ACF estimation via difference schemes for a semiparametric model with mm-dependent errors

In this manuscript, we discuss a class of difference-based estimators of the autocovariance structure in a semiparametric regression model where the signal is discontinuous and the errors are serially correlated. The signal in this model consists of a sum of the function with jumps and an identifiable smooth function. A simpler form of this model has been considered earlier under the name of Nonparametric Jump Regression (NJRM). The estimators proposed allow us to bypass a complicated problem of prior estimation of the mean signal in such a model. We provide finite-sample expressions for biases and variance of the proposed estimators when the errors are Gaussian. Gaussianity in the above is only needed to provide explicit closed form expressions for biases and variances of our estimators. Moreover, we observe that the mean squared error of the proposed variance estimator does not depend on either the unknown smooth function that is a part of the mean signal nor on the values of difference sequence coefficients. Our approach also suggests sufficient conditions for $\sqrt{n}-$ consistency of the proposed estimators.Comment: 30 page

Explaining the dollar/euro exchange rate: the role of policy uncertainty, asymmetric information, and hedging opportunities

Many observers were surprised by the depreciation of the euro after its launch in 1999. Handicapped by a short sample, explanations tended to appeal to anecdotes and lessons learned from the experiences of other currencies. Now sample sizes are just becoming large enough to permit reasonable empirical analyses. This paper begins with a theoretical model addressing transaction costs of trading the euro. The model of pre- and post-euro foreign exchange trading explains wider spreads on the euro as a result of three possible causes: a reduction in hedging opportunities due to the elimination of the legacy currencies, policy uncertainty on the part of the ECB, and asymmetric information due to some traders having prior knowledge of ECB policies. However, even informal empirical evidence tends to reject the hypothesis that spreads were larger on the euro than the mark for all but the first few months. This seems like an unlikely candidate to explain euro depreciation over the prolonged period observed. After addressing spreads, the model is turned toward an explanation of the exchange rate level. By specializing the fundamentals considered to the euro-area inflation rate, the model is structured toward the dynamics of learning about ECB policy with regard to inflation. While a stated target inflation rate of 2 percent existed, it may be that market participants had to be convinced that the ECB would, indeed, generate low and stable inflation. The theory motivates an empirical model of Bayesian updating related to market participants learning about the underlying inflation process under the ECB regime. With a prior distribution drawn from the pre-euro EMS experience and updating based upon the realized experience each month following the introduction of the euro, the evidence suggests that it was not until the fall of 2000 that the market assessed a greater than 50 percent probability that the inflation process had changed to a new regime. From this point on, trend depreciation of the euro ends and further increases in the probability of the new inflation process are associated with euro appreciation.euro, foreign exchange, Bayesian learning

Pull-in dynamics of overdamped microbeams

We study the dynamics of MEMS microbeams undergoing electrostatic pull-in. At DC voltages close to the pull-in voltage, experiments and numerical simulations have reported `bottleneck' behaviour in which the transient dynamics slow down considerably. This slowing down is highly sensitive to external forces, and so has widespread potential for applications that use pull-in time as a sensing mechanism, including high-resolution accelerometers and pressure sensors. Previously, the bottleneck phenomenon has only been understood using lumped mass-spring models that do not account for effects such as variable residual stress and different boundary conditions. We extend these studies to incorporate the beam geometry, developing an asymptotic method to analyse the pull-in dynamics. We attribute bottleneck behaviour to critical slowing down near the pull-in transition, and we obtain a simple expression for the pull-in time in terms of the beam parameters and external damping coefficient. This expression is found to agree well with previous experiments and numerical simulations that incorporate more realistic models of squeeze film damping, and so provides a useful design rule for sensing applications. We also consider the accuracy of a single-mode approximation of the microbeam equations --- an approach that is commonly used to make analytical progress, without systematic investigation of its accuracy. By comparing to our bottleneck analysis, we identify the factors that control the error of this approach, and we demonstrate that this error can indeed be very small.Comment: 18 page

Dynamics of viscoelastic snap-through

We study the dynamics of snap-through when viscoelastic effects are present. To gain analytical insight we analyse a modified form of the Mises truss, a single-degree-of-freedom structure, which features an `inverted' shape that snaps to a `natural' shape. Motivated by the anomalously slow snap-through shown by spherical elastic caps, we consider a thought experiment in which the truss is first indented to an inverted state and allowed to relax while a specified displacement is maintained; the constraint of an imposed displacement is then removed. Focussing on the dynamics for the limit in which the timescale of viscous relaxation is much larger than the characteristic elastic timescale, we show that two types of snap-through are possible: the truss either immediately snaps back over the elastic timescale or it displays `pseudo-bistability', in which it undergoes a slow creeping motion before rapidly accelerating. In particular, we demonstrate that accurately determining when pseudo-bistability occurs requires the consideration of inertial effects immediately after the indentation force is removed. Our analysis also explains many basic features of pseudo-bistability that have been observed previously in experiments and numerical simulations; for example, we show that pseudo-bistability occurs in a narrow parameter range at the bifurcation between bistability and monostability, so that the dynamics is naturally susceptible to critical slowing down. We then study an analogous thought experiment performed on a continuous arch, showing that the qualitative features of the snap-through dynamics are well captured by the truss model. In addition, we analyse experimental and numerical data of viscoelastic snap-through times reported in the literature. Combining these approaches suggests that our conclusions may also extend to more complex viscoelastic structures used in morphing applications.Comment: Main text 37 pages, Appendices 13 page

Passive control of viscous flow via elastic snap-through

We demonstrate the passive control of viscous flow in a channel by using an elastic arch embedded in the flow. Depending on the fluid flux, the arch may `snap' between two states --- constricting and unconstricting --- that differ in hydraulic conductivity by up to an order of magnitude. We use a combination of experiments at a macroscopic scale and theory to study the constricting and unconstricting states, and determine the critical flux required to transition between them. We show that such a device may be precisely tuned for use in a range of applications, and in particular has potential as a passive microfluidic fuse to prevent excessive fluxes in rigid-walled channels.Comment: Main text 5 pages, Supplementary Information 14 page

Delayed pull-in transitions in overdamped MEMS devices

We consider the dynamics of overdamped MEMS devices undergoing the pull-in instability. Numerous previous experiments and numerical simulations have shown a significant increase in the pull-in time under DC voltages close to the pull-in voltage. Here the transient dynamics slow down as the device passes through a meta-stable or bottleneck phase, but this slowing down is not well understood quantitatively. Using a lumped parallel-plate model, we perform a detailed analysis of the pull-in dynamics in this regime. We show that the bottleneck phenomenon is a type of critical slowing down arising from the pull-in transition. This allows us to show that the pull-in time obeys an inverse square-root scaling law as the transition is approached; moreover we determine an analytical expression for this pull-in time. We then compare our prediction to a wide range of pull-in time data reported in the literature, showing that the observed slowing down is well captured by our scaling law, which appears to be generic for overdamped pull-in under DC loads. This realization provides a useful design rule with which to tune dynamic response in applications, including state-of-the-art accelerometers and pressure sensors that use pull-in time as a sensing mechanism. We also propose a method to estimate the pull-in voltage based only on data of the pull-in times.Comment: 17 page

Historical forest biomass dynamics modelled with Landsat spectral trajectories

Acknowledgements National Forest Inventory data are available online, provided by Ministerio de Agricultura, Alimentación y Medio Ambiente (España). Landsat images are available online, provided by the USGS.Peer reviewedPostprin