We study the problem of finding sparse, mean reverting portfolios based on multivariate historical time series. After mapping the optimal portfolio selection problem into a generalized eigenvalue problem, we propose a new optimization approach based on the use of simulated annealing. This new method ensures that the cardinality constraint is automatically satisfied in each step of the optimization by embedding the constraint into the iterative neighbor selection function. We empirically demonstrate that the method produces better mean reversion coefficients than other heuristic methods, but also show that this does not necessarily result in higher profits during convergence trading. This implies that more complex objective functions should be developed for the problem, which can also be optimized under cardinality constraints using the proposed approach.
In this paper, novel energy-aware and reliable routing protocols are proposed. The aim is to maximize the lifespan of wireless sensor networks (WSNs) subject to predefined reliability constraints by using multi-hop routing schemes, in which the source node forwards the packet to the base station (BS) via other nodes as relays. In the first proposed protocol, energy efficiency is achieved by maximizing the minimum residual energy of the path subject to fulfilling a predefined reliability constraints. The second protocol is an optimized version of the first one with respect to lifespan and complexity. The optimal path is the one in which the residual energy distribution of the nodes along the path is as close to uniform as possible and the packet arrives at the base station with a given success probability. To measure the uniformity of the residual energy distribution, we use an entropy like measure. The information about the current energy state of the network is maintained by using a look-up-table from which the optimal routes are computed on the BS. The BS broadcasts the updated optimal paths to each node after each round of packet transmission.
Energy-efficiency and reliability are vital metrics of the robustness of Wireless Sensor Networks (WSNs). Various data reduction techniques are used to improve them, among them compressive sensing (CS) is a data reduction technique used to recover extensive data from fewer samples in case of sparse representation of sensor-readings. Unfortunately, energy-efficiency and accuracy are contradictory metrics, as increased accuracy requires a large number of measurements, and data transmissions. Therefore,, in this paper, a CS-based algorithm is proposed for efficient data transfer through WSNs, which uses multiple objective genetic algorithms (MOGA) to optimize the number of measurements, transmission range, and the sensing matrix. The algorithm aims at striking the right balance between energy-efficiency and accuracy. It constructs a path in a multi hop manner based on the optimized values. Numerical simulations and experiments show that Paretofront, which is the output of MOGA, helps the user to select the right combination of the number of measurements and the transmission range fitting the application at hand, and to strike a good balance between energy efficiency and accuracy. The results also demonstrate the existence of measurement matrices which lower mutual coherency improve the accuracy of CS.
In this paper we investigate trading with optimal mean reverting portfolios subject to cardinality constraints. First, we identify the parameters of the underlying VAR(1) model of asset prices and then the quantities of the corresponding Ornstein-Uhlenbeck (OU) process are estimated by pattern matching techniques. Portfolio optimization is performed according to two approaches: (i) maximizing the predictability by solving the generalized eigenvalue problem or (ii) maximizing the mean return. The optimization itself is carried out by stochastic search algorithms and Feed Forward Neural Networks (FFNNs). The presented solutions satisfy the cardinality constraint thus providing sparse portfolios to minimize the transaction costs and to maximize interpretability of the results. The performance has been tested on historical data (SWAP rates, SP 500, and FOREX). The proposed trading algorithms have achieved 29.57% yearly return on average, on the examined data sets. The algorithms prove to be suitable for high frequency, intraday trading as they can handle financial data up to the arrival rate of every second.
IntroductionMean reversion, as a classic indicator of predictability in financial markets, has received a lot of attention over the last few decades. It has been shown that equity excess returns over long horizons are mean-reverting and therefore contain an element of predictability [8,10,13]. Convergence trading, by estimating the parameters of mean reverting portfolios has also been proposed and studied in a number of previous research publications [2,7] In his recently published article, d'Aspremont in [5] posed the problem of finding mean-reverting portfolios which are sparse. While there exist simple and reliable methods to identify mean reversion in univariate time series, selecting portfolios from multivariate data which exhibit this property is a much more difficult problem. This can be approached by the Box-Tiao procedure [3] to extract cointegrated vectors by solving a generalized eigenvalue problem. On the other hand, sparseness, he argues, is desirable for reducing transaction costs associated with convergence trading as well as for increasing the interpretability of the resulting portfolio. He developed a new approach to solve the problem by using semidefinite relaxation and compared the efficiency of this solution to the simple greedy algorithm in a number of markets.In this paper, we further extend their work by developing a new approach to identifying parameters of the stationary first order vector autoregressive VAR(1) model and we propose a new benchmark for evaluating their proposed polynomial time heuristics to this NP hard problem. Our proposed benchmark is the computationally expensive, but optimal, exhaustive solution. This is an important step missing in [5] which shows the overall reliability and performance of the investigated methods.The structure of the paper is as follows.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.