Heavy Moving Averages and Their Application in Econometric Forecasting

Abstract

This paper presents the heavy ordered weighted moving average (HOWMA) operator. It is an aggregation operator that uses the main characteristics of two well-known techniques: the heavy OWA and the moving averages.Therefore, this operator provides a parameterized family of aggregation operators from the minimum to the total operator and includes the OWA operator as a special case. It uses a heavy weighting vector in the moving average formulation and it represents the information available and the knowledge of the decision maker about the future scenarios of the phenomenon, according to his attitudinal character. Some of the main properties of this operator are studied, including a wide range of families of HOWMA operators such as the heavy moving average and heavy weighted moving average operators. The HOWMA operator is also extended using generalized and quasi-arithmetic means. An example concerning the foreign exchange rate between US dollars (USD) and Mexican pesos (MXN) is also presented. JEL Classification: C43, C44, C53, C58. * Corresponding author Emails: ernesto.leon@udo.mx − +1 * the jth weight of the AOWA operator. Heavy aggregation operatorsThe heavy OWA (HOWA) operator (Yager, 2002) is an extension of the OWA operator. This operator is useful when the available information is not bounded by the maximum or the minimum operator of the usual OWA operator. The main difference between the OWA and HOWA operators is that the sum of the weights of the OWA operator must be 1. This restriction does not exist for the HOWA operator: the sum of the weights can range from 1 to n. In the following, we provide the definition of the HOWMA operator suggested by Yager (2002).

The ordered weighted average in the theory of expertons

“…In future research, other aggregation operators will be used in the construction of the experton, including induced and generalized aggregation operators, weighted averages and probabilities . Moreover, several other applications will be considered, including economics, business, and engineering …”

Variances with Bonferroni means and ordered weighted averages

“…Among the aggregation operators, a common one that can obtain the maximum and minimum operator is the OWA operator devolved by Yager . Since it was developed, many extensions have been done, such as moving averages, induced operators, prioritized operators, distance operators, and many more. The definition is as follows.…”

“…This discussion has generated various debates about the formality of mathematical methods that deal with high complexity and uncertainty, in which the latter have gained ground generating new hybrid models with applications in various fields including business sciences and economics. Among all the studies, the theory of fuzzy subsets applied in business management, basic elements of the mathematics of uncertainty applied in economics, company management techniques, decision‐making in uncertainty, modeling of complex economic phenomenon, sales forecasting, forecasting, entrepreneurship, portfolio selection, stakeholders management, enterprise risk management, transparency, competitiveness, social networks, e‐services, and others can be highlighted. Likewise, it is worth mentioning another author, who, with his contributions, has contributed to the business and economic decision‐making problems: Ronald R. Yager.…”

Fuzzy decision making in complex frameworks with generalized aggregation operators

“…The FGUAO and the Quasi-FUAO operators could be implemented in many areas including statistics, economics, computer science, engineering and management [13][14]17].…”