1 , ( ) t t t t t t Y gX U withU U e − = + = + World Applied Sciences Journal 26 (6): 783-787, 2013 ISSN 1818-4952 © IDOSI Publications, 2013 DOI: 10.5829/idosi.wasj.2013.26.06.523 Corresponding Author: S.J. Mortazavi Amiri, Department of statistics, Science and Research Branch, Islamic Azad University(IAU), Tehran, Iran. 783 The Prediction Nonlinear-Autoregressive Model for Annual Ring Width of Pinus Eldarica with Semi-Parametric Approach S.J. Mortazavi and R. Farnoosh 1 2 Department of statistics, Science and Research Branch, 1 Islamic Azad University(IAU), Tehran, Iran Department of Mathematics, Iran University of Science 2 and Technology, Tehran 16846, Iran Submitted: Feb 20, 2011; Accepted: Jun 16, 2011; Published: Nov 23, 2013 Abstract: The aim of this research is to find the regularity in frequencies of diameter increment and determine the relationship between tree age and fluctuations in radial increment of Pine trees (Pinus Eldarica). In this direction, three normal pine trees from Kelardashat site (north of Iran) were selected. Disks were cut down at breast height and the annual ring width in radial axis (1974-2008) was determined by Binocular system. The additive functional-autoregressive model is considered and semi-parametric method is proposed to forecast regression function. Furthermore, the method is applied for annual ring width prediction. The results showed that the nonlinear time series model is an efficient models for prediction of annual ring width. Key words: Semi-parametric estimation Nonlinear time series models Binocular system Conditional least squares method Annual ring width INTRODUCTION Actually Douglass is not the first discoverer of tree rings Due to increasing wood consumption and the development of the science of Dendrochronology [3]. development of pulp and paper production, plantations of Dendroclimatology looks for a “climatic signal” in the fast growing tree species managed with short rotations annual increment of the tree vascular tissue. The basic have a growing importance for the sustainability of assumption of dendroclimatological analysis is a industrial wood raw material. The softwoods, especially commonly accepted belief that meteorological conditions fast growing pine species, have a higher priority for are the main factor determining the annual fluctuations in plantation forestry due to their adaptation capability to tree-ring sizes. The annual variability of radial increments wide ecological conditions and various usage areas. is recorded in the chronology of the width of tree-rings Therefore, Parks and Forestry officials have imported and it can be interpreted as historical information about approximately 48 foreign fast-grown softwood species the sensitivity and reaction of a particular species to into Iran since 1956 and planted them in different climatological conditions of the environment. ecological conditions [1]. Pinus eldarica was one of the In recent years, a combination of parametric forms softwood species planted in many parts of Iran and has and nonlinear functions have been used to make a more shown a good adaptation to environmental condition. efficient model in various branches of sciences, The discipline of Dendrochronology, which is particularly in applied statistics, econometrics and development and use of time-series by means of annual climatology and forest studies. The nonparametric growth ring of trees, comprises a set of techniques by regression models with linear autoregressive error which the annual growth layers of trees may be assigned considered as the following form to a definite calendar year [2]. Andrew E. Douglass is acknowledged as the father of Dendrochronology [3]. [4, 5], but he utilized the principle as the basis for the