Determine OWA operator weights using kernel density estimation

Some subjective methods should divide input values into local clusters before determining the ordered weighted averaging (OWA) operator weights based on the data distribution characteristics of input values. However, the process of clustering input values is complex. In this paper, a novel probability density based OWA (PDOWA) operator is put forward based on the data distribution characteristics of input values. To capture the local cluster structures of input values, the kernel density estimation (KDE) is used to estimate the probability density function (PDF), which fits to the input values. The derived PDF contains the density information of input values, which reflects the importance of input values. Therefore, the input values with high probability densities (PDs) should be assigned with large weights, while the ones with low PDs should be assigned with small weights. Afterwards, the desirable properties of the proposed PDOWA operator are investigated. Finally, the proposed PDOWA operator is applied to handle the multicriteria decision making problem concerning the evaluation of smart phones and it is compared with some existing OWA operators. The comparative analysis shows that the proposed PDOWA operator is simpler and more efficient than the existing OWA operator

A mathematical morphology approach for a qualitative exploration of drought events in space and time

Drought events occur worldwide and possibly incur severe consequences. Trying to understand and characterize drought events is of considerable importance in order to improve the preparedness for coping with future events. In this paper, we present a methodology that allows for the delineation of drought events by exploiting their spatiotemporal nature. To that end, we apply operators borrowed from mathematical morphology to represent drought events as connected components in space and time. As an illustration, we identify drought events on the basis of a 35-year data set of daily soil moisture values covering mainland Australia. We then extract characteristics reflecting the affected area, duration and intensity from the proposed representation of a drought event in order to illustrate the impact of tuning parameters in the methodology presented. Yet, this paper we refrain from comparing with other drought delineation methods

"The connection between distortion risk measures and ordered weighted averaging operators"

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and nite random variables is presented. This connection oers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable JEL classification:C02,C60

Aggregating sentiment in Europe: the relationship with volatility and returns

This paper presents several proposals for creating an aggregate sentiment index for the European stock market. We achieve this objective by using the OWA and WOWA operators, which have been successful in finance and have a strong financial interpretation. We compute ten different aggregate sentiment indices for the 2007-2021 period and evaluate their ability to provide information about current and future market volatility and returns. We find several results of interest for both investors and policymakers. Sentiment indices have a strong negative relationship with market volatility. Extreme values of sentiment can predict future market returns, with low values indicating positive returns and high values suggesting negative returns. Finally, using stock market capitalisation as an input of the WOWA operator enhances explanatory power of the indices on future market returns compared to the OWA operator

Frequency-based ensemble forecasting model for time series forecasting

The M4 forecasting competition challenged the participants to forecast 100,000 time series with different frequencies: hourly, daily, weekly, monthly, quarterly, and yearly. These series come mainly from the economic, finance, demographics, and industrial areas. This paper describes the model used in the competition, which is a combination of statistical methods, namely auto-regressive integrated moving-average, exponential smoothing (ETS), bagged ETS, temporal hierarchical forecasting method, Box-Cox transformation, ARMA errors, Trend and Seasonal components (BATS), and Trigonometric seasonality BATS (TBATS). Forty-nine submissions were evaluated by the organizers and compared with 12 benchmarks and standards for comparison forecasting methods. Based on the results, the proposed model is listed among the 17 submissions that outperform the 12 benchmarks and standards for comparison forecasting methods, ranked 15th on average and 4th with the weekly time series. In addition, a further comparison was conducted between the proposed model and other forecasting methods on forecasting EUR/USD exchange rate and Bitcoin closing price time series. It is apparent from the results that the proposed model can produce accurate results compared to many forecasting methods.publishedVersio

The connection between distortion risk measures and ordered weighted averaging operators [WP]

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and finite random variables is presented. This connection offers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed

Exchange rate USD/MXN forecast through econometric models, time series and HOWMA operators

This paper aims to provide models that can predict the exchange rate and generate future scenarios of this variable, this because exchange risk management has become a strategic activity of the corporate governance. Also the study aims to expand the uses of operators like Heavy Ordering Weight Moving Average (HOWMA) in different fields of economy and management

The connection between distortion risk measures and ordered weighted averaging operators

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and finite random variables is presented. This connection offers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed

Heavy moving averages and their application in econometric forecasting

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 ordered weighted averaging (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 and Mexican pesos is also presented