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

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.

Paleoseismic and Slip-Rate Observations along the Honey Lake Fault Zone, Northeastern California, USA

The Honey Lake fault is a major strike-slip fault in northeastern California that accommodates northwest-directed right-lateral shear in the northern Walker Lane. We reexamine the fault’s paleoseismic history and slip rate by evaluating a natural stream bank exposure of the fault and offset terrace riser. Structural and stratigraphic relations within the modern stream cut, radiocarbon ages, and a detailed topographic survey of the offset terrace riser are used to estimate a Holocene fault slip rate of 1.7–0.6 mm/yr or more. We also interpret the occurrence of at least four surface-rupturing earthquakes during the last 7025 calendar years before present (B.P.). Three of the surface-rupturing earthquakes occurred prior to 4670 calendar years B.P. and have interevent times that range between 730 and 990 yr. The stratigraphic record is limited after ~4670 calendar years B.P., and records evidence for at least one more subsequent surface-rupturing earthquake

The Structure of AdS Black Holes and Chern Simons Theory in 2+1 Dimensions

We study anti-de Sitter black holes in 2+1 dimensions in terms of Chern Simons gauge theory of anti-de Sitter group coupled to a source. Taking the source to be an anti-de Sitter state specified by its Casimir invariants, we show how all the relevant features of the black hole are accounted for. The requirement that the source be a unitary representation leads to a discrete tower of states which provide a microscopic model for the black hole.Comment: 17 pages, LaTex. The presentation in Section 5 was improved; other minor improvements. Final form of the manuscrip

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