This paper explores the classic single-item newsvendor problem under a novel setting which combines temporal dependence and tractable robust optimization. First, the demand is modeled as a time series which follows an autoregressive process AR(p), p ≥ 1. Second, a robust approach to maximize the worst-case revenue is proposed: a robust distribution-free autoregressive forecasting method, which copes with non-stationary time series, is formulated. A closed-form expression for the optimal solution is found for the problem for p = 1; for the remaining values of p, the problem is expressed as a nonlinear convex optimization program, to be solved numerically. The optimal solution under the robust method is compared with those obtained under two versions of the classic approach, in which either the demand distribution is unknown, and assumed to have no autocorrelation, or it is assumed to follow an AR(p) process with normal error terms. Numerical experiments show that our proposal usually outperforms the previous benchmarks, not only with regard to robustness, but also in terms of the average revenue.

We prove that the portfolio problem with transaction costs is equivalent to three different problems designed to alleviate the impact of estimation error: a robust portfolio optimization problem, a regularized regression problem, and a Bayesian portfolio problem. Motivated by these results, we propose a data-driven approach to portfolio optimization that tackles transaction costs and estimation error simultaneously by treating the transaction costs as a regularization term to be calibrated. Our empirical results demonstrate that the data-driven portfolios perform favorably because they strike an optimal trade-off between rebalancing the portfolio to capture the information in recent historical return data, and avoiding the large transaction costs and impact of estimation error associated with excessive trading.

Most time series forecasting methods assume the series has no missing values. When missing values exist, interpolation methods, while filling in the blanks, may substantially modify the statistical pattern of the data, since critical features such as moments and autocorrelations are not necessarily preserved.In this paper we propose to interpolate missing data in time series by solving a smooth nonconvex optimization problem which aims to preserve moments and autocorrelations. Since the problem may be multimodal, Variable Neighborhood Search is used to trade off quality of the interpolation (in terms of preservation of the statistical pattern) and computing times.Our approach is compared with standard interpolation methods and illustrated on both simulated and real data.

Vector autoregressive (VAR) models constitute a powerful and well studied tool to analyze multivariate time series. Since sparseness, crucial to identify and visualize joint dependencies and relevant causalities, is not expected to happen in the standard VAR model, several sparse variants have been introduced in the literature. However, in some cases it might be of interest to control some dimensions of the sparsity, as e.g. the number of causal features allowed in the prediction. To authors extent none of the existent methods endows the user with full control over the different aspects of the sparsity of the solution. In this article, we propose a versatile sparsity-controlled VAR model which enables a proper visualization of potential causalities while allows the user to control different dimensions of the sparsity if she holds some preferences regarding the sparsity of the outcome. The model coefficients are found as the solution to an optimization problem, solvable by standard numerical optimization routines. The tests performed on both simulated and real-life time series show that our approach may outperform a greedy algorithm and different Lasso approaches in terms of prediction errors and sparsity.

The Markovian arrival process (MAP) is a stochastic process that allows for modeling dependent and nonexponentially distributed observations. Due to its versatility, it has been widely applied in different contexts, from reliability to teletraffic. In this work we show the suitability of the MAP for modeling daily precipitation data, which are often characterized by a non-negligible correlation structure. Specifically, a set of daily precipitation amounts series from the region of Andalusia (Spain) is shown to be correctly fitted with a two-state MAP.