Page 122 - Contributed Paper Session (CPS) - Volume 3

CPS1965 Chin Tsung R. et al.

The modified Lee-Carter model with linearized
cubic spline parameter approximation for
Malaysian mortality data
Chin Tsung Rern, Dharini Pathmanathan, Shafiqah Azman, Nurul Aityqah
Yaacob
Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Malaysia

Abstract
We examine the application of the Lee-Carter (LC) model with parameters
approximated using linearized cubic splines. The original LC model produces
severely fluctuating predicted age-specific mortality. The model is applied to
the Malaysian mortality data (1991 to 2015) to select the model which suits
best to represent Malaysian mortality which was obtained from the
Department of Statistics Malaysia. The base period of this data is only 25 years
compared to other data available in the Human Mortality Database. The
forecasts obtained based on the LC model are unstable when the base period
is short. Hence, a modification of the LC model with linearized cubic spline
parameter approximation for short base periods which was initially applied to
the Chinese mortality data was applied to the Malaysian mortality data. Several
models were studied based on the selection of knots for male and female
mortality data and the best models to represent male and female mortalities
in Malaysia were selected. The modified models attained smaller estimation
errors (with respect to mean absolute percentage error, MAPE and mean
squared error, MSE) compared to the LC model.

Keywords
cubic spline; mortality; Lee-Carter; forecast

1. Introduction:
In recent years, it has been observed that there is a decline in mortality rates.
The most significant effect of this decline is the aging of the population.
The model proposed by Lee and Carter (1992) is as follows:

((, )) = () + ()() + (, ), = 1, … , (1)

where (, ) is the mortality rate of age group in year , is the beginning
of the last age interval, () is the average of ((, )) over time, ()
determines which rates change in response to the changes in for age ,

() is the mortality index in year and (, ) reflects particular age-specific
historical influences not fully captured by the model which is independent and
identically distributed and follows the (0, ) distribution. Lee and Carter
2

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