We address the issue of modelling and forecasting macroeconomic variables using rich datasets by adopting the class of Vector Autoregressive Moving Average (VARMA) models. We overcome the estimation issue that arises with this class of models by implementing an iterative ordinary least squares (IOLS) estimator. We establish the consistency and asymptotic distribution of the estimator for weak and strong VARMA(p,q) models. Monte Carlo results show that IOLS is consistent and feasible for large systems, outperforming the MLE and other linear regression based efficient estimators under alternative scenarios. Our empirical application shows that VARMA models are feasible alternatives when forecasting with many predictors. We show that VARMA models outperform the AR(1), ARMA(1,1), Bayesian VAR, and factor models, considering different model dimensions.
I propose an estimation strategy for the stochastic time-varying risk premium parameter in the context of a time-varying GARCH-in-mean (TVGARCH-inmean) model. A Monte Carlo study shows that the proposed algorithm has good finite sample properties. Using monthly excess returns on the CRSP index, I document that the risk premium parameter is indeed time-varying and shows high degree of persistence.
a b s t r a c tA two-stage forecasting approach for long memory time series is introduced. In the first step, we estimate the fractional exponent and, by applying the fractional differencing operator, obtain the underlying weakly dependent series. In the second step, we produce multi-step-ahead forecasts for the weakly dependent series and obtain their long memory counterparts by applying the fractional cumulation operator. The methodology applies to both stationary and nonstationary cases. Simulations and an application to seven time series provide evidence that the new methodology is more robust to structural change and yields good forecasting results.
The presence of symmetries in the solution set of mathematical programs requires the exploration of symmetric subtrees during the execution of Branch-and-Bound type algorithms and yields increases in computation times. When some of the solution symmetries are evident in the formulation, it is possible to deal with symmetries as a preprocessing step. In this sense, implementation-wise, one of the simplest approaches is to break symmetries by adjoining Symmetry-Breaking Constraints (SBCs) to the formulation. Designed to remove some of the symmetric global optima, these constraints are generated from each orbit of the action of the symmetries on the variable index set. Incompatible SBCs however make all of the global optima infeasible. In this paper we introduce and test a new concept of Orbital Independence which we define as independent sets of orbits. We provide necessary conditions for characterizing independent sets of orbits and also prove that such sets embed sufficient conditions to exploit symmetries from two or more distinct orbits concurrently. The theory developed is used to devise an algorithm that potentially identifies the largest independent set of orbits of any mathematical program. Extensive numerical experiments are provided to validate the theoretical results. Keywords combinatorial optimization • symmetry breaking • group theory • quadratic programming This paper is an extension of the work presented in [5].
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