Abstract— This article describes a common factor model to forecast mortality rates. The proposed model is an extension Lee-Carter state space (LC-SS) model by incorporating multiple common trends through application dynamic factor analysis (DFA) to reduce the dimension of the observed mortality rates in term of common trends. The original, the LC-SS model is formalized the Lee-Carter (LC) model as a statistical model accounting for all source of variability. The proposed model is actually the LC-SS incorporating DFA and being termed as LC-DFA model. The LC-DFA model is designed specifically for analyzing short and non-stationary mortality series. As in LC-SS, the parameters in the proposed LC-DFA model are estimated by maximum likelihood estimation (MLE) through an expectation-maximization (EM) algorithm. The mortality data of Peninsular Malaysia for years 1980 to 2009 were used to illustrate the performance of the proposed model. The data were split according to gender and separate LC-DFA models were each fitted for the males and female population. The LC-DFA performance in terms of the accuracy of prediction based on in-sample fitting and out-of- sample forecasts of the LC-DFA was then evaluated by comparing with the LC-SS and LC models. The most efficient forecasting model was based on lowest values of root mean square error (RMSE) and mean absolute percentage error (MAPE). The results revealed that the proposed LC-DFA model performs the best. Index Terms—Dynamic factor analysis, Expectation- maximum algorithm, Lee-Carter model, mortality, state space model. I. INTRODUCTION IMENSION reduction techniques such as principal component analysis (PCA), factor analysis (FA) or correspondence analysis (CA) have been applied by researchers to analyze sets of data that contain relatively large number of response variables. The main purpose of dimension reduction is to simplify the data without losing relevant information in the data sets. This requires that the simplified structure explains most of the variability in the data. The basic technique of data reduction in multivariate Manuscript received December 24, 2015; revised December 31, 2015. This work was supported in part by the Ministry of Education, Malaysia and Universiti Teknologi MARA, Malaysia under Fundamental Research Grant Scheme (FRGS) (FRGS/1/2014/ST06/UiTM/02/5). W. H. W. Zakiyatussariroh is with the Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia (corresponding author: phone: +6019-3409511; fax: +603-55442000; e-mail: wanzh76@gmail.com). M.S. Zainol, is with the Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia (e-mail: saidzainol@gmail.com). M.R. Norazan is with the Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam,Selangor, Malaysia (e-mail: norazan@tmsk.uitm.edu.my). analysis is PCA. However the PCA technique does not account for temporal variation. Dynamic factor analysis (DFA) (also known as dynamic factor model-DFM) is a dimension-reduction technique that models N observed non- stationary time series in term of M common trends. The principle of DFA is the same as other dimension reduction techniques. However, DFA is designed for time series. Although it is possible to apply PCA to time series data it does not take account of time in any way. Even though it can connect consecutive points in time with each other, interpretation of the results is likely to be difficult [1]. In 1992, Lee and Carter proposed a model which used PCA technique in modeling and forecasting age-specific mortality [2]. The LC model assumes that the log-death rates time series shares one common trend that explained by the first principal component term which represented by mortality index. This first term of principal component can be estimated by the singular value decomposition (SVD). Basically, the LC model is based on a log-bilinear form for age-specific mortality involving two equations. The parameters of these two equations are estimated separately where the first equation is computed from SVD in order to extract the principal component term (the mortality index), while, the second equation is modeled the mortality index using time series methods. The strength of the LC method is in its simplicity and robustness in the context of linear trends in age-specific death rates (ASDR) [3]. The model became the leading stochastic model in the actuarial and demographic literature and was used as a benchmark model in most academic researches and practical applications of mortality forecasting [4]-[7]. The LC method works very well for most of the countries, but, not for some countries. Therefore, the LC model has undergone various extensions and modifications exemplified in the works of [8]-[12]. Most of these extensions used PCA in extracting the first component or single common trend explained by the mortality index. A exception is the work done by [11] that included the incorporation of second and higher order terms into the LC model to cater for the additional component that are not explained by the first component. Apart from this, several extended the concept of LC model by considering multiple PCA components using dynamic factor model (DFM) in forecasting mortality [13], [14]. The extension of LC model also involves a reformulation of the model as state space model as in [15]-[18]. The main reason why a state space formulation of the LC model was suggested is due to the fact that errors of the LC equations were estimated separately. The first equation is estimated by a combination of SVD while the second as a time series model. Reference [15] highlighted the fact that the Common Factor Model with Multiple Trends for Forecasting Short Term Mortality Wan Zakiyatussariroh Wan Husin, Mohammad Said Zainol and Norazan Mohamed Ramli D Engineering Letters, 24:1, EL_24_1_14 (Advance online publication: 29 February 2016) ______________________________________________________________________________________