SummaryWe forecast the old‐age dependency ratio for Australia under various pension age proposals... more SummaryWe forecast the old‐age dependency ratio for Australia under various pension age proposals, and estimate a pension age scheme that will provide a stable old‐age dependency ratio at a specified level. Our approach involves a stochastic population forecasting method based on coherent functional data models for mortality, fertility and net migration, which we use to simulate the future age‐structure of the population. Our results suggest that the Australian pension age should be increased to 68 by 2030, 69 by 2036 and 70 by 2050, in order to maintain the old‐age dependency ratio at 23%, just above the 2018 level. Our general approach can easily be extended to other target levels of the old‐age dependency ratio and to other countries.
Intraday financial data often take the form of a collection of curves that can be observed sequen... more Intraday financial data often take the form of a collection of curves that can be observed sequentially over time, such as intraday stock price curves. These curves can be viewed as a time series of functions observed on equally spaced and dense grids. Due to the curse of dimensionality, high‐dimensional data pose challenges from a statistical aspect; however, it also provides opportunities to analyze a rich source of information so that the dynamic changes within short‐time intervals can be better understood. We consider a sieve bootstrap method to construct 1‐day‐ahead point and interval forecasts in a model‐free way. As we sequentially observe new data, we also implement two dynamic updating methods to update point and interval forecasts for achieving improved accuracy. The forecasting methods are validated through an empirical study of 5‐min cumulative intraday returns of the S&P/ASX All Ordinaries Index.
The problem of estimating missing fragments of curves from a functional sample has been widely co... more The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, most reconstruction methods rely on estimating the covariance matrix or the components of its eigendecomposition, which may be difficult. In particular, the estimation accuracy might be affected by the complexity of the covariance function, the noise of the discrete observations, and the poor availability of complete discrete functional data. We introduce a non-parametric alternative based on depth measures for partially observed functional data. Our simulations point out that the benchmark methods perform better when the data come from one population, curves are smooth, and there is a large proportion of complete data. However, our approach is superior when considering more complex covariance structures, non-smooth curves, and when the proportion of complete functions is scarce. Moreover, even in the most severe case of having all the functions incom...
In this study, we propose a function-on-function linear quantile regression model that allows for... more In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a finitedimensional space via the functional principal component analysis paradigm in the estimation phase. It is then approximated using the estimated functional principal component functions, and the estimated parameter of the quantile regression model is constructed based on the principal component scores. In addition, we propose a Bayesian information criterion to determine the optimum number of truncation constants used in the functional principal component decomposition. Moreover, a stepwise forward procedure and the Bayesian information criterion are used to determine the significant predictors for including in the model. We employ a nonparametric bootstrap procedure to construct prediction intervals for the response functions. The finite sample perfor...
SummaryWe forecast the old‐age dependency ratio for Australia under various pension age proposals... more SummaryWe forecast the old‐age dependency ratio for Australia under various pension age proposals, and estimate a pension age scheme that will provide a stable old‐age dependency ratio at a specified level. Our approach involves a stochastic population forecasting method based on coherent functional data models for mortality, fertility and net migration, which we use to simulate the future age‐structure of the population. Our results suggest that the Australian pension age should be increased to 68 by 2030, 69 by 2036 and 70 by 2050, in order to maintain the old‐age dependency ratio at 23%, just above the 2018 level. Our general approach can easily be extended to other target levels of the old‐age dependency ratio and to other countries.
Intraday financial data often take the form of a collection of curves that can be observed sequen... more Intraday financial data often take the form of a collection of curves that can be observed sequentially over time, such as intraday stock price curves. These curves can be viewed as a time series of functions observed on equally spaced and dense grids. Due to the curse of dimensionality, high‐dimensional data pose challenges from a statistical aspect; however, it also provides opportunities to analyze a rich source of information so that the dynamic changes within short‐time intervals can be better understood. We consider a sieve bootstrap method to construct 1‐day‐ahead point and interval forecasts in a model‐free way. As we sequentially observe new data, we also implement two dynamic updating methods to update point and interval forecasts for achieving improved accuracy. The forecasting methods are validated through an empirical study of 5‐min cumulative intraday returns of the S&P/ASX All Ordinaries Index.
The problem of estimating missing fragments of curves from a functional sample has been widely co... more The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, most reconstruction methods rely on estimating the covariance matrix or the components of its eigendecomposition, which may be difficult. In particular, the estimation accuracy might be affected by the complexity of the covariance function, the noise of the discrete observations, and the poor availability of complete discrete functional data. We introduce a non-parametric alternative based on depth measures for partially observed functional data. Our simulations point out that the benchmark methods perform better when the data come from one population, curves are smooth, and there is a large proportion of complete data. However, our approach is superior when considering more complex covariance structures, non-smooth curves, and when the proportion of complete functions is scarce. Moreover, even in the most severe case of having all the functions incom...
In this study, we propose a function-on-function linear quantile regression model that allows for... more In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a finitedimensional space via the functional principal component analysis paradigm in the estimation phase. It is then approximated using the estimated functional principal component functions, and the estimated parameter of the quantile regression model is constructed based on the principal component scores. In addition, we propose a Bayesian information criterion to determine the optimum number of truncation constants used in the functional principal component decomposition. Moreover, a stepwise forward procedure and the Bayesian information criterion are used to determine the significant predictors for including in the model. We employ a nonparametric bootstrap procedure to construct prediction intervals for the response functions. The finite sample perfor...
Uploads
Papers by Han Lin Shang