臺灣博碩士論文加值系統

死亡率的預測在制定福利政策上扮演了一個十分重要的角色。然而對於老年人口的預測現今的死亡率模型並沒有辦法處理得很好。一個典型的問題就是人口資料的遺失。以台灣為例，由於西元1998年至1997年中死亡人數只統計到94歲，其餘超過94歲的人口資料皆歸類在95+類別中，因此我們無法得知95歲以上每個年齡層真實死亡人數。有鑑於此，在這篇研究中我們提出ㄧ些補遺失值的方法。建構在兩個十分有名的模型，Lee-Carter 模型 (Lee and Carter, 1992) 和修正後的 Age-Period-Cohort 模型 (Renshaw and Haberman, 2006)。並且，我們也比較在模擬的資料與台灣真實資料在交叉驗證上的結果。

Mortality forecasting plays an essential role in designing welfare policies and pricing aged-related financial derivatives. However, most prevailing models do not perform well in mortality forecasting particularly for the elder people. Indeed, the missing mortality data for the elder people is a typical feature in developing countries, because people are shorter-lived in earlier times and hence the mortality is recorded at fewer age categories. For example, in Taiwan, the mortality is recorded up to an age of 95 before 1997, but the mortality is recorded up to an age of 100 afterwards. This paper proposes several methods to augment the missing mortality data based on two famous models: the Lee-Carter model (Lee and Carter, 1992) and the Age-Period-Cohort model (Renshaw and Haberman, 2006). Both simulation and empirical studies demonstrate the improvement in terms of out-of-sample forecasting using a suitable data augmentation technique.

摘 要 i
Abstract ii
誌謝 iii
List of Figures v
List of Tables vi
Chapter 1 Introduction 1
Chapter 2 Review on forecasting models 4
2.1 Notations 4
2.2 The Lee-Carter Model 6
2.3 The Age-Period-Cohort Model 8
Chapter 3 Methods to impute missing data 11
3.1 The toy method 11
3.2 The weighted method 12
3.3 The two-step method 13
3.4 The MLE method 14
Chapter 4 The implementation of the MLE method 16
4.1 Algorithm under the LC model 17
4.2 Algorithm under the APC model 19
Chapter 5 Simulation studies 23
5.1 Simulation data 23
Chapter 6 Empirical analysis 26
6.1 Exploratory data analysis 26
6.2 Comparisons 36
Chapter 7 Conclusion 39
References 41

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