Testing for Common Trends in Semiparametric Panel Data Models with Fixed Effects

This paper proposes a nonparametric test for common trends in semiparametric panel data models with fixed effects based on a measure of nonparametric goodness-of-fit (R^2). We first estimate the model under the null hypothesis of common trends by the method of profile least squares, and obtain the augmented residual which consistently estimates the sum of the fixed effect and the disturbance under the null. Then we run a local linear regression of the augmented residuals on a time trend and calculate the nonparametric R^2 for each cross section unit. The proposed test statistic is obtained by averaging all cross sectional nonparametric R^2's, which is close to zero under the null and deviates from zero under the alternative. We show that after appropriate standardization the test statistic is asymptotically normally distributed under both the null hypothesis and a sequence of Pitman local alternatives. We prove test consistency and propose a bootstrap procedure to obtain p-values. Monte Carlo simulations indicate that the test performs well in finite samples. Empirical applications are conducted exploring the commonality of spatial trends in UK climate change data and idiosyncratic trends in OECD real GDP growth data. Both applications reveal the fragility of the widely adopted common trends assumption.Common trends, Local polynomial estimation, Nonparametric goodness-of-fit, Panel data, Profile least squares

A survey of mathematical modeling based on flocking system

Based on the basics of the flocking, the concept and relationship of individual, cluster and flocking behavior are introduced. Two research methods, which are the macroscopic Angle of Euler method and the Lagrangian method of microcosmic Angle, are elaborated in detail. Then several flocking models and their improvement applications are summarized, the model among them based on dynamic principle is widely used, so the basic mode of its behavior, the following mechanism of an individual in an orderly procession, the mechanism for avoiding obstacles, and the causes of fission behavior are discussed in this paper. Finally, some problems in current researches of flocking are presented and future development are prospected

Full-Duplex Cooperative Cognitive Radio Networks with Wireless Energy Harvesting

This paper proposes and analyzes a new full-duplex (FD) cooperative cognitive radio network with wireless energy harvesting (EH). We consider that the secondary receiver is equipped with a FD radio and acts as a FD hybrid access point (HAP), which aims to collect information from its associated EH secondary transmitter (ST) and relay the signals. The ST is assumed to be equipped with an EH unit and a rechargeable battery such that it can harvest and accumulate energy from radio frequency (RF) signals transmitted by the primary transmitter (PT) and the HAP. We develop a novel cooperative spectrum sharing (CSS) protocol for the considered system. In the proposed protocol, thanks to its FD capability, the HAP can receive the PT's signals and transmit energy-bearing signals to charge the ST simultaneously, or forward the PT's signals and receive the ST's signals at the same time. We derive analytical expressions for the achievable throughput of both primary and secondary links by characterizing the dynamic charging/discharging behaviors of the ST battery as a finite-state Markov chain. We present numerical results to validate our theoretical analysis and demonstrate the merits of the proposed protocol over its non-cooperative counterpart.Comment: 6 pages, 3 figures, conferenc