Lasso-based simulation for high-dimensional multi-period portfolio optimization

2019 ◽  
Vol 31 (3) ◽  
pp. 257-280
Author(s):  
Zhongyu Li ◽  
Ka Ho Tsang ◽  
Hoi Ying Wong
Keyword(s):  
Least Squares ◽  
Portfolio Optimization ◽  
Optimization Problems ◽  
Estimation Error ◽  
Sample Path ◽  
Ordinary Least Squares ◽  
Monte Carlo Algorithm ◽  
High Dimensional ◽  
Finite Sample ◽  
Sample Paths

Abstract This paper proposes a regression-based simulation algorithm for multi-period mean-variance portfolio optimization problems with constraints under a high-dimensional setting. For a high-dimensional portfolio, the least squares Monte Carlo algorithm for portfolio optimization can perform less satisfactorily with finite sample paths due to the estimation error from the ordinary least squares (OLS) in the regression steps. Our algorithm, which resolves this problem e, that demonstrates significant improvements in numerical performance for the case of finite sample path and high dimensionality. Specifically, we replace the OLS by the least absolute shrinkage and selection operator (lasso). Our major contribution is the proof of the asymptotic convergence of the novel lasso-based simulation in a recursive regression setting. Numerical experiments suggest that our algorithm achieves good stability in both low- and higher-dimensional cases.

scholarly journals Indirect Inference Estimation of Spatial Autoregressions

Econometrics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 34
Author(s):  
Yong Bao ◽  
Xiaotian Liu ◽  
Lihong Yang
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Monte Carlo Study ◽  
Ordinary Least Squares ◽  
Indirect Inference ◽  
Finite Sample ◽  
Spatial Unit ◽  
Asymptotically Normal ◽  
Distribution Result

The ordinary least squares (OLS) estimator for spatial autoregressions may be consistent as pointed out by Lee (2002), provided that each spatial unit is influenced aggregately by a significant portion of the total units. This paper presents a unified asymptotic distribution result of the properly recentered OLS estimator and proposes a new estimator that is based on the indirect inference (II) procedure. The resulting estimator can always be used regardless of the degree of aggregate influence on each spatial unit from other units and is consistent and asymptotically normal. The new estimator does not rely on distributional assumptions and is robust to unknown heteroscedasticity. Its good finite-sample performance, in comparison with existing estimators that are also robust to heteroscedasticity, is demonstrated by a Monte Carlo study.

A DETERMINISTIC METHODOLOGY FOR ESTIMATION OF PARAMETERS IN DYNAMIC MARKOV CHAIN MODELS

2011 ◽  
Vol 19 (01) ◽  
pp. 71-100 ◽  
Author(s):  
A. R. ORTIZ ◽  
H. T. BANKS ◽  
C. CASTILLO-CHAVEZ ◽  
G. CHOWELL ◽  
X. WANG
Keyword(s):  
Inverse Problem ◽  
Markov Chain ◽  
Least Squares ◽  
Large Population ◽  
Ordinary Least Squares ◽  
Large Sample Size ◽  
Data Set ◽  
Markov Chain Models ◽  
Sample Paths ◽  
Dynamic Stochastic

A method for estimating parameters in dynamic stochastic (Markov Chain) models based on Kurtz's limit theory coupled with inverse problem methods developed for deterministic dynamical systems is proposed and illustrated in the context of disease dynamics. This methodology relies on finding an approximate large-population behavior of an appropriate scaled stochastic system. The approach leads to a deterministic approximation obtained as solutions of rate equations (ordinary differential equations) in terms of the large sample size average over sample paths or trajectories (limits of pure jump Markov processes). Using the resulting deterministic model, we select parameter subset combinations that can be estimated using an ordinary-least-squares (OLS) or generalized-least-squares (GLS) inverse problem formulation with a given data set. The selection is based on two criteria of the sensitivity matrix: the degree of sensitivity measured in the form of its condition number and the degree of uncertainty measured in the form of its parameter selection score. We illustrate the ideas with a stochastic model for the transmission of vancomycin-resistant enterococcus (VRE) in hospitals and VRE surveillance data from an oncology unit.

General Error Estimates for the Longstaff–Schwartz Least-Squares Monte Carlo Algorithm

2020 ◽  
Vol 45 (3) ◽  
pp. 923-946
Author(s):  
Daniel Z. Zanger
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Error Estimates ◽  
Approximation Error ◽  
Uniform Boundedness ◽  
Monte Carlo Algorithm ◽  
Least Squares Regression ◽  
Vc Dimension ◽  
Sample Paths ◽  
Payoff Functions

We establish error estimates for the Longstaff–Schwartz algorithm, employing just a single set of independent Monte Carlo sample paths that is reused for all exercise time steps. We obtain, within the context of financial derivative payoff functions bounded according to the uniform norm, new bounds on the stochastic part of the error of this algorithm for an approximation architecture that may be any arbitrary set of L2 functions of finite Vapnik–Chervonenkis (VC) dimension whenever the algorithm’s least-squares regression optimization step is solved either exactly or approximately. Moreover, we show how to extend these estimates to the case of payoff functions bounded only in Lp, p a real number greater than [Formula: see text]. We also establish new overall error bounds for the Longstaff–Schwartz algorithm, including estimates on the approximation error also for unconstrained linear, finite-dimensional polynomial approximation. Our results here extend those in the literature by not imposing any uniform boundedness condition on the approximation architectures, allowing each of them to be any set of L2 functions of finite VC dimension and by establishing error estimates as well in the case of ɛ-additive approximate least-squares optimization, ɛ greater than or equal to 0.

scholarly journals HB-PLS: An algorithm for identifying biological process or pathway regulators by integrating Huber loss and Berhu penalty with partial least squares regression

2020 ◽  
Author(s):  
Wenping Deng ◽  
Kui Zhang ◽  
Zhigang Wei ◽  
Lihu Wang ◽  
Cheng He ◽  
...  
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Regulatory Networks ◽  
Biological Process ◽  
Ordinary Least Squares ◽  
Descent Method ◽  
High Dimensional ◽  
Gradient Descent Method ◽  
Least Squares Regression ◽  
Non Gaussian

AbstractGene expression data features high dimensionality, multicollinearity, and the existence of outlier or non-Gaussian distribution noise, which make the identification of true regulatory genes controlling a biological process or pathway difficult. In this study, we embedded the Huber-Berhu (HB) regression into the partial least squares (PLS) framework and created a new method called HB-PLS for predicting biological process or pathway regulators through construction of regulatory networks. PLS is an alternative to ordinary least squares (OLS) for handling multicollinearity in high dimensional data. The Huber loss is more robust to outliers than square loss, and the Berhu penalty can obtain a better balance between the ℓ2 penalty and the ℓ1 penalty. HB-PLS therefore inherits the advantages of the Huber loss, the Berhu penalty, and PLS. To solve the Huber-Berhu regression, a fast proximal gradient descent method was developed; the HB regression runs much faster than CVX, a Matlab-based modeling system for convex optimization. Implementation of HB-PLS to real transcriptomic data from Arabidopsis and maize led to the identification of many pathway regulators that had previously been identified experimentally. In terms of its efficiency in identifying positive biological process or pathway regulators, HB-PLS is comparable to sparse partial least squares (SPLS), a very efficient method developed for variable selection and dimension reduction in handling multicollinearity in high dimensional genomic data. However, HB-PLS is able to identify some distinct regulators, and in one case identify more positive regulators at the top of output list, which can reduce the burden for experimental test of the identified candidate targets. Our study suggests that HB-PLS is instrumental for identifying biological process and pathway genes.

IMPROVED AND EXTENDED END-OF-SAMPLE INSTABILITY TESTS USING A FEASIBLE QUASI-GENERALIZED LEAST SQUARES PROCEDURE

2009 ◽  
Vol 26 (4) ◽  
pp. 994-1031 ◽  
Author(s):  
Dukpa Kim
Keyword(s):  
Least Squares ◽  
Serial Correlation ◽  
Linear Time ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Consistent Estimate ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Error Process ◽  
Economic Statistics

This paper extends the Andrews (2002, Econometrica 71, 1661–1694) and Andrews and Kim (2006, Journal of Business & Economic Statistics 24, 379–394) ordinary least squares–based end-of-sample instability tests for linear regression models. The author proposes to quasi-difference the data first using a consistent estimate of the sum of the autoregressive coefficients of the error process and then test for the end-of-sample instability. For the cointegration model, the feasible quasi-generalized least squares (FQGLS) version of the Andrews and Kim (2006) P test is considered and is shown, by simulations, to be more robust to serial correlation in the error process and to have power no less than Andrews and Kim’s original test. For the linear time trend model, the FQGLS version of the Andrews (2002) S test is considered with the error process allowed to be nonstationary up to one unit root, and the new test is shown to be robust to potentially nonstationary serial correlation. A simulation study also shows that the finite-sample properties of the proposed test can be further improved when the Andrews (1993, Econometrica 61,139–165) or Andrews and Chen (1994, Journal of Business & Economic Statistics 12, 187–204) median unbiased estimate of the sum of the autoregressive coefficients is used.

High-Dimensional Least-Squares with Perfect Positive Correlation

2019 ◽  
Vol 36 (04) ◽  
pp. 1950016
Author(s):  
Zhiyong Huang ◽  
Ziyan Luo ◽  
Naihua Xiu
Keyword(s):  
Least Squares ◽  
Correlation Coefficient ◽  
Large Scale ◽  
Rank Correlation ◽  
Optimal Solution ◽  
Ordinary Least Squares ◽  
High Dimensional ◽  
Dual Algorithm ◽  
Positive Correlation ◽  
Proposed Model

The least-squares is a common and important method in linear regression. However, it often leads to overfitting phenomenon as dealing with high-dimensional problems, and various regularization schemes regarding prior information for specific problems are studied to make up such a deficiency. In the sense of Kendall’s [Formula: see text] from the community of nonparametric analysis, we establish a new model wherein the ordinary least-squares is equipped with perfect positive correlation constraint, sought to maintain the concordance of the rankings of the observations and the systematic components. By sorting the observations into an ascending order, we reduce the perfect positive correlation constraint into a linear inequality system. The resulting linearly constrained least-squares problem together with its dual problem is shown to be solvable. In particular, we introduce a mild assumption on the observations and the measurement matrix which rules out the zero vector from the optimal solution set. This indicates that our proposed model is statistically meaningful. To handle large-scale instances, we propose an efficient alternating direction method of multipliers (ADMM) to solve the proposed model from the dual perspective. The effectiveness of our model compared to ordinary least-squares is evaluated in terms of rank correlation coefficient between outputs and the systematic components, and the efficiency of our dual algorithm is demonstrated with the comparison to three efficient solvers via CVX in terms of computation time, solution accuracy and rank correlation coefficient.

Generalized Forecast Averaging in Autoregressions with a Near Unit Root

2020 ◽  
Author(s):  
Mohitosh Kejriwal ◽  
Xuewen Yu
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Mean Squared Error ◽  
Model Averaging ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Finite Sample ◽  
Deterministic Components ◽  
Asymptotic Mean Squared Error ◽  
Near Unit Root

Summary This paper develops a new approach to forecasting a highly persistent time series that employs feasible generalized least squares (FGLS) estimation of the deterministic components in conjunction with Mallows model averaging. Within a local-to-unity asymptotic framework, we derive analytical expressions for the asymptotic mean squared error and one-step-ahead mean squared forecast risk of the proposed estimator and show that the optimal FGLS weights are different from their ordinary least squares (OLS) counterparts. We also provide theoretical justification for a generalized Mallows averaging estimator that incorporates lag order uncertainty in the construction of the forecast. Monte Carlo simulations demonstrate that the proposed procedure yields a considerably lower finite-sample forecast risk relative to OLS averaging. An application to U.S. macroeconomic time series illustrates the efficacy of the advocated method in practice and finds that both persistence and lag order uncertainty have important implications for the accuracy of forecasts.

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