Dynamic Misspecification in Nonparametric Cointegrating Regression

Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The requisite limit theory involves sample covariances of integrable transformations of non-stationary sequences and time translated sequences, allowing for the presence of a bandwidth parameter so as to accommodate kernel regression. The theory is an extension of Wang and Phillips (2008) and is useful for the analysis of nonparametric regression models with a misspecified lag structure and in situations where temporal aggregation issues arise. The limit properties of the Nadaraya-Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent with a "pseudo-true function" limit that is a local average of the true regression function. In this respect nonlinear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centred on the pseudo-function and appropriately scaled, the NW estimator still has a mixed Gaussian limit distribution. The convergence rates are the same as those obtained under correct specification but the variance of the limit distribution is larger. Some applications of the limit theory to non-linear distributed lag cointegrating regression are given and the practical import of the results for index models, functional regression models, and temporal aggregation are discussed.Dynamic misspecification, Functional regression, Integrable function, Integrated process, Local time, Misspecification, Mixed normality, Nonlinear cointegration, Nonparametric regression

Measurements of DSD Second Moment Based on Laser Extinction

Using a technique recently developed for estimating the density of surface dust dispersed during a rocket landing, measuring the extinction of a laser passing through rain (or dust in the rocket case) yields an estimate of the 2nd moment of the particle cloud, and rainfall drop size distribution (DSD) in the terrestrial meteorological case. With the exception of disdrometers, instruments that measure rainfall make in direct measurements of the DSD. Most common of these instruments are the rainfall rate gauge measuring the 1 1/3 th moment, (when using a D(exp 2/3) dependency on terminal velocity). Instruments that scatter microwaves off of hydrometeors, such as the WSR-880, vertical wind profilers, and microwave disdrometers, measure the 6th moment of the DSD. By projecting a laser onto a target, changes in brightness of the laser spot against the target background during rain, yield a measurement of the DSD 2nd moment, using the Beer-Lambert law. In order to detect the laser attenuation within the 8-bit resolution of most camera image arrays, a minimum path length is required, depending on the intensity of the rainfall rate. For moderate to heavy rainfall, a laser path length of 100 m is sufficient to measure variations in optical extinction using a digital camera. A photo-detector could replace the camera, for automated installations. In order to spatially correlate the 2nd moment measurements to a collocated disdrometer or tipping bucket, the laser's beam path can be reflected multiple times using mirrors to restrict the spatial extent of the measurement. In cases where a disdrometer is not available, complete DSD estimates can be produced by parametric fitting of DSD model to the 2nd moment data in conjunction with tipping bucket data. In cases where a disdrometer is collocated, the laser extinction technique may yield a significant improvement to insitu disdrometer validation and calibration strategie

Analysis of the March 30, 2011 Hail Event at Shuttle Launch Pad 39A

The Kennedy Space Center (KSC) Hail Monitor System, a joint effort of the NASA KSC Physics Lab and the KSC Engineering Services Contract (ESC) Applied Technology Lab, was first deployed for operational testing in the fall of 2006. Volunteers from the Community Collaborative Rain, Hail, and Snow Network (CoCoRaHS) in conjunction with Colorado State University have been instrumental in validation testing using duplicate hail monitor systems at sites in the hail prone high plains of Colorado. The KSC Hail Monitor System (HMS), consisting of three stations positioned approximately 500 ft from the launch pad and forming an approximate equilateral triangle, as shown in Figure 1, was first deployed to Pad 39B for support of STS-115. Two months later, the HMS was deployed to Pad 39A for support of STS-116. During support of STS-117 in late February 2007, an unusually intense (for Florida standards) hail event occurred in the immediate vicinity of the exposed space shuttle and launch pad. Hail data of this event was collected by the HMS and analyzed. Support of STS-118 revealed another important application of the hail monitor system. Ground Instrumentation personnel check the hail monitors daily when a vehicle is on the launch pad, with special attention after any storm suspected of containing hail. If no hail is recorded by the HMS, the vehicle and pad inspection team has no need to conduct a thorough inspection of the vehicle immediately following a storm. On the afternoon of July 13, 2007, hail on the ground was reported by observers at the Vertical Assembly Building (VAB) and Launch Control Center (LCC), about three miles west of Pad 39A, as well as at several other locations at KSC. The HMS showed no impact detections, indicating that the shuttle had not been damaged by any of the numerous hail events which occurred on that day

Hail Disrometer Array for Launch Systems Support

Prior to launch, the space shuttle might be described as a very large thermos bottle containing substantial quantities of cryogenic fuels. Because thermal insulation is a critical design requirement, the external wall of the launch vehicle fuel tank is covered with an insulating foam layer. This foam is fragile and can be damaged by very minor impacts, such as that from small- to medium-size hail, which may go unnoticed. In May 1999, hail damage to the top of the External Tank (ET) of STS-96 required a rollback from the launch pad to the Vehicle Assembly Building (VAB) for repair of the insulating foam. Because of the potential for hail damage to the ET while exposed to the weather, a vigilant hail sentry system using impact transducers was developed as a hail damage warning system and to record and quantify hail events. The Kennedy Space Center (KSC) Hail Monitor System, a joint effort of the NASA and University Affiliated Spaceport Technology Development Contract (USTDC) Physics Labs, was first deployed for operational testing in the fall of 2006. Volunteers from the Community Collaborative Rain. Hail, and Snow Network (CoCoRaHS) in conjunction with Colorado State University were and continue to be active in testing duplicate hail monitor systems at sites in the hail prone high plains of Colorado. The KSC Hail Monitor System (HMS), consisting of three stations positioned approximately 500 ft from the launch pad and forming an approximate equilateral triangle (see Figure 1), was deployed to Pad 39B for support of STS-115. Two months later, the HMS was deployed to Pad 39A for support of STS-116. During support of STS-117 in late February 2007, an unusual hail event occurred in the immediate vicinity of the exposed space shuttle and launch pad. Hail data of this event was collected by the HMS and analyzed. Support of STS-118 revealed another important application of the hail monitor system. Ground Instrumentation personnel check the hail monitors daily when a vehicle is on the launch pad, with special attention after any storm suspected of containing hail. If no hail is recorded by the HMS, the vehicle and pad inspection team has no need to conduct a thorough inspection of the vehicle immediately following a storm. On the afternoon of July 13, 2007, hail on the ground was reported by observers at the VAB, about three miles west of Pad 39A, as well as at several other locations around Kennedy Space Center. The HMS showed no impact detections, indicating that the shuttle had not been damaged by any of the numerous hail events which occurred that day