A Two-Population Extension of the Exponential Smoothing State Space Model with a Smoothing Penalisation Scheme

Abstract

The joint modelling of mortality rates for multiple populations has gained increasing popularity in areas such as government planning and insurance pricing. Sub-groups of a population often preserve similar mortality features with short-term deviations from the common trend. Recent studies indicate that the exponential smoothing state space (ETS) model can produce outstanding prediction performance, while it fails to guarantee the consistency across neighbouring ages. Apart from that, single-population models such as the famous Lee-Carter (LC) may produce divergent forecasts between different populations in the long run and thus lack the property of the so-called coherence. This study extends the original ETS model to a two-population version (2-ETS) and imposes a smoothing penalisation scheme to reduce inconsistency of forecasts across adjacent ages. The exponential smoothing parameters in the 2-ETS model are fitted by a Fourier functional form to reduce dimensionality and thus improve estimation efficiency. We evaluate the performance of the proposed model via an empirical study using Australian female and male population data. Our results demonstrate the superiority of the 2-ETS model over the LC and ETS as well as two multi-population methods - the augmented common factor model (LL) and coherent functional data model (CFDM) regarding forecast accuracy and coherence.

Automatic time series forecasting using nonlinear autoregressive neural network model with exogenous input

“…Based on the empirical study, the proposed automatic method is applied to forecast two real data, i.e., the Indonesian inflation and exchange rates between the Rupiah and US Dollar. Furthermore, the performance of this proposed model is compared with several available automatic methods in the literature, namely exponential smoothing (see discussion in [26]- [29]), ARIMA (see discussion in [30]- [33]), and NAR parallel architecture without feedback. The forecasting accuracy is also being measured by mean squared error (MSE) and mean absolute percent error (MAPE).…”

“…The summary of the forecasting performance was shown in Table 1, and the automatic NARX model that combined the median ensemble operator, hyperbolic-tangent activation function, and rprop+ was observed to have produced the smallest MSE and MAPE values. There was also a performance comparison of the proposed methods with the other forecasting models, including automatic exponential smoothing (see discussion in [26]- [29]), automatic ARIMA (see discussion in [30]- [33]), and automatic NAR parallel architecture without feedback (see discussion in [8], [11]- [13]), respectively. Furthermore, the plot of in-sample fitting and out-sample forecasts for inflation rate data were shown in Figure 1, by using considered automatic algorithms.…”