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We develop a method for constructing prediction intervals for a nonstationary variable, such as GDP. The method uses a factor augmented regression [FAR] model. The predictors in the model includes a small number of factors generated to extract most of the information in a set of panel data on a large number of macroeconomic variables considered to be potential predictors. The novelty of this paper is that it provides a method and justification for a mixture of stationary and nonstationary factors as predictors in the FAR model; we refer to this as mixture-FAR method. This method is important because typically such a large set of panel data, for example the FRED-MD, is likely to contain a mixture of stationary and nonstationary variables. In our simulation study, we observed that the proposed mixture-FAR method performed better than its competitor that requires all the predictors to be nonstationary; the MSE of prediction was at least 33% lower for mixture-FAR. Using the data in FRED-QD for the US, we evaluated the aforementioned methods for forecasting the nonstationary variables, GDP and Industrial Production. We observed that the mixture-FAR method performed better than its competitors.

A semiparametric method is studied for estimating the dependence parameter and the joint distribution of the error term in a class of multivariate time series models when the marginal distributions of the errors are unknown. This method is a natural extension of Genest et al. (1995a) for independent and identically distributed observations. The proposed method first obtains √n-consistent estimates of the parameters of each univariate marginal time-series, and computes the corresponding residuals. These are then used to estimate the joint distribution of the multivariate error terms, which is specified using a copula. Our developments and proofs make use of, and build upon, recent elegant results of Koul and Ling (2006) and Koul (2002) for these models. The rigorous proofs provided here also lay the foundation and collect together the technical arguments that would be useful for other potential extensions of this semiparametric approach. It is shown that the proposed estimator of the dependence parameter of the multivariate error term is asymptotically normal, and a consistent estimator of its large sample variance is also given so that confidence intervals may be constructed. A large scale simulation study was carried out to compare the estimators particularly when the error distributions are unknown, which is almost always the case in practice. In this simulation study, our proposed semiparametric method performed better than the well-known parametric methods. An example on exchange rates is used to illustrate the method.

This paper explores the hypothesis that international capital flows are driven in part by the level of economic activity. It investigates the existence of the income mobility of capital, as distinct from the interest mobility of capital, by using Hsiao's approach to testing for Granger causality to model the relationship between Australian investment abroad and the Australian real GDP. We find some evidence that income causes capital flows but no evidence to support reverse causation from capital flows to income. This result suggests that the analytical construct of the income mobility of capital has empirical content.

This paper proposes improvements to advanced measurement approach (AMA) to estimating operational risks, and applies the improved methods to US business losses categorised into five business lines and three event types operational losses. The AMA involves, among others, modelling a loss severity distribution and estimating the Expected Loss and the 99.9% operational value-at-risk (OpVaR). These measures form a basis for calculating the levels of regulatory and economic capitals required to cover risks arising from operational losses. In this paper, Expected Loss and OpVaR are estimated consistently and efficiently by nonparametric methods, which use the large (tail) losses as primary inputs. In addition, the 95% intervals for the underlying true OpVaR are estimated by the weighted empirical likelihood method. As an alternate measure to OpVaR, the Expected Shortfall - a coherent risk- is also estimated. The empirical findings show that the interval estimates are asymmetric, with very large upper bounds, highlighting the extent of uncertainties associated with the 99.9% OpVaR point estimates. The Expected Shortfalls are invariably greater than the corresponding OpVaRs. The heavier the loss severity distribution the greater the difference between OpVaR and Expected Shortfall, from which we infer that the latter would provide the right level of capital to cover risks than would the former, particularly during

A semiparametric method is developed for estimating the dependence parameter and the joint distribution of the error term in the multivariate linear regression model. The nonpara- metric part of the method treats the marginal distributions of the error term as unknown, and estimates them by suitable empirical distribution functions. Then a pseudolikelihood is maximized to estimate the dependence parameter. It is shown that this estimator is as- ymptotically normal, and a consistent estimator of its large sample variance is given. A simulation study shows that the proposed semiparametric estimator is better than the para- metric methods available when the error distribution is unknown, which is almost always the case in practice. It turns out that there is no loss of asymptotic e±ciency due to the estimation of the regression parameters. An empirical example on portfolio management is used to illustrate the method. This is an extension of earlier work by Oakes (1994) and Genest et al. (1995) for the case when the observations are independent and identically distributed, and Oakes and Ritz (2000) for the multivariate regression model.

This paper investigates whether or not there are significant changes in the dependence between the Thai equity market and six Asian markets - namely, Singaporean, Malaysian, Hong Kong, Korean, Indonesian and Taiwanese markets - due to 1997-July financial crisis. If so, this may be an indication that the underlying bivariate joint distributions capturing the dependence between the Thai market and these six markets have changed. We employ the chi-plot proposed by Fisher and Switzer (2001) and the Kendall plot proposed by Genest and Boies (2003) to examine the dependence in these six markets for the pre- and post-1997 financial crisis periods. We find that marginal distributions of all seven markets have notably changed due to this financial crisis, and that the functional forms of the underlying joint distributions generating the dependence in the Korean, Indonesian and Taiwan markets have also changed for the post-crisis period. It appears that the same parametric copula can capture the dependence in the Singapore, Malaysia and Hong Kong markets for both pre- and post-crisis periods, and that only the tail indices of bivariate distributions between the Thai and these three markets have changed. It is interesting to observe that the same conclusions can be drawn using both chi- and Kendall plots.