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This paper intends to meet recent claims for the attainment of more rigorous statistical methodology within the econophysics literature. To this end, we consider an econometric approach to investigate the outcomes of the log-periodic model of price movements, which has been largely used to forecast financial crashes. In order to accomplish reliable statistical inference for unknown parameters, we incorporate an autoregressive dynamic and a conditional heteroskedasticity structure in the error term of the original model, yielding the log-periodic-AR(1)-GARCH(1,1) model. Both the original and the extended models are fitted to financial indices of U. S. market, namely S&P500 and NASDAQ. Our analysis reveal two main points: (i) the log-periodic-AR(1)-GARCH(1,1) model has residuals with better statistical properties and (ii) the estimation of the parameter concerning the time of the financial crash has been improved.

The issue of modeling and forecasting IBNR (incurred but not reported) actuarial reserve under Kalman filter techniques and extensions, using data arranged in a runoff triangle, is a frequent theme in the literature. One quite recent approach is to order the runoff triangle under a row-wise fashion and use linear state-space models for the resulting data set. To allow new possibilities for short-term IBNR reserves as well as to mitigate insolvency risk, in this paper we extend such a state-space method by: (i) a calendar year IBNR reserve prediction; and (ii) a tail effect for the row-wise ordered triangle. The extension is implemented with a real runoff triangle and compared with some traditional IBNR predictors. Empirical results indicate that the approach of this paper outperforms the competing methods in terms of out-of-sample comparisons and gives more conservative IBNR reserves than the original statespace method.

This paper presents a framework and methods for the estimation of linear and non-linear state space (SS) models, occasionally subject to restrictions, to construct and estimate several models for style analysis with time varying exposures. The study is conducted by applying these models to an artificial portfolio and to return series of Brazilian investment funds. The results confirm the belief that dynamic allocations in a portfolio are a more realistic assumption for investment funds management.

This paper deals with linear state space modelling subject to general linear constraints on the state vector. The discussion concentrates on four topics: the constrained Kalman filtering versus the recursive restricted least squares estimator; a new proof of the constrained Kalman filtering under a conditional expectation framework; linear constraints under a reduced state space modelling; and state vector prediction under linear constraints. The techniques proposed are illustrated in two real problems. The first problem is related to investment analysis under a dynamic factor model, whereas the second is about making constrained predictions within a GDP benchmarking estimation. Copyright (c) 2010 The Author. Journal compilation (c) 2010 International Statistical Institute.

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Benchmarking, Engle–Granger’s equation, Kalman’s filter, State space models, GDP, C32, C51, C52, E01, C10,

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