Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.

Learning in neural networks and stochastic approximation methods with averaging

The problem of adjusting the weights (learning) in multilayer feedforward neural networks (NN) is known to be of a high importance when utilizing NN techniques in various practical applications. The learning procedure is to be performed as fast as possible and in a simple computational fashion, the two requirements which are usually not satisfied practically by the methods developed so far. Moreover, the presence of random inaccuracies are usually not taken into account. In view of these three issues, an alternative stochastic approximation approach discussed in the paper, seems to be very promising.

Disentangling multi-level systems: averaging, correlations and memory

We consider two weakly coupled systems and adopt a perturbative approach based on the Ruelle response theory to study their interaction. We propose a systematic way of parameterizing the effect of the coupling as a function of only the variables of a system of interest. Our focus is on describing the impacts of the coupling on the long term statistics rather than on the finite-time behavior. By direct calculation, we find that, at first order, the coupling can be surrogated by adding a deterministic perturbation to the autonomous dynamics of the system of interest. At second order, there are additionally two separate and very different contributions. One is a term taking into account the second-order contributions of the fluctuations in the coupling, which can be parameterized as a stochastic forcing with given spectral properties. The other one is a memory term, coupling the system of interest to its previous history, through the correlations of the second system. If these correlations are known, this effect can be implemented as a perturbation with memory on the single system. In order to treat this case, we present an extension to Ruelle's response theory able to deal with integral operators. We discuss our results in the context of other methods previously proposed for disentangling the dynamics of two coupled systems. We emphasize that our results do not rely on assuming a time scale separation, and, if such a separation exists, can be used equally well to study the statistics of the slow variables and that of the fast variables. By recursively applying the technique proposed here, we can treat the general case of multi-level systems.

Averaging, slaving and balance dynamics in a simple atmospheric model

We report numerical results from a study of balance dynamics using a simple model of atmospheric motion that is designed to help address the question of why balance dynamics is so stable. The non-autonomous Hamiltonian model has a chaotic slow degree of freedom (representing vortical modes) coupled to one or two linear fast oscillators (representing inertia-gravity waves). The system is said to be balanced when the fast and slow degrees of freedom are separated. We find adiabatic invariants that drift slowly in time. This drift is consistent with a random-walk behaviour at a speed which qualitatively scales, even for modest time scale separations, as the upper bound given by Neishtadt’s and Nekhoroshev’s theorems. Moreover, a similar type of scaling is observed for solutions obtained using a singular perturbation (‘slaving’) technique in resonant cases where Nekhoroshev’s theorem does not apply. We present evidence that the smaller Lyapunov exponents of the system scale exponentially as well. The results suggest that the observed stability of nearly-slow motion is a consequence of the approximate adiabatic invariance of the fast motion.

Radiative forcing and climate metrics for ozone precursor emissions: the impact of multi-model averaging

Multi-model ensembles are frequently used to assess understanding of the response of ozone and methane lifetime to changes in emissions of ozone precursors such as NOx, VOCs (volatile organic compounds) and CO. When these ozone changes are used to calculate radiative forcing (RF) (and climate metrics such as the global warming potential (GWP) and global temperature-change potential (GTP)) there is a methodological choice, determined partly by the available computing resources, as to whether the mean ozone (and methane) concentration changes are input to the radiation code, or whether each model's ozone and methane changes are used as input, with the average RF computed from the individual model RFs. We use data from the Task Force on Hemispheric Transport of Air Pollution source–receptor global chemical transport model ensemble to assess the impact of this choice for emission changes in four regions (East Asia, Europe, North America and South Asia). We conclude that using the multi-model mean ozone and methane responses is accurate for calculating the mean RF, with differences up to 0.6% for CO, 0.7% for VOCs and 2% for NOx. Differences of up to 60% for NOx 7% for VOCs and 3% for CO are introduced into the 20 year GWP. The differences for the 20 year GTP are smaller than for the GWP for NOx, and similar for the other species. However, estimates of the standard deviation calculated from the ensemble-mean input fields (where the standard deviation at each point on the model grid is added to or subtracted from the mean field) are almost always substantially larger in RF, GWP and GTP metrics than the true standard deviation, and can be larger than the model range for short-lived ozone RF, and for the 20 and 100 year GWP and 100 year GTP. The order of averaging has most impact on the metrics for NOx, as the net values for these quantities is the residual of the sum of terms of opposing signs. For example, the standard deviation for the 20 year GWP is 2–3 times larger using the ensemble-mean fields than using the individual models to calculate the RF. The source of this effect is largely due to the construction of the input ozone fields, which overestimate the true ensemble spread. Hence, while the average of multi-model fields are normally appropriate for calculating mean RF, GWP and GTP, they are not a reliable method for calculating the uncertainty in these fields, and in general overestimate the uncertainty.

Improving climate change detection through optimal seasonal averaging: the case of the North Atlantic jet and European precipitation

The detection of anthropogenic climate change can be improved by recognising the seasonality in the climate change response. This is demonstrated for the North Atlantic jet (zonal wind at 850 hPa, U850) and European precipitation responses projected by the CMIP5 climate models. The U850 future response is characterised by a marked seasonality: an eastward extension of the North Atlantic jet into Europe in November-April, and a poleward shift in May-October. Under the RCP8.5 scenario, the multi-model mean response in U850 in these two extended seasonal means emerges by 2035-2040 for the lower--latitude features and by 2050-2070 for the higher--latitude features, relative to the 1960-1990 climate. This is 5-15 years earlier than when evaluated in the traditional meteorological seasons (December--February, June--August), and it results from an increase in the signal to noise ratio associated with the spatial coherence of the response within the extended seasons. The annual mean response lacks important information on the seasonality of the response without improving the signal to noise ratio. The same two extended seasons are demonstrated to capture the seasonality of the European precipitation response to climate change and to anticipate its emergence by 10-20 years. Furthermore, some of the regional responses, such as the Mediterranean precipitation decline and the U850 response in North Africa in the extended winter, are projected to emerge by 2020-2025, according to the models with a strong response. Therefore, observations might soon be useful to test aspects of the atmospheric circulation response predicted by some of the CMIP5 models.

Averaging for retarded functional differential equations

We consider retarded functional differential equations in the setting of Kurzweil-Henstock integrable functions and we state an averaging result for these equations. Our result generalizes previous ones. (C) 2011 Elsevier Inc. All rights reserved.

Quantitative comparisons and models of time-averaging in bivalve and brachiopod shell accumulations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Quantitative estimates of time-averaging in terebratulid brachiopod shell accumulations from a modern tropical shelf

Quantitative estimates of time-averaging in marine shell accumulations available to date are limited primarily to aragonitic mollusk shells. We assessed time-averaging in Holocene assemblages of calcitic brachiopod shells by direct dating of individual specimens of the terebratulid brachiopod Bouchardia rosea. The data were collected from exceptional (brachiopod-rich) shell assemblages, occurring surficially on a tropical mixed carbonate-siliciclastic shelf (the Southeast Brazilian Bight, SW Atlantic), a setting that provides a good climatic and environmental analog for many Paleozoic brachiopod shell beds of North America and Europe. A total of 82 individual brachiopod shells, collected from four shallow (5-25 m) nearshore (<2.5 km from the shore) localities, were dated by using amino acid racemization (D-alloisoleucine/L-isoleucine value) calibrated with five AMS-radiocarbon dates (r(2) = 0.933). This is the first study to demonstrate that amino acid racemization methods can provide accurate and precise ages for individual shells of calcitic brachiopods.The dated shells vary in age from modern to 3000 years, with a standard deviation of 690 years. The age distribution is strongly right-skewed: the young shells dominate the dated specimens and older shells are increasingly less common. However, the four localities display significant differences in the range of time-averaging and the form of the age distribution. The dated shells vary notably in the quality of preservation, but there is no significant correlation between taphonomic condition and age, either for individual shells or at assemblage level.These results demonstrate that fossil brachiopods may show considerable time-averaging, but the scale and nature of that mixing may vary greatly among sites. Moreover, taphonomic condition is not a reliable indicator of pre-burial history of individual brachiopod shells or the scale of temporal mixing within the entire assemblage. The results obtained for brachiopods are strikingly similar to results previously documented for mollusks and suggest that differences in mineralogy and shell microstructure are unlikely to be the primary factors controlling the nature and scale of time-averaging. Environmental factors and local fluctuations in populations of shell-producing organisms are more likely to be the principal determinants of time-averaging in marine benthic shelly assemblages. The long-term survival of brachiopod shells is incongruent with the rapid shell destruction observed in taphonomic experiments. The results support the taphonomic model that shells remain protected below (but perhaps near) the surface through their early taphonomic history. They may be brought back up to the surface intermittently by bioturbation and physical reworking, but only for short periods of time. This model explains the striking similarities in time-averaging among different types of organisms and the lack of correlation between time-since-death and shell taphonomy.

On non-ideal and non-linear portal frame dynamics analysis using Bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

3-Dimensional hopf bifurcation via averaging theory

We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br - b, r - 1), in the Lorenz case, and at s± = (c+√c2-4ab/2, -c+√c2-4ab/2a, c±√c2-4ab/2a) in the Rössler case. As usual this Hopf bifurcation is in the sense that an one-parameter family in ε of limit cycles bifurcates from the singular point when ε = 0. Moreover, we can determine the kind of stability of these limit cycles. In fact, for both systems we can prove that all the bifurcated limit cycles in a neighborhood of the singular point are either a local attractor, or a local repeller, or they have two invariant manifolds, one stable and the other unstable, which locally are formed by two 2-dimensional cylinders. These results are proved using averaging theory. The method of studying the Hopf bifurcation using the averaging theory is relatively general and can be applied to other 3- or n-dimensional differential systems.

Quenching in a non-ideal mechanical system and the Averaging Method

In this paper, for the first time, a quenching result in a non-ideal system is rigorously obtained. In order to do this a new mechanical hypothesis is assumed, it means that the moment of inertia of the rotating parts of the energy source is big. From this is possible to use the Averaging Method. © 2012 American Institute of Physics.

String-averaging expectation-maximization for maximum likelihood estimation in emission tomography

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Periodic averaging theorems for various types of equations

We prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily from this general theorem. We also present a periodic averaging theorem for a large class of retarded equations.