669 Proc. ICCS-12, Doha, Qatar December 19-22, 2012, Vol. 23, pp. 669-674 FORECASTING AGE-SPECIFIC FERTILITY RATES OF PAKISTAN USING FUNCTIONAL TIME SERIES MODELS Farah Yasmeen and Zahid Mahmood Department of Statistics, University of Karachi, Karachi, Pakistan Email: riazfarah@yahoo.com ABSTRACT The purpose of this study is to model and forecast the trend and patterns of fertility rates in Pakistan. We use functional time series (FTS) models to obtain the forecast for the next twenty years. The secondary data of age-specific fertility rates from 1984 to 2005, obtained from Pakistan Demographic Surveys (PDS) are used. These data are available for 1984-1986, 1988-1992, 1995-1997, 1999-2001, 2003 and 2005. Age- specific fertility rates are missing for rest of the years, so we estimate them using interpolation splines. Before applying FTS models, the data are smoothed using non- parametric smoothing methods. We use weighted regression B-splines with a concavity constraint. Finally we fit a model with four basis functions, which shows the major modes of variations. We obtain the forecasts for the next twenty years (2006-2025). KEY WORDS Age-specific fertility rates, fertility pattern, functional time series, forecast, forecast error. 1. INTRODUCTION In many fields of statistical research, data arise in the form of curves or surfaces rather than collection of simple points. Such data are termed "functional data". Functional data analysis (FDA) has attained substantial development in recent years. Functional time series (FTS) encompasses data in the form of curves that are observed at regular intervals in time. The applications of functional time series include Hyndman and Ullah 2007, Erbas etal 2007 and Yasmeen et al 2010. In this paper, we will apply the functional time series (FTS) models to the age- specific fertility rates of Pakistan. A variety of mathematical models have been proposed to describe the reproductivity and fertility pattern. They include Pollard et al. (1990), and Peristera and Kostaki (2007). The other useful references are Sathar and Casterline (1998) and Sathar and Kazi (1990). However to study the fertility, the existing literature is lacking the modelling approach. Also, neither of these studies has considered the forecasting of fertility curve for future. Current piece of work mainly concentrates on the modelling and forecasting age-specific fertility rates for Pakistan. The main objectives of this paper are: To study the behaviour and patterns of the age specific fertility rates (ASFR) for available years;