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

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

Time Series Forecasting: The Case for the Single Source of Error State Space

The state space approach to modelling univariate time series is now widely used both in theory and in applications. However, the very richness of the framework means that quite different model formulations are possible, even when they purport to describe the same phenomena. In this paper, we examine the single source of error [SSOE] scheme, which has perfectly correlated error components. We then proceed to compare SSOE to the more common version of the state space models, for which all the error terms are independent; we refer to this as the multiple source of error [MSOE] scheme. As expected, there are many similarities between the MSOE and SSOE schemes, but also some important differences. Both have ARIMA models as their reduced forms, although the mapping is more transparent for SSOE. Further, SSOE does not require a canonical form to complete its specification. An appealing feature of SSOE is that the estimates of the state variables converge in probability to their true values, thereby leading to a formal inferential structure for the ad-hoc exponential smoothing methods for forecasting. The parameter space for SSOE models may be specified to match that of the corresponding ARIMA scheme, or it may be restricted to meaningful sub-spaces, as for MSOE but with somewhat different outcomes. The SSOE formulation enables straightforward extensions to certain classes of non-linear models, including a linear trend with multiplicative seasonals version that underlies the Holt-Winters forecasting method. Conditionally heteroscedastic models may be developed in a similar manner. Finally we note that smoothing and decomposition, two crucial practical issues, may be performed within the SSOE framework.ARIMA, Dynamic Linear Models, Equivalence, Exponential Smoothing, Forecasting, GARCH, Holt's Method, Holt-Winters Method, Kalman Filter, Prediction Intervals.

Forecasting Time-Series with Correlated Seasonality

A new approach is proposed for forecasting a time series with multiple seasonal patterns. A state space model is developed for the series using the single source of error approach which enables us to develop explicit models for both additive and multiplicative seasonality. Parameter estimates may be obtained using methods adapted from general exponential smoothing, although the Kalman filter may also be used. The proposed model is used to examine hourly and daily patterns in hourly data for both utility loads and traffic flows. Our formulation provides a model for several existing seasonal methods and also provides new options, which result in superior forecasting performance over a range of prediction horizons. The approach is likely to be useful in a wide range of applications involving both high and low frequency data, and it handles missing values in a straightforward manner.Exponential smoothing; Holt-Winters; Seasonality; Structural time series model

Forecasting for inventory control with exponential smoothing

Exponential smoothing, often used for sales forecasting in inventory control, has always been rationalized in terms of statistical models that possess errors with constant variances. It is shown in this paper that exponential smoothing remains the appropriate approach under more general conditions where the variances are allowed to grow and contract with corresponding movements in the underlying level. The implications for estimation and prediction are explored. In particular the problem of finding the prediction distribution of aggregate lead-time demand for use in inventory control calculations is considered. It is found that unless a drift term is added to simple exponential smoothing, the prediction distribution is largely unaffected by the variance assumption. A method for establishing order-up-to levels and reorder levels directly from the simulated prediction distributions is also proposed

Bacterial Adaptation to Venom in Snakes and Arachnida

Animal venoms are considered sterile sources of antimicrobial compounds with strong membrane-disrupting activity against multidrug-resistant bacteria. However, venomous bite wound infections are common in developing nations. Investigating the envenomation organ and venom microbiota of five snake and two spider species, we observed venom community structures that depend on the host venomous animal species and evidenced recovery of viable microorganisms from black-necked spitting cobra (Naja nigricollis) and Indian ornamental tarantula (Poecilotheria regalis) venoms. Among the bacterial isolates recovered from , we identified two venom-resistant, novel sequence types of Enterococcus faecalis whose genomes feature 16 virulence genes, indicating infectious potential, and 45 additional genes, nearly half of which improve bacterial membrane integrity. Our findings challenge the dogma of venom sterility and indicate an increased primary infection risk in the clinical management of venomous animal bite wounds. Notwithstanding their 3 to 5% mortality, the 2.7 million envenomation-related injuries occurring annually-predominantly across Africa, Asia, and Latin America-are also major causes of morbidity. Venom toxin-damaged tissue will develop infections in some 75% of envenomation victims, with E. faecalis being a common culprit of disease; however, such infections are generally considered to be independent of envenomation. Here, we provide evidence on venom microbiota across snakes and arachnida and report on the convergent evolution mechanisms that can facilitate adaptation to black-necked cobra venom in two independent E. faecalis strains, easily misidentified by biochemical diagnostics. Therefore, since inoculation with viable and virulence gene-harboring bacteria can occur during envenomation, acute infection risk management following envenomation is warranted, particularly for immunocompromised and malnourished victims in resource-limited settings. These results shed light on how bacteria evolve for survival in one of the most extreme environments on Earth and how venomous bites must be also treated for infections