Large Vector Auto Regressions

One popular approach for nonstructural economic and financial forecasting is to include a large number of economic and financial variables, which has been shown to lead to significant improvements for forecasting, for example, by the dynamic factor models. A challenging issue is to determine which variables and (their) lags are relevant, especially when there is a mixture of serial correlation (temporal dynamics), high dimensional (spatial) dependence structure and moderate sample size (relative to dimensionality and lags). To this end, an \textit{integrated} solution that addresses these three challenges simultaneously is appealing. We study the large vector auto regressions here with three types of estimates. We treat each variable's own lags different from other variables' lags, distinguish various lags over time, and is able to select the variables and lags simultaneously. We first show the consequences of using Lasso type estimate directly for time series without considering the temporal dependence. In contrast, our proposed method can still produce an estimate as efficient as an \textit{oracle} under such scenarios. The tuning parameters are chosen via a data driven "rolling scheme" method to optimize the forecasting performance. A macroeconomic and financial forecasting problem is considered to illustrate its superiority over existing estimators

Large Vector Auto Regressions

One popular approach for nonstructural economic and financial forecasting is to include a large number of economic and financial variables, which has been shown to lead to significant improvements for forecasting, for example, by the dynamic factor models. A challenging issue is to determine which variables and (their) lags are relevant, especially when there is a mixture of serial correlation (temporal dynamics), high dimensional (spatial) dependence structure and moderate sample size (relative to dimensionality and lags). To this end, an integrated solution that addresses these three challenges simultaneously is appealing. We study the large vector auto regressions here with three types of estimates. We treat each variable's own lags different from other variables' lags, distinguish various lags over time, and is able to select the variables and lags simultaneously. We first show the consequences of using Lasso type estimate directly for time series without considering the temporal dependence. In contrast, our proposed method can still produce an estimate as efficient as an oracle under such scenarios. The tuning parameters are chosen via a data driven "rolling scheme" method to optimize the forecasting performance. A macroeconomic and financial forecasting problem is considered to illustrate its superiority over existing estimators.Time Series, Vector Auto Regression, Regularization, Lasso, Group Lasso, Oracle estimator

Randomized Matrix Decompositions Using R

Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality reduction, and data compression. Massive datasets, however, pose a computational challenge for traditional algorithms, placing significant constraints on both memory and processing power. Recently, the powerful concept of randomness has been introduced as a strategy to ease the computational load. The essential idea of probabilistic algorithms is to employ some amount of randomness in order to derive a smaller matrix from a high-dimensional data matrix. The smaller matrix is then used to compute the desired low-rank approximation. Such algorithms are shown to be computationally efficient for approximating matrices with low-rank structure. We present the R package rsvd, and provide a tutorial introduction to randomized matrix decompositions. Specifically, randomized routines for the singular value decomposition, (robust) principal component analysis, interpolative decomposition, and CUR decomposition are discussed. Several examples demonstrate the routines, and show the computational advantage over other methods implemented in R

Models for Flexible Supply Chain Network Design

Arguably Supply Chain Management (SCM) is one of the central problems in Operations Research and Management Science (OR/MS). Supply Chain Network Design (SCND) is one of the most crucial strategic problems in the context of SCM. SCND involves decisions on the number, location, and capacity, of production/distribution facilities of a manufacturing company and/or its suppliers operating in an uncertain environment. Specifically, in the automotive industry, manufacturing companies constantly need to examine and improve their supply chain strategies due to uncertainty in the parameters that impact the design of supply chains. The rise of the Asian markets, introduction of new technologies (hybrid and electric cars), fluctuations in exchange rates, and volatile fuel costs are a few examples of these uncertainties. Therefore, our goal in this dissertation is to investigate the need for accurate quantitative decision support methods for decision makers and to show different applications of OR/MS models in the SCND realm. In the first technical chapter of the dissertation, we proposed a framework that enables the decision makers to systematically incorporate uncertainty in their designs, plan for many plausible future scenarios, and assess the quality of service and robustness of their decisions. Further, we discuss the details of the implementation of our framework for a case study in the automotive industry. Our analysis related to the uncertainty quantification, and network's design performance illustrates the benefits of using our framework in different settings of uncertainty. Although this chapter is focused on our case study in the automotive industry, it can be generalized to the SCND problem in any industry. We have outline the shortcomings of the current literature in incorporating the correlation among design parameters of the supply chains in the second technical chapter. In this chapter, we relax the traditional assumption of knowing the distribution of the uncertain parameters. We develop a methodology based on Distributionally Robust Optimization (DRO) with marginal uncertainty sets to incorporate the correlation among uncertain parameters into the designing process. Further, we propose a delayed generation constraint algorithm to solve the NP-hard correlated model in significantly less time than that required by commercial solvers. Further, we show that the price of ignoring this correlation in the parameters increases when we have less information about the uncertain parameters and that the correlated model gives higher profit when exchange rates are high compared to the stochastic model (with the independence assumption). We extended our models in previous chapters by presenting capacity options as a mechanism to hedge against uncertainty in the input parameters. The concept of capacity options similar to financial options constitute the right, but not the obligation, to buy more commodities from suppliers with a predetermined price, if necessary. In capital-intensive industries like the automotive industry, the lost capital investment for excess capacity and the opportunity costs of underutilized capacity have been important drivers for improving flexibility in supply contracts. Our proposed mechanism for high tooling cost parts decreases the total costs of the SCND and creates flexibility within the structure of the designed SCNs. Moreover, we draw several insights from our numerical analyses and discuss the possibility of price negotiations between suppliers and manufacturers over the hedging fixed costs and variable costs. Overall, the findings from this dissertation contribute to improve the flexibility, reliability, and robustness of the SCNs for a wide-ranging set of industries.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145819/1/nsalehi_1.pd