Adaptive Estimation of Autoregressive Models with Time-Varying Variances

Stable autoregressive models of known finite order are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the pattern of variance change over time is unknown and may involve shifts at unknown discrete points in time, continuous evolution or combinations of the two. This paper develops kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. These are shown to be asymptotically efficient, having the same limit distribution as the infeasible generalized least squares (GLS). Comparisons of the efficient procedure and the ordinary least squares (OLS) reveal that least squares can be extremely inefficient in some cases while nearly optimal in others. Simulations show that, when least squares work well, the adaptive estimators perform comparably well, whereas when least squares work poorly, major efficiency gains are achieved by the new estimators.Adaptive estimation, Autoregression, Heterogeneity, Weighted regression

Adaptive Estimation of Autoregressive Models with Time-Varying Variances

Stable autoregressive models of known finite order are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the pattern of variance change over time is unknown and may involve shifts at unknown discrete points in time, continuous evolution or combinations of the two. This paper develops kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. These are shown to be asymptotically efficient, having the same limit distribution as the infeasible generalized least squares (GLS). Comparisons of the efficient procedure and ordinary least squares (OLS) reveal that least squares can be extremely inefficient in some cases while nearly optimal in others. Simulations show that, when least squares work well, the adaptive estimators perform comparably well, whereas when least squares work poorly, major efficiency gains are achieved by the new estimators.Adaptive estimation, Autoregression, Heterogeneity, Weighted regression

Tilted Nonparametric Estimation of Volatility Functions with Empirical Applications

This paper proposes a novel positive nonparametric estimator of the conditional variance function without reliance on logarithmic or other transformations. The estimator is based on an empirical likelihood modification of conventional local level nonparametric regression applied to squared mean regression residuals. The estimator is shown to be asymptotically equivalent to the local linear estimator in the case of unbounded support but, unlike that estimator, is restricted to be non-negative in finite samples. It is fully adaptive to the unknown conditional mean function. Simulations are conducted to evaluate the finite sample performance of the estimator. Two empirical applications are reported. One uses cross section data and studies the relationship between occupational prestige and income. The other uses time series data on Treasury bill rates to fit the total volatility function in a continuous-time jump diffusion model

High-Dimensional VARs with Common Factors

This paper studies high-dimensional vector autoregressions (VARs) augmented with common factors that allow for strong cross section dependence. Models of this type provide a convenient mechanism for accommodating the interconnectedness and temporal co-variability that are often present in large dimensional systems. We propose an `1-nuclear-norm regularized estimator and derive non-asymptotic upper bounds for the estimation errors as well as large sample asymptotics for the estimates. A singular value thresholding procedure is used to determine the correct number of factors with probability approaching one. Both the LASSO estimator and the conservative LASSO estimator are employed to improve estimation precision. The conservative LASSO estimates of the non-zero coefficients are shown to be asymptotically equivalent to the oracle least squares estimates. Simulations demonstrate that our estimators perform reasonably well in finite samples given the complex high dimensional nature of the model with multiple unobserved components. In an empirical illustration we apply the methodology to explore the dynamic connectedness in the volatilities of financial asset prices and the transmission of investor fear. The findings reveal that a large proportion of connectedness is due to common factors. Conditional on the presence of these common factors, the results still document remarkable connectedness due to the interactions between the individual variables, thereby supporting a common factor augmented VAR specification

Challenges in the clinical assessment of novel tuberculosis drugs

To effectively tackle the global TB epidemic, novel treatment strategies are critically needed to shorten the duration of TB therapy and treat drug-resistant TB. Drug development for TB, stymied for decades, has enjoyed a renaissance over the past several years. However, development of new TB regimens is hindered by the limitations in our understanding and use of preclinical models; the paucity of accurate, early surrogate markers of cure, and challenges in untangling the individual contributions of drugs to multidrug regimens in a complex, multi-compartment disease. Lack of profit motive, advocacy, and imagination has contributed mightily to the dearth of drugs we have on the shelf to treat this ancient disease. Areas that will speed the development of new regimens for TB include novel murine and in vitro pharmacodynamics models, clinical endpoints that are not culture-based, innovative clinical trial designs, and an infusion of much-needed funding

Unified Factor Model Estimation and Inference under Short and Long Memory

This paper studies a linear panel data model with interactive fixed effects wherein regressors, factors and idiosyncratic error terms are all stationary but with potential long memory. The setup involves a new factor model formulation for which weakly dependent regressors, factors and innovations are embedded as a special case. Standard methods based on principal component decomposition and least squares estimation, as in Bai (2009), are found to suffer bias correction failure because the order of magnitude of the bias is determined in a complex manner by the memory parameters. To cope with this failure and to provide a simple implementable estimation procedure, frequency domain least squares estimation is proposed. The limit distribution of this frequency domain approach is established and a hybrid selection method is developed to determine the number of factors. Simulations show that the frequency domain estimator is robust to short memory and outperforms the time domain estimator when long range dependence is present. An empirical illustration of the approach is provided, examining the long-run relationship between stock return and realized volatility

Adaptive Estimation of Autoregressive Models with Time-Varying Variances

Stable autoregressive models of known finite order are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the pattern of variance change over time is unknown and may involve shifts at unknown discrete points in time, continuous evolution or combinations of the two. This paper develops kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. These are shown to be asymptotically efficient, having the same limit distribution as the infeasible generalized least squares (GLS). Comparisons of the efficient procedure and ordinary least squares (OLS) reveal that least squares can be extremely inefficient in some cases while nearly optimal in others. Simulations show that, when least squares work well, the adaptive estimators perform comparably well, whereas when least squares work poorly, major efficiency gains are achieved by the new estimators

Experimental Biological Protocols with Formal Semantics

Both experimental and computational biology is becoming increasingly automated. Laboratory experiments are now performed automatically on high-throughput machinery, while computational models are synthesized or inferred automatically from data. However, integration between automated tasks in the process of biological discovery is still lacking, largely due to incompatible or missing formal representations. While theories are expressed formally as computational models, existing languages for encoding and automating experimental protocols often lack formal semantics. This makes it challenging to extract novel understanding by identifying when theory and experimental evidence disagree due to errors in the models or the protocols used to validate them. To address this, we formalize the syntax of a core protocol language, which provides a unified description for the models of biochemical systems being experimented on, together with the discrete events representing the liquid-handling steps of biological protocols. We present both a deterministic and a stochastic semantics to this language, both defined in terms of hybrid processes. In particular, the stochastic semantics captures uncertainties in equipment tolerances, making it a suitable tool for both experimental and computational biologists. We illustrate how the proposed protocol language can be used for automated verification and synthesis of laboratory experiments on case studies from the fields of chemistry and molecular programming

Protein/polysaccharide intramolecular electrostatic complex as superior food-grade foaming agent

High-performance foaming agents are widely required in the food industry. In this study, the relationship between electrostatic interaction of whey protein isolate (WPI)/alginate (ALG) and the resultant foaming properties were investigated systematically. The phase diagram of WPI/ALG was established in terms of protein/polysaccharide mixing ratio (r) and pH. The results show that the foaming capacity of WPI/ALG complexes is almost the same across different regions of the phase diagram, while the foam stability varies significantly. At pHs 7.0 and 0.5 where no electrostatic complexation occurs, the foam stability is found to decrease monotonically with decreasing r. At pH 4.0 and particular mixing ratios, i.e., r = 1 and 2, intramolecular soluble complexes are formed and the particular WPI/ALG complexes yield the best foam stability, as compared to other electrostatic complexes or individual components. The half-life (t1/2) of the foams stabilized by the intramolecular electrostatic complexes is as long as 4000 s at a very low WPI/ALG concentration of 0.1% w/w. The foaming properties are in line with the foam viscosity, interfacial adsorption behavior and microstructures of the complexes observed at the air-water interface. This demonstrates that the protein/polysaccharide intramolecular electrostatic complex, more specifically at the stoichiometry, could potentially act as a superior foaming agent in the food industry

Performance evaluation of digital pulse position modulation for wavelength division multiplexing FSO systems impaired by interchannel crosstalk

Wavelength division multiplexing (WDM) has been proposed for fibre, intersatellite, free space and indoor optical communication systems. Digital pulse position modulation (DPPM) is a more power efficient modulation format than on-off keying (OOK) and a strong contender for the modulation of free-space systems. Although DPPM obtains this advantage in exchange for a bandwidth expansion, WDM systems using it are still potentially attractive, particularly for moderate coding levels. However, WDM systems are susceptible to interchannel crosstalk and modelling this in a WDM DPPM system is necessary. Models of varying complexity, based on simplifying assumptions, are presented and evaluated for the case of a single crosstalk wavelength. For a single crosstalk, results can be straightforwardly obtained by artificially imposing the computationally convenient constraint that frames (and thus slots also) align. Multiple crosstalk effects are additionally investigated, for the most practically relevant cases of modest coding level, and using both simulation and analytical methods. In general, DPPM maintains its sensitivity advantage over OOK even in the presence of crosstalk while predicting lower power penalty at low coding level in WDM systems