In this investigation, the Sinc collocation method based on double exponential transformation is developed to solve the Troesche's problem. Properties of this method are utilized to reduce the system of strongly nonlinear two point boundary value problem to same nonlinear algebraic equations. Combining double exponential transformation through Sinc collocation method causes the remarkable resul...

Damped trend exponential smoothing models have gained importance in empirical studies due to their remarkable forecasting performance. This paper derives their theoretical forecast error variance, based on the implied ARIMA model, as algebraic function of the structural parameters. As a consequence, the minimum mean squared error (MMSE) forecasts as well as the h-step ahead theoretical forecast...

We consider the properties of nonlinear exponential smoothing state space models under various assumptions about the innovations, or error, process. Our interest is restricted to those models that are used to describe non-negative observations, because many series of practical interest are so constrained. We first demonstrate that when the innovations process is assumed to be Gaussian, the resu...

The Boot.EXPOS procedure is an algorithm that combines the use of exponential smoothing methods with the bootstrap methodology for obtaining forecasts. In previous works the authors have studied and analyzed the interaction between these two methodologies. The initial sketch of the procedure was developed, modified and evaluated until its final form designated as Boot.EXPOS.

Using an innovations state space approach, it has been found that the Akaike information criterion (AIC) works slightly better, on average, than prediction validation on withheld data, for choosing between the various common methods of exponential smoothing for forecasting. There is, however, a puzzle. Should the count of the seed states be incorporated into the penalty term in the AIC formula?...

The most common forecasting methods in business are based on exponential smoothing, and the most common time series in business are inherently non-negative. Therefore it is of interest to consider the properties of the potential stochastic models underlying exponential smoothing when applied to non-negative data. We explore exponential smoothing state space models for non-negative data under va...

In this article we discuss invertibility conditions for some state space models, including the models that underly simple exponential smoothing, Holt’s linear method, Holt-Winters’ additive method and damped trend versions of Holt’s and Holt-Winters’ methods. The parameter space for which the model is invertible is compared to the usual parameter regions. We find that the usual parameter restri...

Exponential smoothing methods gave poor forecast accuracy in Fildes et al.’s study of telecommunications time series. We reexamine this study and show that parameter optimization improves the accuracy of the Holt and damped trend methods. Further improvement occurs when the time series are trimmed to eliminate irrelevant early data, and when the methods are fitted to minimize the MAD rather tha...