking PD symptoms may under-represent the true time scale of PD fluctuations and may result in an overall inaccurate assessment. Current technologies for at-home PD treatment are based on data-driven approaches for which the interpretation and reproduction of results are problematic.  The overall objective of this thesis is to develop and evaluate unobtrusive computer methods for enabling remote monitoring of patients with PD. It investigates first-principle data-driven model based novel signal and image processing techniques for extraction of clinically useful information from audio recordings of speech (in texts read aloud) and video recordings of gait and finger-tapping motor examinations. The aim is to map between PD symptoms severities estimated using novel computer methods and the clinical ratings based on UPDRS part-III (motor examination). A web-based test battery system consisting of self-assessment of symptoms and motor function tests was previously constructed for a touch screen mobile device. A comprehensive speech framework has been developed for this device to analyze text-dependent running speech by: (1) extracting novel signal features that are able to represent PD deficits in each individual component of the speech system, (2) mapping between clinical ratings and feature estimates of speech symptom severity, and (3) classifying between UPDRS part-III severity levels using speech features and statistical machine learning tools. A novel speech processing method called cepstral separation difference showed stronger ability to classify between speech symptom severities as compared to existing features of PD speech. In the case of finger tapping, the recorded videos of rapid finger tapping examination were processed using a novel computer-vision (CV) algorithm that extracts symptom information from video-based tapping signals using motion analysis of the index-finger which incorporates a face detection module for signal calibration. This algorithm was able to discriminate between UPDRS part III severity levels of finger tapping with high classification rates. Further analysis was performed on novel CV based gait features constructed using a standard human model to discriminate between a healthy gait and a Parkinsonian gait. The findings of this study suggest that the symptom severity levels in PD can be discriminated with high accuracies by involving a combination of first-principle (features) and data-driven (classification) approaches. The processing of audio and video recordings on one hand allows remote monitoring of speech, gait and finger-tapping examinations by the clinical staff. On the other hand, the first-principles approach eases the understanding of symptom estimates for clinicians. We have demonstrated that the selected features of speech, gait and finger tapping were able to discriminate between symptom severity levels, as well as, between healthy controls and PD patients with high classification rates. The findings support suitability of these methods to be used as decision support tools in the context of PD assessment.

Fitting spatial models in the R package: hglm

We present a new version of the hglm package for fittinghierarchical generalized linear models (HGLM) with spatially correlated random effects. A CAR family for conditional autoregressive random effects was implemented. Eigen decomposition of the matrix describing the spatial structure (e.g. the neighborhood matrix) was used to transform the CAR random effectsinto an independent, but heteroscedastic, gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR model.This gives a computationally efficient algorithm for moderately sized problems (e.g. n<5000).