TY - JOUR
T1 - State space modeling of non-standard actuarial time series
AU - Carlin, Bradley P.
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1992/10
Y1 - 1992/10
N2 - Insurance professionals have long recognized the value of time series methods in analyzing sequential business and economic data. However, the usual class of Box-Jenkins models are sometimes not flexible enough to adequately describe many practically-arising time series. By way of contrast, the state-space model offers a general approach for multivariate time-series modeling, forecasting, and smoothing. Versions of these models having linear mean structure and Gaussian error distributions have enjoyed actuarial application (for instance, in credibility theory) using the simple recursive updating formulae provided by the Kalman filter algorithm. Recently, fitting these models in more challenging non-linear and non-Gaussian scenarios has become feasible using Monte Carlo integration techniques [Carlin, Polson and Stoffer (J. Amer. Statist. Assoc., 1992)]. This paper gives a brief review of this new methodology, and subsequently demonstrates its usefulness in actuarial settings via three data examples. The non-standard modeling features illustrated include the explicit incorporation of covariates, direct modeling of non-stationary series without differencing, multivariate analysis, comparison of results under normal and non-normal error assumptions, density estimation for future observations, and non-linear model building and testing.
AB - Insurance professionals have long recognized the value of time series methods in analyzing sequential business and economic data. However, the usual class of Box-Jenkins models are sometimes not flexible enough to adequately describe many practically-arising time series. By way of contrast, the state-space model offers a general approach for multivariate time-series modeling, forecasting, and smoothing. Versions of these models having linear mean structure and Gaussian error distributions have enjoyed actuarial application (for instance, in credibility theory) using the simple recursive updating formulae provided by the Kalman filter algorithm. Recently, fitting these models in more challenging non-linear and non-Gaussian scenarios has become feasible using Monte Carlo integration techniques [Carlin, Polson and Stoffer (J. Amer. Statist. Assoc., 1992)]. This paper gives a brief review of this new methodology, and subsequently demonstrates its usefulness in actuarial settings via three data examples. The non-standard modeling features illustrated include the explicit incorporation of covariates, direct modeling of non-stationary series without differencing, multivariate analysis, comparison of results under normal and non-normal error assumptions, density estimation for future observations, and non-linear model building and testing.
KW - Bayes methods
KW - Credibility
KW - Gibbs sampling
KW - Kalman filter
KW - Monte Carlo methods
KW - Non-Gaussian errors
KW - Non-linear models
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U2 - 10.1016/0167-6687(92)90027-9
DO - 10.1016/0167-6687(92)90027-9
M3 - Article
AN - SCOPUS:44049109739
SN - 0167-6687
VL - 11
SP - 209
EP - 222
JO - Insurance Mathematics and Economics
JF - Insurance Mathematics and Economics
IS - 3
ER -