Elsevier

Knowledge-Based Systems

Volume 248, 19 July 2022, 108863
Knowledge-Based Systems

Forecasting the exchange rate with multiple linear regression and heavy ordered weighted average operators

https://doi.org/10.1016/j.knosys.2022.108863Get rights and content

Abstract

This paper introduces the multiple linear regression heavy ordered weighted average (MLR-HOWA) operator. On the MLR-HOWA operator, the beta values are obtained with the use of the HOWA means. In that sense, it provides a new range of possibilities by under or overestimating the result based on the decision maker’s expectations and knowledge. Therefore, the MLR-HOWA provides a forecasting tool that can analyze multiple scenarios from minimum to maximum. The main properties and two extensions using induced and generalized variables are also presented. An application in exchange rate forecasting based on inflation and interest rate as independent variables for five Latin American countries is submitted. Among the main results, it is possible to identify that the forecasting error is reduced when different combinations of MLR with OWA operators are done.

Introduction

Exchange rates have been at the center of economic debates in emerging economies. In Latin America, the exchange rate has matured in recent decades; its ability to absorb changes in external conditions has grown in a context of more open and stable economies [1], [2]. However, the dynamics of exchange rates in the region are characterized by long periods of oscillations, intense volatility, and persistent misalignments [3], [4], [5].

The different behaviors of the exchange rate between countries make the analysis more complicated. Therefore, an increase in the literature on the topic has been developed. Rossi [6] explains how predictability in the exchange rate is more evident when one or more of the following points are valid: the predictors are the Taylor rule or the net external assets. The model is linear, and a small number of parameters are estimated. In this sense, research on economic policy, macroeconomics, and financial uncertainty are essential for constructing models [7], [8].

Meanwhile, Kilian and Taylor [9] continue the difficulty of explaining and forecasting exchange rates proposed by Meese and Rogoff [10], where the time-series behavior of the exchange rate is well approximated by a nonlinear and its defined by a random walk. In order to include all these characteristics in the process of estimating and forecasting exchange rates, methodologies such as neural networks [11], [12] and fuzzy logic [13], [14] have been used. Tseng et al. [15] propose a model that uses interval parameters to analyze some scenarios and provide the worst and the best possible situation using an ARIMA time series model. Chen and Tanuwijaya [16] extend the previous proposal in the same way by using autoregressive fuzzy models with moving averages intervals are built; the methodology proposes an algorithm that groups intervals to adapt to specific cases; the objective is to minimize forecast error measures. Meanwhile, Chionis and MacDonald [17] use aggregation systems to calculate the risk premium in currencies to verify that expectations do not fluctuate in totally rational results. The aggregation is resumed by Garg and Garg [18] using ordered aggregation operators to handle large numbers of data impacted by complex factors. It is demonstrated how the help of these tools facilitates good estimation and forecasting. León-Castro et al. [19] propose an aggregation operator that includes moving averages to estimate and forecast in scenarios that go from minimum to maximum according to a vector of weight and a given order of the series of exchange rates. In the same way, Papatsimpas et al. [20] propose a moving average aggregation method combined with an algorithm applied to FOREX prices. Flores-Sosa et al. [21] use these ideas to estimate the ordinary least squares (OLS) in GARCH models for the volatility of currencies. Among the aggregation operators is the ordered weight average (OWA) operator [22]. This operator is a technique that provides an aggregation that lies in between the two extremes, the maximum and the minimum, proposing a parameterized average [23]. This idea is generated using a weighting vector and a reordering step based on the value of the arguments. The main idea is to include in the weighting vector the expectations and knowledge of the decision maker in the problem that wants to be analyzed.

After its presentation, many extensions of the OWA operator have been developed. On the induced OWA (IOWA) [24] operator, the ordering of the arguments is induced by other values. It can be used in more complex scenarios or when a specific weight wants to be assigned to an argument. Another extension is the generalized ordered weight average (GOWA) operator [25], [26], which uses generalized means to regulate the intensity of the argument values. In order to perform an intense process of overestimation or underestimation, the heavy OWA [27] has the main characters where the weighting vector is not bounded to one. The family of OWA operators has been used in a wide range of applications such as decision making [28], [29], portfolio selection [30], [31] and forecasting [20], [32].

This paper proposes to include the HOWA operator in a multiple linear regression model. By using heavy operators on the means of the variances in the OLS process, the parameters can be overestimated or underestimated according to the perspectives of the decision maker. Specifically, in the case of heavy operators, this estimate can move between more extensive ranges. Therefore, a large number of scenarios can be analyzed ranging from minimum to maximum HOWA. This idea extends the propositions presented by Merigó [33] and Flores-Sosa et al. [34] about the use of the OWA with OLS. The analysis is made for five Latin American exchange rates compared with the USA dollar. These are: USD/ARS, USD/COP, USD/BRLT, USD/CLP and USD/MXN. The main purpose is to compare the forecast in the different cases and to identify how the new methodology works in each one based on the results of mean absolute deviation (MAD), root means squared error (RMSE) and mean absolute percentage error (MAPE).

The remainder of the paper is organized as follows. Section 2 presents the preliminaries of the MLR and OWA operators. Section 3 introduces the MLR with heavy aggregation operators. Section 4 analyzes the use of the MLR-HOWA operator and its extensions in exchange rate forecasting and Sections 5 Discussions, 6 Conclusions summarize the discussion and main conclusions of the paper.

Section snippets

Preliminaries

In this section, the main definitions that will be used are presented. Among them are the multiple linear regression (MLR) and different operators such as the OWA, HOWA and IOWA operators and other extensions.

MLR with heavy aggregation operators

The multiple regression with HOWA operator (MLR-HOWA) is an estimator that combines into one formulation two characteristics: (1) the estimation of parameters using OLS for two independent variables, and (2) the HOWA operator as means in the estimation process. Note that HOWA variances and covariances varHOWA;covHOWA are calculated in the formulation of the parameters. It can be defined as follows:

Definition 8

An MLR-HOWA of dimension n is a model HOWA:RnR given the variables sets xkUn,ykU and zkUn such

Forecasting exchange rates in latin america with MLR and aggregation operators

Finding factors involved in determining the exchange rate can be complex since it depends on the characteristics of each currency. However, some studies have focused on numbering the predominant factors that affect currency movements. Mishkin [36] considers factors such as price levels, tariffs, productivity and preferences to hold domestic or foreign assets as determinants of the exchange rate. Then, the exchange rate variations reflect a series of decisions by financial agents based on

Discussions

The estimation methodology proposed in this work offers a simple alternative for estimating and forecasting models with two independent variables. The novelty of this is to provide an estimator that uses aggregation operators, which allow the analysis of results in multiple scenarios that go from a minimum to a maximum. This feature offers the opportunity to work with data impregnated not only with statistical information but also with non-statistical or subjective information available.

A case

Conclusions

The objective of the paper is to propose new ways to formulate MLR models based on the use of the HOWA operators and some extensions such as the IOWA operator and generalized operators. This new formulation is called the multiple linear regression heavy ordered weighted average (MLR-HOWA). Its main characteristic is the use of HOWA operators to obtain the β values for each independent variable. By doing this, it is possible to under or overestimate the β according to the decision maker’s

CRediT authorship contribution statement

Martha Flores-Sosa: Conceptualization, Validation, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Supervision. Ernesto León-Castro: Validation, Formal analysis, Resources, Data curation, Writing – original draft, Writing – review & editing. José M. Merigó: Conceptualization, Methodology, Formal analysis, Investigation, Writing – original draft, Writing – review & editing, Supervision. Ronald R. Yager: Methodology, Validation, Writing – original

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

Author number 2 acknowledges support from the Chilean Government through FONDECYT initiation grant No.11190056

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