I-Lok Chang

A Computational Approach to Finding Causal Economic Laws

This paper states four realities of econometric model buildingand shows that an econometric model can be causal only if theinterpretations given to its coefficients are consistent withthese realities. A numerically stable algorithm for estimatingsuch a model subject to equality and inequality constraints onthe model parameters is presented. This algorithm is designed insuch a way that it can be applied even when the matrix ofobservations on the models independent variables and thecovariance matrix of the models errors are deficient in rank.

Empirical best linear unbiased prediction in misspecified and improved panel data models with an application to gasoline demand

We emphasize using our solutions to the problems of omitted variables, measurement errors, and unknown functional forms to improve model specification, and to estimate the mean square error of an empirical best linear unbiased predictor of an individual drawing of the dependent variable of an improved model. We illustrate using data to compare the forecasting performances of misspecified and improved models of the U.S. gasoline market. The performance criterion used is the tightness of the distribution of the absolute relative errors in out-of-sample multi-step-ahead forecasts around zero. The results show that significant improvements in forecasting accuracy can be obtained by improving the specifications of misspecified models. Numerical algorithms for generating forecasts from a rolling forecast method are presented

Calibration of GOES imager visible channels

Abstract : Four options for the post-launch calibration of GOES Imager visible channel were examined, including those based on the EDF, on desert measurements, on star observations, and on MODIS data. The basic assumptions and methodologies of these options were summarized in this paper, as well as major advantages and disadvantages, from both theoretical and operational perspectives. These discussions provide a basis for further evaluation of these and other methods, with the goal of selecting an operational post-launch calibration algorithm that incorporates the strength of all the methods.

An efficient method of estimating the true value of a population characteristic from its discrepant estimates

A fruitful method of pooling data from disparate sources, such as a set of sample surveys, is developed. This method proceeds by finding the first two moments of two conditional distributions derived from a joint distribution of two sample estimators of employment for each of several geographical areas. The nature of the two estimators is such that one of them can yield a better estimate of national employment than the other. The regression of the former estimator on the latter estimator with stochastic intercept and slope is used to generate an improved estimator that is equal to bias- and error-corrected estimator for each area with probability 1. This analysis is extended to cases where more than two estimates of employment are available for each area.

Monitoring GOES Imager visible-channel responsivities using empirical distribution functions of Earth data

Although the visible channel of the Imagers carried by NOAAs operational Geostationary Operational Environmental Satellites (GOES) has no onboard calibration device, the decrease in the responsivity of this channel over time must be known if we are to make the data in this channel useful for detecting trends in the signals from the Earth. Therefore, some external method is required to provide this information. In this paper, we examine an external technique for monitoring responsivity changes based on empirical distribution functions (EDFs) of observations of the Earths full disk. A time series of instrument outputs (in digital counts) at fixed levels at the tops of the EDFs is produced. A nonlinear least squares technique is then employed to adjust the time series for solar and seasonal effects and to fit it with an exponential, whose argument provides the rate of degradation of the responsivity. This technique assumes that the probabilistic structure of the signal from the earth does not change over time. The resulting time series and estimated responsivity degradation rates for the visible channels of GOES-8 and -10 Imagers will be presented. These results are similar to those obtained earlier with a star-based technique, thus increasing our confidence in the results of both techniques. The EDF technique and the star-based technique are synergistic, as they use very different approaches and data sets. Also, the star based technique works at the low end of the Imagers output signal range, whereas the EDF technique works at the high end.

Data selection criteria in star-based monitoring of GOES imager visible-channel responsivities

Monitoring the responsivities of the visible channels of the operational Geostationary Operational Environmental Satellites (GOES) is an on-going effort at NOAA. Various techniques are being used. In this paper we describe the technique based on the analysis of star signals that are used in the GOES Orbit and Attitude Tracking System (OATS) for satellite attitude and orbit determination. Time series of OATS star observations give information on the degradation of the detectors of a visible channel. Investigations of star data from the past three years have led to several modifications of the method we initially used to calculate the exponential degradation coefficient of a star-signal time series. First we observed that different patterns of detector output versus time result when star images drift across the detector array along different trajectories. We found that certain trajectories should be rejected in the data analysis. We found also that some detector-dependent weighting coefficients used in the OATS analysis tend to scatter the star signals measured by different detectors. We present a set of modifications to our star monitoring algorithms for resolving such problems. Other simple enhancements on the algorithms will also be described. With these modifications, the time series of the star signals show less scatter. This allows for more confidence in the estimated degradation rates and a more realistic statistical analysis on the extent of uncertainty in those rates. The resulting time series and estimated degradation rates for the visible channels of GOES-8 and GOES-10 Imagers will be presented.

Recent advances in calibration of the GOES Imager visible channel at NOAA

To track the degradation of the Imager visible channel on board NOAA’s Geostationary Operation Environmental Satellite (GOES), a research program has been developed using the stellar observations obtained for the purpose of instrument navigation. For monitoring the responsivity of the visible channel, we use observations of approximately fifty stars for each Imager. The degradation of the responsivity is estimated from a single time series based on 30-day averages of the normalized signals from all the stars. Referencing the 30-day averages to the first averaged period of operation, we are able to compute a relative calibration coefficient relative to the first period. Coupling this calibration coefficient with a GOES-MODIS intercalibration technique allows a direct comparison of the star-based relative GOES calibration to a MODIS-based absolute GOES calibration, thus translating the relative star-based calibration to an absolute star-based calibration. We conclude with a discussion of the accuracy of the intercalibrated GOES Imager visible channel radiance measurements.

Refined algorithms for star-based monitoring of GOES Imager visible-channel responsivities

Monitoring the responsivities of the visible channels of the Imagers on GOES satellites is a continuing effort at the National Environmental Satellite, Data and Information Service of NOAA. At this point, a large part of the initial processing of the star data depends on the operationalGOES Sensor Processing System(SPS) and GOES Orbit and AttitudeTracking System (OATS) for detecting the presence of stars and computing the amplitudes of the star signals. However, the algorithms of the SPS and the OATS are not optimized for calculating the amplitudes of the star signals, as they had been developed to determine pixel location and observation time of a star, not amplitude. Motivated by our wish to be independent of the SPS and the OATS for data processing and to improve the accuracy of the computed star signals, we have developed our own methods for such computations. We describe the principal algorithms and discuss their implementation. Next we show our monitoring statistics derived from star observations by the Imagers aboard GOES-8, -10, -11, -12 and -13. We give a brief introduction to a new class of time series that have improved the stability and reliability of our degradation estimates.

A sampling technique in the star-based monitoring of GOES imager visible-channel responsivities

Monitoring the responsivities of the visible channel of the Imagers on operational GOES satellites is a continuing effort at NOAA. To estimate the rate of degradation of the responsivity, we have been analyzing the time series of star signals measured by the Imagers for attitude and orbit determination. In this report, we begin by showing our latest results of monitoring of the responsivities of the visible channels of GOES-8, GOES-9, GOES-10, GOES-11, GOES-12, and GOES-13. One complicating factor in the analysis has been the presence in the time series of an annual cycle that modulates the gradual long-term degradation whose rate we are trying to infer. We describe a method we are developing to reduce the influence of the annual cycle on the analysis. The method enables us to include in the analysis the star observations near local midnight, which had been excluded in the past to prevent loss of accuracy in the derived long-term degradation rate. With a fuller set of data, we can subdivide the data within each year into 48 bins and estimate the degradation separately in each bin, thereby reducing the influence of the annual cycle on the derived degradation rates. One indication that the method is valid is that the degradation rates estimated in all the bins are consistent.