Incorporating a Tracking Signal into State Space Models for Exponential Smoothing

It is a common practice to complement a forecasting method such as simple exponential smoothing with a monitoring scheme to detect those situations where forecasts have failed to adapt to structural change. It will be suggested in this paper that the equations for simple exponential smoothing can be augmented by a common monitoring statistic to provide a method that automatically adapts to structural change without human intervention. It is shown that the resulting equations conform to those of damped trend corrected exponential smoothing. In a similar manner, exponential smoothing with drift, when augmented by the same monitoring statistic, produces equations that split the trend into long term and short term components.Forecasting, exponential smoothing, tracking signals.

A View of Damped Trend as Incorporating a Tracking Signal into a State Space Model

Damped trend exponential smoothing has previously been established as an important forecasting method. Here, it is shown to have close links to simple exponential smoothing with a smoothed error tracking signal. A special case of damped trend exponential smoothing emerges from our analysis, one that is more parsimonious because it effectively relies on one less parameter. This special case is compared with its traditional counterpart in an application to the annual data from the M3 competition and is shown to be quite competitive.Exponential smoothing, monitoring forecasts, structural change, adjusting forecasts, state space models, damped trend

Empirical Information Criteria for Time Series Forecasting Model Selection

In this paper, we propose a new Empirical Information Criterion (EIC) for model selection which penalizes the likelihood of the data by a function of the number of parameters in the model. It is designed to be used where there are a large number of time series to be forecast. However, a bootstrap version of the EIC can be used where there is a single time series to be forecast. The EIC provides a data-driven model selection tool that can be tuned to the particular forecasting task. We compare the EIC with other model selection criteria including Akaike's Information Criterion (AIC) and Schwarz's Bayesian Information Criterion (BIC). The comparisons show that for the M3 forecasting competition data, the EIC outperforms both the AIC and BIC, particularly for longer forecast horizons. We also compare the criteria on simulated data and find that the EIC does better than existing criteria in that case also.Exponential smoothing; forecasting; information criteria; M3 competition; model selection.

Investigation of the chemical kinetics of an advanced high energy propellant system Quarterly progress report, 1 Jun. - 1 Sep. 1968

Reaction kinetics of high energy oxygen difluoride diborane propellant syste

Another Look at Measures of Forecast Accuracy

We discuss and compare measures of accuracy of univariate time series forecasts. The methods used in the M-competition and the M3-competition, and many of the measures recommended by previous authors on this topic, are found to be inadequate, and many of them are degenerate in commonly occurring situations. Instead, we propose that the mean absolute scaled error become the standard measure for comparing forecast accuracy across multiple time series.Forecast accuracy, Forecast evaluation, Forecast error measures, M-competition, Mean absolute scaled error.

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

Differential Relationship between Physical Activity and Intake of Added Sugar and Nutrient-Dense Foods: A Cross-Sectional Analysis

A curvilinear relationship exists between physical activity (PA) and dietary energy intake (EI), which is reduced in moderately active when compared to inactive and highly active individuals, but the impact of PA on eating patterns remains poorly understood. Our goal was to establish the relationship between PA and intake of foods with varying energy and nutrient density. Data from the 2009–2010 United States National Health and Nutrition Examination Survey were used to include a Dietary Screener Questionnaire for estimated intakes of added sugar, fruits and vegetables, whole grains, fiber, and dairy. Participants (n = 4766; 49.7% women) were divided into sex-specific quintiles based on their habitual PA. After adjustment for age, body mass index, household income, and education, intakes were compared between PA quartiles, using the lowest activity quintile (Q1) as reference. Women in the second to fourth quintile (Q2-Q4) consumed less added sugar from sugary foods (+2 tsp/day) and from sweetened beverages (+2 tsp/day; all p \u3c 0.05 vs. Q1). In men, added sugar intake was elevated in the highest activity quintile (Q5: +3 ± 1 tsp/day, p = 0.007 vs. Q1). Fruit and vegetable intake increased (women: Q1-Q4 +0.3 ± 0.1 cup eq/day; p \u3c 0.001; men: Q1-Q3 +0.3 ± 0.1 cup eq/day, p = 0.002) and stagnated in higher quintiles. Dairy intake increased with PA only in men (Q5: +0.3 ± 0.1 cup eq/day, p \u3c 0.001 vs. Q1). Results demonstrate a differential relationship between habitual PA and dietary intakes, whereby moderate but not necessarily highest PA levels are associated with reduced added sugar and increased nutrient-dense food consumption. Future research should examine specific mechanisms of food choices at various PA levels to ensure dietary behaviors (i.e., increased sugary food intake) do not negate positive effects of PA

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.

Modeling pN2 through Geological Time: Implications for Planetary Climates and Atmospheric Biosignatures

Nitrogen is a major nutrient for all life on Earth and could plausibly play a similar role in extraterrestrial biospheres. The major reservoir of nitrogen at Earth's surface is atmospheric N2, but recent studies have proposed that the size of this reservoir may have fluctuated significantly over the course of Earth's history with particularly low levels in the Neoarchean - presumably as a result of biological activity. We used a biogeochemical box model to test which conditions are necessary to cause large swings in atmospheric N2 pressure. Parameters for our model are constrained by observations of modern Earth and reconstructions of biomass burial and oxidative weathering in deep time. A 1-D climate model was used to model potential effects on atmospheric climate. In a second set of tests, we perturbed our box model to investigate which parameters have the greatest impact on the evolution of atmospheric pN2 and consider possible implications for nitrogen cycling on other planets. Our results suggest that (a) a high rate of biomass burial would have been needed in the Archean to draw down atmospheric pN2 to less than half modern levels, (b) the resulting effect on temperature could probably have been compensated by increasing solar luminosity and a mild increase in pCO2, and (c) atmospheric oxygenation could have initiated a stepwise pN2 rebound through oxidative weathering. In general, life appears to be necessary for significant atmospheric pN2 swings on Earth-like planets. Our results further support the idea that an exoplanetary atmosphere rich in both N2 and O2 is a signature of an oxygen-producing biosphere.Comment: 33 pages, 11 figures, 2 tables (includes appendix), published in Astrobiolog