Mathematics

Research

15 pages, 4437 KiB

Open AccessArticle

The Impact of Regulatory Reforms on Demand Weighted Average Prices

by Sherzod N. Tashpulatov

Mathematics 2021, 9(10), 1112; https://doi.org/10.3390/math9101112 - 14 May 2021

Cited by 2 | Viewed by 1225

Average prices are popularly used in the literature on price modeling. Calculating daily or weekly prices as an average over hourly or half-hourly trading periods assumes the same weight ignoring demand or traded volumes during those periods. Analyzing demand weighted average prices is [...] Read more.

Average prices are popularly used in the literature on price modeling. Calculating daily or weekly prices as an average over hourly or half-hourly trading periods assumes the same weight ignoring demand or traded volumes during those periods. Analyzing demand weighted average prices is important if producers may affect prices by decreasing them during low-demand periods and increasing them during high-demand periods within a day. The prediction of this price manipulation might have motivated the regulatory authority to introduce price caps not only on annual average prices but also on annual demand weighted average prices in the England and Wales wholesale electricity market. The dynamics of demand weighted average prices of electricity has been analyzed little in the literature. We show that skew generalized error distribution (SGED) is the appropriate assumption for model residuals. The estimated volatility model is used for evaluating the impact of regulatory reforms on demand weighted average prices during the complete history of the England and Wales wholesale electricity market. Full article

(This article belongs to the Special Issue Volatility Models Applied to Geophysics, Financial Market Data and Other Disciplines)

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30 pages, 1533 KiB

Open AccessArticle

Analyzing Medical Data by Using Statistical Learning Models

by Maria C. Mariani, Francis Biney and Osei K. Tweneboah

Mathematics 2021, 9(9), 968; https://doi.org/10.3390/math9090968 - 26 Apr 2021

Cited by 1 | Viewed by 2352

Abstract

In this work, we investigated the prognosis of three medical data specifically, breast cancer, heart disease, and prostate cancer by using 10 machine learning models. We applied all 10 models to each dataset to identify patterns in them. Furthermore, we use the models [...] Read more.

In this work, we investigated the prognosis of three medical data specifically, breast cancer, heart disease, and prostate cancer by using 10 machine learning models. We applied all 10 models to each dataset to identify patterns in them. Furthermore, we use the models to diagnose risk factors that increases the chance of these diseases. All the statistical learning techniques discussed were grouped into linear and nonlinear models based on their similarities and learning styles. The models performances were significantly improved by selecting models while taking into account the bias-variance tradeoffs and using cross-validation for selecting the tuning parameter. Our results suggests that no particular class of models or learning style dominated the prognosis and diagnosis for all three medical datasets. However nonlinear models gave the best predictive performance for breast cancer data. Linear models on the other hand gave the best predictive performance for heart disease data and a combination of linear and nonlinear models for the prostate cancer dataset. Full article

(This article belongs to the Special Issue Volatility Models Applied to Geophysics, Financial Market Data and Other Disciplines)

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11 pages, 1676 KiB

Open AccessArticle

Modeling and Estimating Volatility of Day-Ahead Electricity Prices

by Sherzod N. Tashpulatov

Mathematics 2021, 9(7), 750; https://doi.org/10.3390/math9070750 - 31 Mar 2021

Cited by 3 | Viewed by 1691

Abstract

We model day-ahead electricity prices of the UK power market using skew generalized error distribution. This distribution allows us to take into account the features of asymmetry, heavy tails, and a peak higher than in normal or Student’s t distributions. The adequacy of [...] Read more.

We model day-ahead electricity prices of the UK power market using skew generalized error distribution. This distribution allows us to take into account the features of asymmetry, heavy tails, and a peak higher than in normal or Student’s t distributions. The adequacy of the estimated volatility model is verified using various tests and criteria. A correctly specified volatility model can be used for analyzing the impact of reforms or other events. We find that, after the start of the COVID-19 pandemic, price level and volatility increased. Full article

(This article belongs to the Special Issue Volatility Models Applied to Geophysics, Financial Market Data and Other Disciplines)

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17 pages, 1849 KiB

Open AccessArticle

Volatility Forecasting for High-Frequency Financial Data Based on Web Search Index and Deep Learning Model

by Bolin Lei, Boyu Zhang and Yuping Song

Mathematics 2021, 9(4), 320; https://doi.org/10.3390/math9040320 - 05 Feb 2021

Cited by 10 | Viewed by 5447

Abstract

The existing index system for volatility forecasting only focuses on asset return series or historical volatility, and the prediction model cannot effectively describe the highly complex and nonlinear characteristics of the stock market. In this study, we construct an investor attention factor through [...] Read more.

The existing index system for volatility forecasting only focuses on asset return series or historical volatility, and the prediction model cannot effectively describe the highly complex and nonlinear characteristics of the stock market. In this study, we construct an investor attention factor through a Baidu search index of antecedent keywords, and then combine other trading information such as the trading volume, trend indicator, quote change rate, etc., as input indicators, and finally employ the deep learning model via temporal convolutional networks (TCN) to forecast the volatility under high-frequency financial data. We found that the prediction accuracy of the TCN model with investor attention is better than those of the TCN model without investor attention, the traditional econometric model as the generalized autoregressive conditional heteroscedasticity (GARCH), the heterogeneous autoregressive model of realized volatility (HAR-RV), autoregressive fractionally integrated moving average (ARFIMA) models, and the long short-term memory (LSTM) model with investor attention. Compared with the traditional econometric models, the multi-step prediction results for the TCN model remain robust. Our findings provide a more accurate and robust method for volatility forecasting for big data and enrich the index system of volatility forecasting. Full article

(This article belongs to the Special Issue Volatility Models Applied to Geophysics, Financial Market Data and Other Disciplines)

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25 pages, 2473 KiB

Open AccessFeature PaperArticle

Applying Heath-Jarrow-Morton Model to Forecasting the US Treasury Daily Yield Curve Rates

by Valerii Maltsev and Michael Pokojovy

Mathematics 2021, 9(2), 114; https://doi.org/10.3390/math9020114 - 06 Jan 2021

Cited by 2 | Viewed by 3122

Abstract

The Heath-Jarrow-Morton (HJM) model is a powerful instrument for describing the stochastic evolution of interest rate curves under no-arbitrage assumption. An important feature of the HJM approach is the fact that the drifts can be expressed as functions of respective volatilities and the [...] Read more.

The Heath-Jarrow-Morton (HJM) model is a powerful instrument for describing the stochastic evolution of interest rate curves under no-arbitrage assumption. An important feature of the HJM approach is the fact that the drifts can be expressed as functions of respective volatilities and the underlying correlation structure. Aimed at researchers and practitioners, the purpose of this article is to present a self-contained, but concise review of the abstract HJM framework founded upon the theory of interest and stochastic partial differential equations in infinite dimensions. To illustrate the predictive power of this theory, we apply it to modeling and forecasting the US Treasury daily yield curve rates. We fit a non-parametric model to real data available from the US Department of the Treasury and illustrate its statistical performance in forecasting future yield curve rates. Full article

(This article belongs to the Special Issue Volatility Models Applied to Geophysics, Financial Market Data and Other Disciplines)

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12 pages, 281 KiB

Open AccessArticle

GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio

by Kei Nakagawa and Yusuke Uchiyama

Mathematics 2020, 8(11), 1990; https://doi.org/10.3390/math8111990 - 07 Nov 2020

Cited by 4 | Viewed by 2364

Abstract

There are three distinguishing features in the financial time series, such as stock prices, are as follows: (1) Non-normality, (2) serial correlation, and (3) leverage effect. All three points need to be taken into account to model the financial time series. However, multivariate [...] Read more.

There are three distinguishing features in the financial time series, such as stock prices, are as follows: (1) Non-normality, (2) serial correlation, and (3) leverage effect. All three points need to be taken into account to model the financial time series. However, multivariate financial time series modeling involves a large number of stocks, with many parameters to be estimated. Therefore, there are few examples of multivariate financial time series modeling that explicitly deal with higher-order moments. Furthermore, there is no multivariate financial time series model that takes all three characteristics above into account. In this study, we propose the generalized orthogonal (GO)-Glosten, Jagannathan, and Runkle GARCH (GJR) model which extends the GO-generalized autoregressive conditional heteroscedasticity (GARCH) model and incorporates the three features of the financial time series. We confirm the effectiveness of the proposed model by comparing the performance of risk-based portfolios with higher-order moments. The results show that the performance with our proposed model is superior to that with baseline methods, and indicate that estimation methods are important in risk-based portfolios with higher moments. Full article

(This article belongs to the Special Issue Volatility Models Applied to Geophysics, Financial Market Data and Other Disciplines)

20 pages, 1706 KiB

Open AccessArticle

by Maria C. Mariani, William Kubin, Peter K. Asante, Osei K. Tweneboah, Maria P. Beccar-Varela, Sebastian Jaroszewicz and Hector Gonzalez-Huizar

Mathematics 2020, 8(7), 1046; https://doi.org/10.3390/math8071046 - 30 Jun 2020

Cited by 4 | Viewed by 1997

Abstract

Financial and geophysical data, like many other low and high frequency time series, are known to exhibit some memory effects. These memory effects may be long or short, permanent or temporal depending on the event that is being modeled. The purpose of this [...] Read more.

Financial and geophysical data, like many other low and high frequency time series, are known to exhibit some memory effects. These memory effects may be long or short, permanent or temporal depending on the event that is being modeled. The purpose of this study is to investigate the memory effects characterized by the financial market closing values and volcanic eruption time series as well as to investigate the relation between the self-similar models used and the Lévy process. This paper uses highly effective scaling methods including Lévy processes, Detrended Fluctuation Analysis (DFA) and Diffusion Entropy Analysis (DEA) to examine long-range persistence behavior in time series by estimating their respective parameters. We use the parameter of the Lévy process (α) characterizing the data and the scaling parameters of DFA (H) and DEA (δ) characterizing the self-similar property to generate a relationship between the three (3) aforementioned scaling methods. Findings from the numerical simulations confirm the existence of long-range persistence (long-memory behavior) in both the financial and geophysical time series. Furthermore, the numerical results from this study indicates an approximate inverse relationship between the parameter of the Lévy process and the scaling parameters of the DFA and DEA (i.e.,

H, δ \approx \frac{1}{α}

), which we prove analytically. Full article

(This article belongs to the Special Issue Volatility Models Applied to Geophysics, Financial Market Data and Other Disciplines)

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10 pages, 278 KiB

Open AccessArticle

TPLVM: Portfolio Construction by Student’s t-Process Latent Variable Model

by Yusuke Uchiyama and Kei Nakagawa

Mathematics 2020, 8(3), 449; https://doi.org/10.3390/math8030449 - 19 Mar 2020

Cited by 8 | Viewed by 3320

Abstract

Optimal asset allocation is a key topic in modern finance theory. To realize the optimal asset allocation on investor’s risk aversion, various portfolio construction methods have been proposed. Recently, the applications of machine learning are rapidly growing in the area of finance. In [...] Read more.

Optimal asset allocation is a key topic in modern finance theory. To realize the optimal asset allocation on investor’s risk aversion, various portfolio construction methods have been proposed. Recently, the applications of machine learning are rapidly growing in the area of finance. In this article, we propose the Student’s t-process latent variable model (TPLVM) to describe non-Gaussian fluctuations of financial timeseries by lower dimensional latent variables. Subsequently, we apply the TPLVM to portfolio construction as an alternative of existing nonlinear factor models. To test the performance of the proposed method, we construct minimum-variance portfolios of global stock market indices based on the TPLVM or Gaussian process latent variable model. By comparing these portfolios, we confirm the proposed portfolio outperforms that of the existing Gaussian process latent variable model. Full article

(This article belongs to the Special Issue Volatility Models Applied to Geophysics, Financial Market Data and Other Disciplines)

18 pages, 1272 KiB

Open AccessArticle

Long-Range Correlations and Characterization of Financial and Volcanic Time Series

by Maria C. Mariani, Peter K. Asante, Md Al Masum Bhuiyan, Maria P. Beccar-Varela, Sebastian Jaroszewicz and Osei K. Tweneboah

Mathematics 2020, 8(3), 441; https://doi.org/10.3390/math8030441 - 18 Mar 2020

Cited by 12 | Viewed by 3755

Abstract

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series [...] Read more.

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight. Full article

(This article belongs to the Special Issue Volatility Models Applied to Geophysics, Financial Market Data and Other Disciplines)

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