Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.

Estimating economic relationships subject to firm- and time-varying equality and inequality constraints

Applied econometricians often fail to impose economic regularity constraints in the exact form economic theory prescribes. We show how the Singular Value Decomposition (SVD) Theorem and Markov Chain Monte Carlo (MCMC) methods can be used to rigorously impose time- and firm-varying equality and inequality constraints. To illustrate the technique we estimate a system of translog input demand functions subject to all the constraints implied by economic theory, including observation-varying symmetry and concavity constraints. Results are presented in the form of characteristics of the estimated posterior distributions of functions of the parameters. Copyright (C) 2001 John Wiley Sons, Ltd.

An aggregate sales model for consumer durables incorporating a time-varying mean replacement age

Forecasting category or industry sales is a vital component of a company's planning and control activities. Sales for most mature durable product categories are dominated by replacement purchases. Previous sales models which explicitly incorporate a component of sales due to replacement assume there is an age distribution for replacements of existing units which remains constant over time. However, there is evidence that changes in factors such as product reliability/durability, price, repair costs, scrapping values, styling and economic conditions will result in changes in the mean replacement age of units. This paper develops a model for such time-varying replacement behaviour and empirically tests it in the Australian automotive industry. Both longitudinal census data and the empirical analysis of the replacement sales model confirm that there has been a substantial increase in the average aggregate replacement age for motor vehicles over the past 20 years. Further, much of this variation could be explained by real price increases and a linear temporal trend. Consequently, the time-varying model significantly outperformed previous models both in terms of fitting and forecasting the sales data. Copyright (C) 2001 John Wiley & Sons, Ltd.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

Search for time variation of the fine structure constant

An order of magnitude sensitivity gain is described for using quasar spectra to investigate possible time or space variation in the fine structure constant alpha. Applied to a sample of 30 absorption systems, spanning redshifts 0.5 < z < 1.6, we derive limits on variations in alpha over a wide range of epochs. For the whole sample, Delta alpha/alpha = (-1.1 +/- 0.4) x 10(-5). This deviation is dominated by measurements at z > 1, where Delta alpha/alpha = (-1.9 +/- 0.5) x 10(-5). For z < 1, Delta alpha/alpha = (-0.2 +/- 0.4) x 10(-5). While this is consistent with a time-varying alpha, further work is required to explore possible systematic errors in the data, although careful searches have so far revealed none.

Enhanced detection-guided NLMS estimation of sparse FIR-modeled signal channels

In various signal-channel-estimation problems, the channel being estimated may be well approximated by a discrete finite impulse response (FIR) model with sparsely separated active or nonzero taps. A common approach to estimating such channels involves a discrete normalized least-mean-square (NLMS) adaptive FIR filter, every tap of which is adapted at each sample interval. Such an approach suffers from slow convergence rates and poor tracking when the required FIR filter is "long." Recently, NLMS-based algorithms have been proposed that employ least-squares-based structural detection techniques to exploit possible sparse channel structure and subsequently provide improved estimation performance. However, these algorithms perform poorly when there is a large dynamic range amongst the active taps. In this paper, we propose two modifications to the previous algorithms, which essentially remove this limitation. The modifications also significantly improve the applicability of the detection technique to structurally time varying channels. Importantly, for sparse channels, the computational cost of the newly proposed detection-guided NLMS estimator is only marginally greater than that of the standard NLMS estimator. Simulations demonstrate the favourable performance of the newly proposed algorithm. © 2006 IEEE.

Modelling pre-clearing vegetation distribution using GIS-integrated statistical, ecological and data models: A case study from the wet tropics of Northeastern Australia

Traditional vegetation mapping methods use high cost, labour-intensive aerial photography interpretation. This approach can be subjective and is limited by factors such as the extent of remnant vegetation, and the differing scale and quality of aerial photography over time. An alternative approach is proposed which integrates a data model, a statistical model and an ecological model using sophisticated Geographic Information Systems (GIS) techniques and rule-based systems to support fine-scale vegetation community modelling. This approach is based on a more realistic representation of vegetation patterns with transitional gradients from one vegetation community to another. Arbitrary, though often unrealistic, sharp boundaries can be imposed on the model by the application of statistical methods. This GIS-integrated multivariate approach is applied to the problem of vegetation mapping in the complex vegetation communities of the Innisfail Lowlands in the Wet Tropics bioregion of Northeastern Australia. The paper presents the full cycle of this vegetation modelling approach including sampling sites, variable selection, model selection, model implementation, internal model assessment, model prediction assessments, models integration of discrete vegetation community models to generate a composite pre-clearing vegetation map, independent data set model validation and model prediction's scale assessments. An accurate pre-clearing vegetation map of the Innisfail Lowlands was generated (0.83r(2)) through GIS integration of 28 separate statistical models. This modelling approach has good potential for wider application, including provision of. vital information for conservation planning and management; a scientific basis for rehabilitation of disturbed and cleared areas; a viable method for the production of adequate vegetation maps for conservation and forestry planning of poorly-studied areas. (c) 2006 Elsevier B.V. All rights reserved.

Heart rate variability characterization using a time-frequency based instantaneous frequency estimation technique

In this paper, a new method for characterizing the newborn heart rate variability (HRV) is proposed. The central of the method is the newly proposed technique for instantaneous frequency (IF) estimation specifically designed for nonstationary multicomponen signals such as HRV. The new method attempts to characterize the newborn HRV using features extracted from the time–frequency (TF) domain of the signal. These features comprise the IF, the instantaneous bandwidth (IB) and instantaneous energy (IE) of the different TF components of the HRV. Applied to the HRV of both normal and seizure suffering newborns, this method clearly reveals the locations of the spectral peaks and their time-varying nature. The total energy of HRV components, ET and ratio of energy concentrated in the low-frequency (LF) to that in high frequency (HF) components have been shown to be significant features in identifying the HRV of newborn with seizures.

A Nonstationary Model of Newborn EEG

The detection of seizure in the newborn is a critical aspect of neurological research. Current automatic detection techniques are difficult to assess due to the problems associated with acquiring and labelling newborn electroencephalogram (EEG) data. A realistic model for newborn EEG would allow confident development, assessment and comparison of these detection techniques. This paper presents a model for newborn EEG that accounts for its self-similar and non-stationary nature. The model consists of background and seizure sub-models. The newborn EEG background model is based on the short-time power spectrum with a time-varying power law. The relationship between the fractal dimension and the power law of a power spectrum is utilized for accurate estimation of the short-time power law exponent. The newborn EEG seizure model is based on a well-known time-frequency signal model. This model addresses all significant time-frequency characteristics of newborn EEG seizure which include; multiple components or harmonics, piecewise linear instantaneous frequency laws and harmonic amplitude modulation. Estimates of the parameters of both models are shown to be random and are modelled using the data from a total of 500 background epochs and 204 seizure epochs. The newborn EEG background and seizure models are validated against real newborn EEG data using the correlation coefficient. The results show that the output of the proposed models has a higher correlation with real newborn EEG than currently accepted models (a 10% and 38% improvement for background and seizure models, respectively).

Determination of T1pH relaxation rates in charred and uncharred wood and consequences for NMR quantitation

The performance of three different techniques for determining proton rotating frame relaxation rates (T1pH) in charred and uncharred woods is compared. The variable contact time (VCT) experiment is shown to over-estimate T1pH, particularly for the charred samples, due to the presence of slowly cross-polarizing C-13 nuclei. The variable spin (VSL) or delayed contact experiment is shown to overcome these problems; however, care is needed in the analysis to ensure rapidly relaxing components are not overlooked. T1pH is shown to be non-uniform for both charred and uncharred wood samples; a rapidly relaxing component (T1pH = 0.46-1.07 ms) and a slowly relaxing component (T1pH = 3.58-7.49) is detected in each sample. T1pH for each component generally decreases with heating temperature (degree of charring) and the proportion of rapidly relaxing component increases. Direct T1pH determination (via H-1 detection) shows that all samples contain an even faster relaxing component (0.09-0.24 ms) that is virtually undetectable by the indirect (VCT and VSL) techniques. A new method for correcting for T1pH signal losses in spin counting experiments is developed to deal with the rapidly relaxing component detected in the VSL experiment. Implementation of this correction increased the proportion of potential C-13 CPMAS NMR signal that can be accounted for by up to 50% for the charred samples. An even greater proportion of potential signal can be accounted for if the very rapidly relaxing component detected in the direct T1pH determination is included; however, it must be kept in mind that this experiment also detects H-1 pools which may not be involved in H-1-C-13 cross-polarization. (C) 2002 Elsevier Science (USA).

On a possible mechanism for peripheral nerve stimulation during magnetic resonance imaging scans

When patients undergo a magnetic resonance imaging scan, they are subject to both strong static and temporal magnetic fields. The temporal fields are designed to vary at each point in the region being imaged. This is achieved by the use of gradient coils. However, when the gradient coils are switched very rapidly, the strongly time-varying magnetic fields produced can be responsible for stimulating nerves in the peripheral regions of the body. This paper gives a somewhat novel explanation for this phenomenon. The physical mechanism suggested is supported by an illustrative theoretical calculation.

Shear stress and sediment transport calculations for sheet flow under waves

A simple method is provided for calculating transport rates of not too fine (d(50) greater than or equal to 0.20 mm) sand under sheet flow conditions. The method consists of a Meyer-Peter-type transport formula operating on a time-varying Shields parameter, which accounts for both acceleration-asymmetry and boundary layer streaming. While velocity moment formulae, e.g.., = Constant x calibrated against U-tube measurements, fail spectacularly under some real waves (Ribberink, J.S., Dohmen-Janssen, C.M., Hanes, D.M., McLean, S.R., Vincent, C., 2000. Near-bed sand transport mechanisms under waves. Proc. 27th Int. Conf. Coastal Engineering, Sydney, ASCE, New York, pp. 3263-3276, Fig. 12), the new method predicts the real wave observations equally well. The reason that the velocity moment formulae fail under these waves is partly the presence of boundary layer streaming and partly the saw-tooth asymmetry, i.e., the front of the waves being steeper than the back. Waves with saw-tooth asymmetry may generate a net landward sediment transport even if = 0, because of the more abrupt acceleration under the steep front. More abrupt accelerations are associated with thinner boundary layers and greater pressure gradients for a given velocity magnitude. The two real wave effects are incorporated in a model of the form Q(s)(t) = Q(s)[theta(t)] rather than Q(S)(t) = Q(S)[u(infinity)(t)], i.e., by expressing the transport rate in terms of an instantaneous Shields parameter rather than in terms of the free stream velocity, and accounting for both streaming and accelerations in the 0(t) calculations. The instantaneous friction velocities u(*)(t) and subsequently theta(t) are calculated as follows. Firstly, a linear filter incorporating the grain roughness friction factor f(2.5) and a phase angle phi(tau) is applied to u(infinity)(t). This delivers u(*)(t) which is used to calculate an instantaneous grain roughness Shields parameter theta(2.5)(t). Secondly, a constant bed shear stress is added which corresponds to the streaming related bed shear stress -rho ($) over bar((u) over tilde(w) over tilde)(infinity) . The method can be applied to any u(infinity)(t) time series, but further experimental validation is recommended before application to conditions that differ strongly from the ones considered below. The method is not recommended for rippled beds or for sheet flow with typical prototype wave periods and d(50) < 0.20 turn. In such scenarios, time lags related to vertical sediment movement become important, and these are not considered by the present model. (C) 2002 Elsevier Science B.V. All rights reserved.

On the induced electric field gradients in the human body for magnetic stimulation by gradient coils in MRI

Prior theoretical studies indicate that the negative spatial derivative of the electric field induced by magnetic stimulation may he one of the main factors contributing to depolarization of the nerve fiber. This paper studies this parameter for peripheral nerve stimulation (PNS) induced by time.-varying gradient fields during MRI scans. The numerical calculations are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic human, full-body model. Whole-body cylindrical and planar gradient sets in MRI systems and various input signals have been explored. The spatial distributions of the induced electric field and their gradients are calculated and attempts are made to correlate these areas with reported experimental stimulation data. The induced electrical field pattern is similar for both the planar coils and cylindrical coils. This study provides some insight into the spatial characteristics of the induced field gradients for PNS in MRI, which may be used to further evaluate the sites where magnetic stimulation is likely to occur and to optimize gradient coil design.