Forecasting Compositional Time Series with Exponential Smoothing Methods

Compositional time series are formed from measurements of proportions that sum to one in each period of time. We might be interested in forecasting the proportion of home loans that have adjustable rates, the proportion of nonagricultural jobs in manufacturing, the proportion of a rock's geochemical composition that is a specific oxide, or the proportion of an election betting market choosing a particular candidate. A problem may involve many related time series of proportions. There could be several categories of nonagricultural jobs or several oxides in the geochemical composition of a rock that are of interest. In this paper we provide a statistical framework for forecasting these special kinds of time series. We build on the innovations state space framework underpinning the widely used methods of exponential smoothing. We couple this with a generalized logistic transformation to convert the measurements from the unit interval to the entire real line. The approach is illustrated with two applications: the proportion of new home loans in the U.S. that have adjustable rates; and four probabilities for specified candidates winning the 2008 democratic presidential nomination.compositional time series, innovations state space models, exponential smoothing, forecasting proportions

Interferometric Imaging with the 32 Element Murchison Wide-Field Array

The Murchison Wide-Field Array (MWA) is a low-frequency radio telescope, currently under construction, intended to search for the spectral signature of the epoch of reionization (EOR) and to probe the structure of the solar corona. Sited in western Australia, the full MWA will comprise 8192 dipoles grouped into 512 tiles and will be capable of imaging the sky south of 40° declination, from 80 MHz to 300 MHz with an instantaneous field of view that is tens of degrees wide and a resolution of a few arcminutes. A 32 station prototype of the MWA has been recently commissioned and a set of observations has been taken that exercise the whole acquisition and processing pipeline. We present Stokes I, Q, and U images from two ~4 hr integrations of a field 20° wide centered on Pictoris A. These images demonstrate the capacity and stability of a real-time calibration and imaging technique employing the weighted addition of warped snapshots to counter extreme wide-field imaging distortions

Exponential Smoothing for Inventory Control: Means and Variances of Lead-Time Demand

Exponential smoothing is often used to forecast lead-time demand for inventory control. In this paper, formulae are provided for calculating means and variances of lead-time demand for a wide variety of exponential smoothing methods. A feature of many of the formulae is that variances, as well as the means, depend on trends and seasonal effects. Thus, these formulae provide the opportunity to implement methods that ensure that safety stocks adjust to changes in trend or changes in season.Forecasting; inventory control; lead-time demand; exponential smoothing; forecast variance.

Monitoring Processes with Changing Variances

Statistical process control (SPC) has evolved beyond its classical applications in manufacturing to monitoring economic and social phenomena. This extension requires consideration of autocorrelated and possibly non-stationary time series. Less attention has been paid to the possibility that the variance of the process may also change over time. In this paper we use the innovations state space modeling framework to develop conditionally heteroscedastic models. We provide examples to show that the incorrect use of homoscedastic models may lead to erroneous decisions about the nature of the process. The framework is extended to include counts data, when we also introduce a new type of chart, the P-value chart, to accommodate the changes in distributional form from one period to the next.Control charts, count data, GARCH, heteroscedasticity, innovations, state space, statistical process control