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...

The study has been carried out to measure the incidence of government spending on education in Pakistan at the provincial (both rural and urban) level, using the primary data of the Pakistan Social Standard Living Measures Survey (PSLM), 2004-2005, and by employing the three-step Benefit...

The study has been carried out to measure the incidence of government spending on health in Pakistan at provincial, both rural and urban level; using the primary data of the Pakistan Social Standard Living Measures Survey (PSLM), 2004-05, and by employing the three-step Benefit Incidence...

The purpose this study was to identify the short-run and long-run relationship between income level and saving behaviour in Pakistan along with inflation and age dependency ratio by using co-integration and error correction model (ECM) for the period of 1985-2009. Auto regressive distributed lag...

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...

The study has been carried out to measure the incidence of government spending on education in Pakistan at the provincial (both rural and urban) level, using the primary data of the Pakistan Social Standard Living Measures Survey (PSLM), 2004-2005, and by employing the three-step Benefit...

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...

This paper discusses the instability of eleven nonlinear state space models that underly exponential smoothing. Hyndman et al. (2002) proposed a framework of 24 state space models for exponential smoothing, including the well-known simple exponential smoothing, Holt's linear and Holt-Winters'...

We compare the small sample performance (in terms of bias and root mean squared error) of L-moment estimator of 3-parameter Weibull distribution with Maximum likelihood Estimation (MLE), Moment Estimation (MoE), Least squared estimation (LSE), the Modified MLE (MMLE), Modified MoE (MMoE), and...