First formal announcement of many of these results appeared in Some of the refereed papers relative to MA-model concepts and its mathematical construction.

Abstract—In this paper, we study the rainfall using a time series for weather stations in Nakhon Ratchasima province in Thailand by various statistical methods to enable us to analyse the behaviour of rainfall in the study areas. Time-series analysis is an important tool in modelling and forecasting rainfall. The ARIMA and Holt-Winter models were built on the basis of exponential smoothing. All...

The main objective of this paper is to provide analytical expressions for forecast variances that can be used in prediction intervals for the exponential smoothing methods. These expressions are based on state space models with a single source of error that underlie the exponential smoothing methods. Three general classes of the state space models are presented. The first class is the standard ...

Automatic forecasts of large numbers of univariate time series are often needed in business and other contexts. We describe two automatic forecasting algorithms that have been implemented in the forecast package for R. The first is based on innovations state space models that underly exponential smoothing methods. The second is a step-wise algorithm for forecasting with ARIMA models. The algori...

The success of the company requires careful planning. Perusahaan Daerah Air Minum (PDAM) is a drinking water facility management that plays an important role in supporting smooth development region with influence revenue targets. Prediction targets deemed necessary for accurate and effective decision making. Predictions are made by comparing double moving average (DMA) exponential smoothing (DE...

Oil palm is one of the largest agricultural products in Indonesia and has high economic value can improve welfare oil farmers. The research was conducted at PT. Agro Putra Lestari regarding production, having its address Jln.Imam Bonjol No.179 Kisaran with name leader being Mr. Anda Puta Lubis, SE, M, Ma. a company that produces fruit which still running. spread across Asahan area, including Me...

In the exponential smoothing approach to forecasting, restrictions are often imposed on the smoothing parameters which ensure that certain components are exponentially weighted averages. In this paper, a new general restriction is derived on the basis that the one-step ahead prediction error can be decomposed into permanent and transient components. It is found that this general restriction red...

We develop a class of numerical methods for stiff systems, based on the method of exponential time differencing. We describe schemes with secondand higher-order accuracy, introduce new Runge–Kutta versions of these schemes, and extend the method to show how it may be applied to systems whose linear part is nondiagonal. We test the method against other common schemes, including integrating facto...

We study the impact of alternative detrending techniques on the distributional properties of U.S. output time series. We detrend GDP and industrial production time series employing first-differencing, Hodrick-Prescott and bandpass filters. We show that the resulting distributions can be approximated by symmetric Exponential-Power densities, with tails fatter than those of a Gaussian. We also em...