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Register a new userSemiparametric time series models driven by latent factor
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Added by
Wagner Barreto-Souza
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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We introduce a class of semiparametric time series models by assuming a quasi-likelihood approach driven by a latent factor process. More specifically, given the latent process, we only specify the conditional mean and variance of the time series and enjoy a quasi-likelihood function for estimating parameters related to the mean. This proposed methodology has three remarkable features: (i) no parametric form is assumed for the conditional distribution of the time series given the latent process; (ii) able for modelling non-negative, count, bounded/binary and real-valued time series; (iii) dispersion parameter is not assumed to be known. Further, we obtain explicit expressions for the marginal moments and for the autocorrelation function of the time series process so that a method of moments can be employed for estimating the dispersion parameter and also parameters related to the latent process. Simulated results aiming to check the proposed estimation procedure are presented. Real data analysis on unemployment rate and precipitation time series illustrate the potencial for practice of our methodology.
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Many existing mortality models follow the framework of classical factor models, such as the Lee-Carter model and its variants. Latent common factors in factor models are defined as time-related mortality indices (such as $kappa_t$ in the Lee-Carter model). Factor loadings, which capture the linear relationship between age variables and latent common factors (such as $beta_x$ in the Lee-Carter model), are assumed to be time-invariant in the classical framework. This assumption is usually too restrictive in reality as mortality datasets typically span a long period of time. Driving forces such as medical improvement of certain diseases, environmental changes and technological progress may significantly influence the relationship of different variables. In this paper, we first develop a factor model with time-varying factor loadings (time-varying factor model) as an extension of the classical factor model for mortality modelling. Two forecasting methods to extrapolate the factor loadings, the local regression method and the naive method, are proposed for the time-varying factor model. From the empirical data analysis, we find that the new model can capture the empirical feature of time-varying factor loadings and improve mortality forecasting over different horizons and countries. Further, we propose a novel approach based on change point analysis to estimate the optimal `boundary between short-term and long-term forecasting, which is favoured by the local linear regression and naive method, respectively. Additionally, simulation studies are provided to show the performance of the time-varying factor model under various scenarios.
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