A Research Report submitted to the Faculty of Science in partial fulfilment of the requirements for the degree of Master of Science in the School of Statistics and Actuarial Science. 26 May 2016 / Exponential smoothing is a recursive time series technique whereby forecasts are updated for each new incoming data values. The technique has been widely used in forecasting, particularly in business and inventory modelling. Up until the early 2000s, exponential smoothing methods were often criticized by statisticians for lacking an objective statistical basis for model selection and modelling errors. Despite this, exponential smoothing methods appealed to forecasters due to their forecasting performance and relative ease of use. In this research report, we apply three commonly used exponential smoothing methods to two datasets which exhibit both trend and seasonality. We apply the method directly on the data without de-seasonalizing the data first. We also apply a seasonal naive method for benchmarking the performance of exponential smoothing methods. We compare both in-sample and out-of-sample forecasting performance of the methods. The performance of the methods is assessed using forecast accuracy measures. Results show that the Holt-Winters exponential smoothing method with additive seasonality performed best for forecasting monthly rainfall data. The simple exponential smoothing method outperformed the Holt’s and Holt-Winters methods for forecasting daily temperature data.

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One way to smooth earnings is to use accounting changes. This paper focuses on discretionary accounting changes as the smoothing device used by firms. This paper tests for smoothing behavior as a function of incentives. The association between the smoothing behavior displayed within a sample of firms and firm-specific explanatory variables is examined.

My research is concentrated on applications of linear algebra in engineering, including wavelet analysis and structured matrices. This paper will appear in the book Mathematical Systems Theory (J. Rosenthal and D. Gilliam, editors) IMA Volumes in Mathematics, Springer 2002. / Singapore-MIT Alliance (SMA)

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Dissertation (PhD)--University of Stellenbosch, 2007. / Bibliography. Also available via the Internet.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaves 332-336).

This thesis provides a survey study on applications of spline functions to statistics. We start with a brief history of splines. Then, we discuss the application of splines to statistics as they are applied today. Several topics included in the discussion are splines, spline regression, spline smoothing, and estimating the smoothing parameter for spline regression. Also, we give a very brief discussion of multivariate splines in statistics and wavelets in statistics. Both of these topics are currently subjects for continuing research by many mathematicians.

Spline smoothing is a popular technique for creating maps of a spatial phenomenon. Most smoothers use the Euclidean metric to measure the distance between data. This approach is flawed since the distances between points in the domain as experienced by the objects within the domain are rarely Euclidean. For example, the movements of animals and people are subject to both physical and political boundaries (respectively) which must be navigated. Measuring distances between the objects using the incorrect (Euclidean) metric leads to incorrect inference. The first part of this thesis develops a finite area smoother which does not su↵er from this problem when the shape of the area is complex. It begins by rejecting the use of the Schwarz-Christo↵el transform as a method for morphing complex domains due to its squashing of space. From there a method based on preserving within-area distances using multidimensional scaling is developed. High dimensional projections of the data are necessary to avoid a loss of ordering in the points. To smooth reliably in high dimensions Duchon splines are used. The model developed rivals the current best finite area method in prediction error terms and fits easily into larger models. Finally, the utility of projection methods to smooth general distances is explored. The second part of the thesis concerns distance sampling, a widely used set of methods for estimating the abundance of biological populations. The work presented here introduces mixture formulation for the detection function used to model the probability of detection. The use of mixture models leads to flexible but monotonic detection functions, avoiding the unrealistic shapes which conventional methods are prone to. These new models are then applied to several existing, problematic data sets.