Bootstrap prediction intervals in State Space models

Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series.Backward representation, Kalman filter, Local Level Model, Unobserved Components

Near-field thermal upconversion and energy transfer through a Kerr medium : Theory

We present an approach for achieving large Kerr $\chi^{(3)}$--mediated thermal energy transfer at the nanoscale that exploits a general coupled-mode description of triply resonant, four-wave mixing processes. We analyze the efficiency of thermal upconversion and energy transfer from mid- to near-infrared wavelengths in planar geometries involving two slabs supporting far-apart surface plasmon polaritons and separated by a nonlinear $\chi^{(3)}$ medium that is irradiated by externally incident light. We study multiple geometric and material configurations and different classes of interveening mediums---either bulk or nanostructured lattices of nanoparticles embedded in nonlinear materials---designed to resonantly enhance the interaction of the incident light with thermal slab resonances. We find that even when the entire system is in thermodynamic equilibrium (at room temperature) and under typical drive intensities $\sim\mathrm{W}/\mu\mathrm{m}^2$, the resulting upconversion rates can approach and even exceed thermal flux rates achieved in typical symmetric and non-equilibrium configurations of vacuum-separated slabs. The proposed nonlinear scheme could potentially be exploited to achieve thermal cooling and refrigeration at the nanoscale, and to actively control heat transfer between materials with dramatically different resonant responses

Applying the interaction equivalency theorem to online courses in a large organization

Finding effective ways of designing online courses is a priority for corporate organizations. The interaction equivalency theorem states that meaningful learning can be achieved as long as courses are designed with at least a high level of one of three types of interactions (learner-content, learner-teacher or learner-learner). This study aimed to establish whether the interaction equivalency theorem applies to online learning in the corporate sector. The research was conducted in a large Mexican commercial organization, and involved 147 learners (sales supervisors), 30 teachers (sales managers and directors) and 3 academic assistants (course designers, or Education support staff). Three courses of an existing Leadership Program (Situational Leadership, Empowering Beliefs and Effective Performance) were redesigned and developed to test three course designs, each emphasizing a different type of interaction (learner-content, learner-teacher or learner-learner). Data were collected through surveys (for diagnostic and evaluation purposes) and exams. All courses yielded high levels of effectiveness, in terms of satisfaction, learning, perceived readiness for knowledge transfer and return on expectations. This suggests that the interaction equivalency theorem not only applies in a business setting but might also include other indicators of course effectiveness, such as satisfaction, learning transfer and return on expectations. Further research is needed to explore the possible expansion of the theorem

Student engagement with a content-based learning design

While learning is commonly conceptualised as a social, collaborative process in organisations, online courses often provide limited opportunities for communication between people. How do students engage with content-based courses? How do they find answers to their questions? How do they achieve the learning outcomes? This paper aims to answer these questions by focusing on students’ experiences in an online content-based course delivered in a large Mexican organisation. Sales supervisors (n=47) participated as students. Four main data sources were used to evaluate engagement with and learning from the course: surveys (n=40), think-aloud sessions (n=8), activity logs (n=47) and exams (n=43). Findings suggest that: (1) Students engage with a content-based course by following the guidance available and attempting to make the materials relevant to their own context. (2) Students are resourceful when trying to find support. If the materials do not provide the answers to their questions, they search for alternatives such as colleagues to talk to. (3) Content-based online learning designs may be engaging and effective. However, broadening the range of support options available to students may derive in more meaningful, contextualised and rewarding learning experiences

Formulas for Consumer Price Index at the elementary aggregate - A new proposal from the economic point of view

The price level in the aggregate economy and, more concretely, controlling its changes, has become one of the high-priority objectives within the framework of the regional macroeconomic analysis. Its different evolution could modify the interregional capital and commercial flows, being able to cause strong shocks, and of asymmetric nature, in each economy. The first step to reach this objective is obtaining a trustworthy and comparable measurement of the inflation in the different regions to be compared. The Index Number Theory is then used to calculate Consumer Price Indexes (CPI) the regional level. The calculation of CPI is made, at least, in two phases. In the first one, Elementary Price Index is considered (EPI). In the second and later phases, these EPI are combined, along with weighting information based on household’s expenditure, to obtain CPI for different aggregation levels to the country level. As previous step to the calculation of the IPE and CPI, the set of goods and services has to be defined based on households’ consumption behaviour. These sets are grouped in layers, named elementary aggregates, based on their homogeneity of satisfying consumer’s necessities. The COICOP (Classification Of Individual Consumption by Purpose) has important implications at the time of analyzing the behaviour of the consumer within each elementary aggregate, because of a high possibility of substitution between products. Nevertheless, this possibility diminishes and can get to be null when the goods and services satisfy necessities with very different nature. Whether what is wanted it is to calculate an EPI that correctly reflects the consumer behaviour, the described homogenous character cannot be forgotten, especially if, in addition, we take into account that National Statistics Agencies have no expenditure information available for weighting purposes, only data of prices to calculate EPI. This paper is focussed on analysis of the formula used to obtain the IPE, with the limitations of available information just commented. The election of the formula for the IPE has not been widely studied in the economic literature, being the proposal by Carli in 1764 and Dutot in 1738 [ extracted Reference of OIT (2003), chapter 20, pages 12-13 ] the most often used for practical purposes. Nevertheless, Fisher (1922) had already recommended not using the Carli’s formula because of the bias to the rise that it introduces [Fisher (1922), pages 29-30]. Throughout the 20th century different authors has continued looking for the ideal formula extending possible approaches to the subject: the approach of Divisia, the stochastic approach, the economic approach and the axiomatic approach. The final summary of these studies can be synthesized in "Toward to Dwells Accurate Measure of The Cost of Living” by the Advisory Commission To The Study The Consumer Price Index presented in 1996. This report, also known as Boskin’s Report, suggests the use of geometric mean price indices at the elementary aggregate for the EPI, this formula is attributed to Jevons in 1983 [OIT (2003), chapter 20, pages 12-13 ]. In the present paper, we demonstrate that all usually formulas for the calculation of the IPE are incoherent with the theory of consumer behaviour, in an aggregate characterized by the high level of substitution caused by homogeneity in the consumption purpose. In addition, the formula proposed by Rodriguez, González and Rodriguez (2004), is not only superior from the axiomatic point of view, but also from the economic approach, is the only one that is able to reflect the expected consumer behaviour.

Thermal bistability through coupled photonic resonances

We present a scheme for achieving thermal bistability based on the selective coupling of three optical resonances. This approach requires one of the resonant frequencies to be temperature dependent, which can occur in materials exhibiting strong thermo-optic effects. For illustration, we explore thermal bistability in two different passive systems, involving either a periodic array of Si ring resonators or parallel GaAs thin films separated by vacuum and exchanging heat in the near field. Such a scheme could prove useful for thermal memory devices operating with transition times $\lesssim$ hundreds of milliseconds