Testing for a unit root in a process exhibiting a structural break in the presence of GARCH errors

This paper considers the effect of GARCH errors on the tests proposed byPerron (1997) for a unit root in the presence of a structural break. We assessthe impact of degeneracy and integratedness of the conditional varianceindividually and find that, apart from in the limit, the testing procedure isinsensitive to the degree of degeneracy but does exhibit an increasingover-sizing as the process becomes more integrated. When we consider the GARCHspecifications that we are likely to encounter in empirical research, we findthat the Perron tests are reasonably robust to the presence of GARCH and donot suffer from severe over-or under-rejection of a correct null hypothesis.

Parallel pipelined histogram architectures

Proposed is a unique cell histogram architecture which will process k data items in parallel to compute 2q histogram bins per time step. An array of m/2q cells computes an m-bin histogram with a speed-up factor of k; k ⩾ 2 makes it faster than current dual-ported memory implementations. Furthermore, simple mechanisms for conflict-free storing of the histogram bins into an external memory array are discussed.

Energy at work: a measurement validation and linkage to unit effectiveness

We introduce the notion that the energy of individuals can manifest as a higher-level, collective construct. To this end, we conducted four independent studies to investigate the viability and importance of the collective energy construct as assessed by a new survey instrument—the productive energy measure (PEM). Study 1 (n = 2208) included exploratory and confirmatory factor analyses to explore the underlying factor structure of PEM. Study 2 (n = 660) cross-validated the same factor structure in an independent sample. In study 3, we administered the PEM to more than 5000 employees from 145 departments located in five countries. Results from measurement invariance, statistical aggregation, convergent, and discriminant-validity assessments offered additional support for the construct validity of PEM. In terms of predictive and incremental validity, the PEM was positively associated with three collective attitudes—units' commitment to goals, the organization, and overall satisfaction. In study 4, we explored the relationship between the productive energy of firms and their overall performance. Using data from 92 firms (n = 5939employees), we found a positive relationship between the PEM (aggregated to the firm level) and the performance of those firms. Copyright © 2011 John Wiley & Sons, Ltd.

Parallel pipelined array architectures for real-time histogram computation in consumer devices

The real-time parallel computation of histograms using an array of pipelined cells is proposed and prototyped in this paper with application to consumer imaging products. The array operates in two modes: histogram computation and histogram reading. The proposed parallel computation method does not use any memory blocks. The resulting histogram bins can be stored into an external memory block in a pipelined fashion for subsequent reading or streaming of the results. The array of cells can be tuned to accommodate the required data path width in a VLSI image processing engine as present in many imaging consumer devices. Synthesis of the architectures presented in this paper in FPGA are shown to compute the real-time histogram of images streamed at over 36 megapixels at 30 frames/s by processing in parallel 1, 2 or 4 pixels per clock cycle.

Parallel pipelined histogram architecture via c-slow retiming

A parallel pipelined array of cells suitable for realtime computation of histograms is proposed. The cell architecture builds on previous work to now allow operating on a stream of data at 1 pixel per clock cycle. This new cell is more suitable for interfacing to camera sensors or to microprocessors of 8-bit data buses which are common in consumer digital cameras. Arrays using the new proposed cells are obtained via C-slow retiming techniques and can be clocked at a 65% faster frequency than previous arrays. This achieves over 80% of the performance of two-pixel per clock cycle parallel pipelined arrays.

Alternating sums of binomial coefficients with unit fraction arithmetic sequence coefficients

Expressions for finite sums involving the binomial coefficients with unit fraction coefficients whose denominators form an arithmetic sequence are determined.

Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain

A representation of the conformal mapping g of the interior or exterior of the unit circle onto a simply-connected domain Ω as a boundary integral in terms ofƒ|∂Ω is obtained, whereƒ :=g -l. A product integration scheme for the approximation of the boundary integral is described and analysed. An ill-conditioning problem related to the domain geometry is discussed. Numerical examples confirm the conclusions of this discussion and support the analysis of the quadrature scheme.

Linear vs. log-linear unit-root specification: an application of mis-specification encompassing

The objective of this paper is to apply the mis-specification (M-S) encompassing perspective to the problem of choosing between linear and log-linear unit-root models. A simple M-S encompassing test, based on an auxiliary regression stemming from the conditional second moment, is proposed and its empirical size and power are investigated using Monte Carlo simulations. It is shown that by focusing on the conditional process the sampling distributions of the relevant statistics are well behaved under both the null and alternative hypotheses. The proposed M-S encompassing test is illustrated using US total disposable income quarterly data.

Testing for unit roots in bounded time series

Many key economic and financial series are bounded either by construction or through policy controls. Conventional unit root tests are potentially unreliable in the presence of bounds, since they tend to over-reject the null hypothesis of a unit root, even asymptotically. So far, very little work has been undertaken to develop unit root tests which can be applied to bounded time series. In this paper we address this gap in the literature by proposing unit root tests which are valid in the presence of bounds. We present new augmented Dickey–Fuller type tests as well as new versions of the modified ‘M’ tests developed by Ng and Perron [Ng, S., Perron, P., 2001. LAG length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554] and demonstrate how these tests, combined with a simulation-based method to retrieve the relevant critical values, make it possible to control size asymptotically. A Monte Carlo study suggests that the proposed tests perform well in finite samples. Moreover, the tests outperform the Phillips–Perron type tests originally proposed in Cavaliere [Cavaliere, G., 2005. Limited time series with a unit root. Econometric Theory 21, 907–945]. An illustrative application to U.S. interest rate data is provided

Transdifferential and transintegral calculus

The set of transreal numbers is a superset of the real numbers. It totalises real arithmetic by defining division by zero in terms of three def- inite, non-finite numbers: positive infinity, negative infinity and nullity. Elsewhere, in this proceedings, we extended continuity and limits from the real domain to the transreal domain, here we extended the real derivative to the transreal derivative. This continues to demonstrate that transreal analysis contains real analysis and operates at singularities where real analysis fails. Hence computer programs that rely on computing deriva- tives { such as those used in scientific, engineering and financial applica- tions { are extended to operate at singularities where they currently fail. This promises to make software, that computes derivatives, both more competent and more reliable. We also extended the integration of absolutely convergent functions from the real domain to the transreal domain.