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.

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.

Dependence of transient dynamics in a class-C laser upon variation of inversion with time

The transient statistics of a gain-switched coherently pumped class-C laser displays a linear correlation between the first passage time and subsequent peak intensity. Measurements are reported showing a positive or negative sign of this linear correlation, controlled through the switching time and the laser detuning. Further measurements of the small-signal laser gain combined with calculations involving a three-level laser model indicate that this sign fundamentally depends upon the way the laser inversion varies during the gain switching, despite the added dynamics of the laser polarization in the class-C laser. [S1050-2947(97)07112-6].

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.

Modelling trickle irrigation: Comparison of analytical and numerical models for estimation of wetting front position with time

Irrigation practices that are profligate in their use of water have come under closer scrutiny by water managers and the public. Trickle irrigation has the propensity to increase water use efficiency but only if the system is designed to meet the soil and plant conditions. Recently we have provided a software tool, WetUp (http://www.clw.csiro.au/products/wetup/), to calculate the wetting patterns from trickle irrigation emitters. WetUp uses an analytical solution to calculate the wetted perimeter for both buried and surface emitters. This analytical solution has a number of assumptions, two of which are that the wetting front is defined by water content at which the hydraulic conductivity (K) is I mm day(-1) and that the flow occurs from a point source. Here we compare the wetting patterns calculated with a 2-dimensional numerical model, HYDRUS2D, for solving the water flow into typical soils with the analytical solution. The results show that the wetting patterns are similar, except when the soil properties result in the assumption of a point source no longer being a good description of the flow regime. Difficulties were also experienced with getting stable solutions with HYDRUS2D for soils with low hydraulic conductivities. (c) 2005 Elsevier Ltd. All rights reserved.

Changes in organic matter production and accumulation as a mechanism for isotopic evolution in the Mesoproterozoic ocean

Mesoproterozoic marine successions worldwide record a shift in average delta(13)C values from 0 to +3.5parts per thousand, with the latter value evident in successions younger than 1250 Ma. New carbon isotope data from the similar to 1300 to 1270 Ma Dismal Lakes Group, Arctic Canada, provide further insight into this fundamental transition. Data reveal that the shift to higher VC values was gradual and marked by occasional excursions to values less than 0 parts per thousand. When compared to records from older and younger marine successions, it is evident that the difference between isotopic minima and maxima increased with time, indicating that the marine system evolved to become isotopically more variable. We interpret these patterns to record an increase in the crustal inventory of organic carbon, reflecting eukaryotic diversification and a change in the locus of organic carbon burial to include anoxic deep marine sites where preservation potential was high. We speculate that the release of O-2 to Earth's surface environments associated with increased organic carbon storage induced irreversible changes in the Mesoproterozoic biosphere, presaging the more extreme environmental and evolutionary developments of the Neoproterozoic.

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.

Depositional environments for strata cored in CRP-3 (Cape Roberts Project), Victoria Land Basin, Antarctica: palaeoglaciological and palaeoclimatological inferences

Cape Roberts Project drill core 3 (CRP-3) was obtained from Roberts ridge, a sea-floor high located at 77°S, 12 km offshore from Cape Roberts in western McMurdo Sound, Antarctica. The recovered core is about 939 m long and comprises strata dated as being early Oligocene (possibly latest Eocene) in age, resting unconformably on ∼ 116 m of basement rocks consisting of Palaeozoic Beacon Supergroup sediments. The core includes ten facies commonly occuring in five major associations that are repeated in particular sequences throughout the core and which are interpreted as representing different depositional environments through time. Depositional systems inferred to be represented in the succession include: outer shelf, inner shelf, nearshore to shoreface each under iceberg influence, deltaic and/or grounding-line fan, and ice proximal-ice marginal-subglacial (mass flow/rainout diamictite/subglacial till) singly or in combination. The record is taken to represent the initial talus/alluvial fan setting of a glaciated rift margin adjacent to the block-uplifted Transantarctic Mountains. Development of a deltaic succession upcore was probably associated with the formation of palaeo-Mackay valley with temperate glaciers in its headwaters. At that stage glaciation was intense enough to support glaciers ending in the sea elsewhere along the coast, but a local glacier was fluctuating down to the sea by the time the youngest part of CRP-3 was being deposited. Changes in palaeoenvironmental interpretations in this youngest part of the core are used to estimate relative glacial proximity to the drillsite through time. These inferred glacial fluctuations are compared with the global δ18O and Mg/Ca curves to evaluate the potential of glacial fluctuations on Antarctica for influencing these records of global change. Although the comparisons are tentative at present, the records do have similarities, but there are also some differences that require further evaluation.

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.

Transformation processes, pathways, and possible sources of distinctive polychlorinated dibenzo-p-dioxin signatures in sink environments

In recent years, studies on environmental samples with unusual dibenzo-p-dioxin (PCDD) congener profiles were reported from a range of countries. These profiles, characterized by a dominance of octachlorinated dibenzodioxin (OCDD) and relatively low in dibenzofuran (PCDF) concentrations, could not be attributed to known sources or formation processes. In the present study, the processes that result in these unusual profiles were assessed using the concentrations and isomer signatures of PCDDs from dated estuarine sediment cores in Queensland, Australia. Increases in relative concentrations of lower chlorinated PODS and a relative decrease of OCDD were correlated with time of sediment deposition. Preferred lateral, anaerobic dechlorination of OCDD represents a likely pathway for these changes. In Queensland sediments, these transformations result in a distinct dominance of isomers fully chlorinated in the 1,4,6,9-positions (1,4-patterns), and similar 1,4-patterns were observed in sediments from elsewhere. Consequently, these environmental samples may not reflect the signatures of the original source, and a reevaluation of source inputs was undertaken. Natural formation of PCDDs, which has previously been suggested, is discussed; however, based on the present results and literature comparisons, we propose an alternative scenario. This scenario hypothesizes that an anthropogenic PCDD precursor input (e.g. pentachlorophenol) results in the contamination. These results and hypothesis imply further investigations are warrented into possible anthropogenic sources in areas where natural PCDD formation has been suggested.

Marine and estuarine reservoir effects in central Queensland, Australia: Determination of Delta R values

As a component of archaeological investigations on the central Queensland coast, a series of five marine shell specimens live-collected between A.D. 1904 and A.D. 1929 and 11 shell/ charcoal paired samples from archaeological contexts were radiocarbon dated to determine local DeltaR values. The object of the study was to assess the potential influence of localized variation in marine reservoir effect in accurately determining the age of marine and estuarine shell from archaeological deposits in the area. Results indicate that the routinely applied DeltaR value of -5 +/- 35 for northeast Australia is erroneously calculated. The determined values suggest a minor revision to Reimer and Reimer's (2000) recommended value for northeast Australia from DeltaR = +11 +/- 5 to + 12 +/- 7, and specifically for central Queensland to DeltaR = +10 +/- 7, for near-shore open marine environments. In contrast, data obtained from estuarine shell/charcoal pairs demonstrate a general lack of consistency, suggesting estuary-specific patterns of variation in terrestrial carbon input and exchange with the open ocean. Preliminary data indicate that in some estuaries, at some time periods, a DeltaR value of more than - 155 +/- 55 may be appropriate, In estuarine contexts in central Queensland, a localized estuary-specific correction factor is recommended to account for geographical and temporal variation in C-14 activity. (C) 2002 Wiley Periodicals.