scholarly journals Objective Bayesian Prediction of Future Record Statistics Based on the Exponentiated Gumbel Distribution: Comparison with Time-Series Prediction

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1443
Author(s):  
Yongku Kim ◽  
Jung In Seo
Keyword(s):  
Time Series ◽  
Time Series Prediction ◽  
Information Matrix ◽  
Simple Algorithm ◽  
Gumbel Distribution ◽  
Real Data ◽  
Good Alternative ◽  
Record Values ◽  
Shape Parameters ◽  
Record Statistics

The interest in the study of record statistics has been increasing in recent years in the context of predicting stock markets and addressing global warming and climate change problems such as cyclones and floods. However, because record values are mostly rare observed, its probability distribution may be skewed or asymmetric. In this case, the Bayesian approach with a reasonable choice of the prior distribution can be a good alternative. This paper presents an objective Bayesian method for predicting future record values when observed record values have a two-parameter exponentiated Gumbel distribution with the scale and shape parameters. For objective Bayesian analysis, objective priors such as the Jeffreys and reference priors are first derived from the Fisher information matrix for the scale and shape parameters, and an analysis of the resulting posterior distribution is then performed to examine its properness and validity. In addition, under the derived objective prior distributions, a simple algorithm using a pivotal quantity is proposed to predict future record values. To validate the proposed approach, it was applied to a real dataset. For a closer examination and demonstration of the superiority of the proposed predictive method, it was compared to time-series models such as the autoregressive integrated moving average and dynamic linear model in an analysis of real data that can be observed from an infinite time series comprising independent sample values.

scholarly journals Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249028
Author(s):  
Ehsan Fayyazishishavan ◽  
Serpil Kılıç Depren
Keyword(s):  
Information Matrix ◽  
Gumbel Distribution ◽  
Sampling Technique ◽  
Real Data ◽  
Record Values ◽  
Unknown Parameters ◽  
Data Set ◽  
Credible Intervals ◽  
Lower Records ◽  
Two Parameter

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This paper investigates the estimation of the parameters of this distribution by using lower records values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real data set is provided to illustrate the proposed methods.

scholarly journals Local Prediction of Chaotic Time Series Based on Polynomial Coefficient Autoregressive Model

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Liyun Su ◽  
Chenlong Li
Keyword(s):  
Time Series ◽  
Autoregressive Model ◽  
Time Series Prediction ◽  
Real Data ◽  
Chaotic Time Series ◽  
Polynomial Coefficient ◽  
State Dependent ◽  
Forecasting Performance ◽  
One Step ◽  
Chaotic Time Series Prediction

We apply the polynomial function to approximate the functional coefficients of the state-dependent autoregressive model for chaotic time series prediction. We present a novel local nonlinear model called local polynomial coefficient autoregressive prediction (LPP) model based on the phase space reconstruction. The LPP model can effectively fit nonlinear characteristics of chaotic time series with simple structure and have excellent one-step forecasting performance. We have also proposed a kernel LPP (KLPP) model which applies the kernel technique for the LPP model to obtain better multistep forecasting performance. The proposed models are flexible to analyze complex and multivariate nonlinear structures. Both simulated and real data examples are used for illustration.

scholarly journals The beta compound Rayleigh distribution : Properties and applications

2017 ◽  
Vol 5 (1) ◽  
pp. 57
Author(s):  
Hesham Reyad ◽  
Soha Ibrahim
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Continuous Model ◽  
Rayleigh Distribution ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Record Statistics ◽  
Mean Variance ◽  
Compound Rayleigh Distribution

In this paper, we introduce a new four parameter continuous model, called the beta compound Rayleigh (BCR) distribution that extends the compound Rayleigh distribution. Basic properties of the proposed distribution such as; mean, variance, coefficient of variation, raw and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, Rényi of entropy, order statistics and record statistics are investigated. We obtain the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the usefulness of the new model.

Neural Network Techniques for Time Series Prediction: A Review

2019 ◽  
Vol 3 (3) ◽  
Author(s):  
Muhammad Faheem Mushtaq ◽  
Urooj Akram ◽  
Muhammad Aamir ◽  
Haseeb Ali ◽  
Muhammad Zulqarnain
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Time Series ◽  
Time Series Data ◽  
Weather Prediction ◽  
Time Series Prediction ◽  
Series Data ◽  
Prediction Problem ◽  
Neural Network Models ◽  
Physical Time

It is important to predict a time series because many problems that are related to prediction such as health prediction problem, climate change prediction problem and weather prediction problem include a time component. To solve the time series prediction problem various techniques have been developed over many years to enhance the accuracy of forecasting. This paper presents a review of the prediction of physical time series applications using the neural network models. Neural Networks (NN) have appeared as an effective tool for forecasting of time series.  Moreover, to resolve the problems related to time series data, there is a need of network with single layer trainable weights that is Higher Order Neural Network (HONN) which can perform nonlinearity mapping of input-output. So, the developers are focusing on HONN that has been recently considered to develop the input representation spaces broadly. The HONN model has the ability of functional mapping which determined through some time series problems and it shows the more benefits as compared to conventional Artificial Neural Networks (ANN). The goal of this research is to present the reader awareness about HONN for physical time series prediction, to highlight some benefits and challenges using HONN.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

Making investment decisions in stock markets using a forecasting-Markowitz based decision-making approaches

2019 ◽  
Vol 15 (2) ◽  
pp. 647-659 ◽  
Author(s):  
Zahra Moeini Najafabadi ◽  
Mehdi Bijari ◽  
Mehdi Khashei
Keyword(s):  
Decision Making ◽  
Time Series ◽  
Stock Markets ◽  
Time Series Prediction ◽  
Investment Decisions ◽  
Rate Of Return ◽  
Expected Returns ◽  
Prediction Methods ◽  
Content Type ◽  
Markowitz Model

Purpose This study aims to make investment decisions in stock markets using forecasting-Markowitz based decision-making approaches. Design/methodology/approach The authors’ approach offers the use of time series prediction methods including autoregressive, autoregressive moving average and artificial neural network, rather than calculating the expected rate of return based on distribution. Findings The results show that using time series prediction methods has a significant effect on improving investment decisions and the performance of the investments. Originality/value In this study, in contrast to previous studies, the alteration in the Markowitz model started with the investment expected rate of return. For this purpose, instead of considering the distribution of returns and determining the expected returns, time series prediction methods were used to calculate the future return of each asset. Then, the results of different time series methods replaced the expected returns in the Markowitz model. Finally, the overall performance of the method, as well as the performance of each of the prediction methods used, was examined in relation to nine stock market indices.

scholarly journals A Time Series Sustainability Assessment of a Partial Energy Portfolio Transition

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 141
Author(s):  
Jacob Hale ◽  
Suzanna Long
Keyword(s):  
Time Series ◽  
Electricity Generation ◽  
Sustainability Assessment ◽  
Moving Average ◽  
Time Series Prediction ◽  
State Level ◽  
Autoregressive Integrated Moving Average ◽  
Energy Transitions ◽  
Univariate Time Series ◽  
Partial Energy

Energy portfolios are overwhelmingly dependent on fossil fuel resources that perpetuate the consequences associated with climate change. Therefore, it is imperative to transition to more renewable alternatives to limit further harm to the environment. This study presents a univariate time series prediction model that evaluates sustainability outcomes of partial energy transitions. Future electricity generation at the state-level is predicted using exponential smoothing and autoregressive integrated moving average (ARIMA). The best prediction results are then used as an input for a sustainability assessment of a proposed transition by calculating carbon, water, land, and cost footprints. Missouri, USA was selected as a model testbed due to its dependence on coal. Of the time series methods, ARIMA exhibited the best performance and was used to predict annual electricity generation over a 10-year period. The proposed transition consisted of a one-percent annual decrease of coal’s portfolio share to be replaced with an equal share of solar and wind supply. The sustainability outcomes of the transition demonstrate decreases in carbon and water footprints but increases in land and cost footprints. Decision makers can use the results presented here to better inform strategic provisioning of critical resources in the context of proposed energy transitions.

scholarly journals COVID-19 Time Series Prediction

2021 ◽  
Vol 181 ◽  
pp. 973-980
Author(s):  
Leonardo Sestrem de Oliveira ◽  
Sarah Beatriz Gruetzmacher ◽  
João Paulo Teixeira
Keyword(s):  
Time Series ◽  
Time Series Prediction

scholarly journals Modeling Best Practice Life Expectancy Using Gumbel Autoregressive Models

Risks ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 51
Author(s):  
Anthony Medford
Keyword(s):  
Time Series ◽  
Life Expectancy ◽  
Extreme Value Theory ◽  
Autoregressive Model ◽  
Best Practice ◽  
Gumbel Distribution ◽  
Value Theory ◽  
Model Diagnostics ◽  
Temporal Dependence ◽  
Simulation Results

Best practice life expectancy has recently been modeled using extreme value theory. In this paper we present the Gumbel autoregressive model of order one—Gumbel AR(1)—as an option for modeling best practice life expectancy. This class of model represents a neat and coherent framework for modeling time series extremes. The Gumbel distribution accounts for the extreme nature of best practice life expectancy, while the AR structure accounts for the temporal dependence in the time series. Model diagnostics and simulation results indicate that these models present a viable alternative to Gaussian AR(1) models when dealing with time series of extremes and merit further exploration.

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