scholarly journals Modelling High Dimensional Paddy Production Data using Copulas

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Nuranisyha Mohd Roslan ◽  
Wendy Ling Shinyie ◽  
Sim Siew Ling
Keyword(s):  
Time Series ◽  
Marginal Distribution ◽  
Reference Group ◽  
Estimation Method ◽  
Information Criterion ◽  
Copula Function ◽  
Archimedean Copula ◽  
Copula Functions ◽  
Estimation Errors ◽  
Elliptical Copula

As the climate change is likely to be adversely affecting the yield of paddy production, thence it has brought a limelight of the probable challenges on human particularly regional food security issues. This paper aims to fit multivariate time series of paddy production variables using copula functions and predicts the next year event based on the data of five countries in southeast Asia. In particular, the most appropriate marginal distribution for each univariate time series was first identified using maximum likelihood parameter estimation method. Next, we performed multivariate copula fitting using two types of copula families, namely, elliptical copula family and Archimedean copula family. Elliptical copula family studied are normal and t copula, while Archimedean copula family considered are Joe, Clayton and Gumbel copulas. The performance of marginal distribution and copula fitting was examined using Akaike information criterion (AIC) values. Finally, we used the best fitted copula model to forecast the succeeding event. In order to assess the performance of copula function, we computed the forecast means and estimation errors of copula function with a generalized autoregressive conditional heteroskedasticity model as reference group. Based on the smallest AIC, the majority of the data favoured the Gumbel copula, which belongs to Archimedean copula family as well as extreme value copula family. Likewise, applying the historical data to forecast the future trends may assist all relevant stakeholders, for instance government, NGO agencies, and professional practitioners in making informed decisions without compromising the environmental as well as economical sustainability in the region.

COMPOSITE BERNSTEIN COPULAS

2015 ◽  
Vol 45 (2) ◽  
pp. 445-475 ◽  
Author(s):  
Jingping Yang ◽  
Zhijin Chen ◽  
Fang Wang ◽  
Ruodu Wang
Keyword(s):  
Prior Information ◽  
Estimation Method ◽  
Tail Dependence ◽  
Estimation Procedure ◽  
Copula Function ◽  
Simulation Studies ◽  
Copula Functions ◽  
New Class ◽  
Copula Estimation ◽  
Dependency Structures

AbstractCopula function has been widely used in insurance and finance for modeling inter-dependency between risks. Inspired by the Bernstein copula put forward by Sancetta and Satchell (2004, Econometric Theory, 20, 535–562), we introduce a new class of multivariate copulas, the composite Bernstein copula, generated from a composition of two copulas. This new class of copula functions is able to capture tail dependence, and it has a reproduction property for the three important dependency structures: comonotonicity, countermonotonicity and independence. We introduce an estimation procedure based on the empirical composite Bernstein copula which incorporates both prior information and data into the estimation. Simulation studies and an empirical study on financial data illustrate the advantages of the empirical composite Bernstein copula estimation method, especially in capturing tail dependence.

scholarly journals Bivariate Frequency of Meteorological Drought in the Upper Minjiang River Based on Copula Function

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2056
Author(s):  
Fangling Qin ◽  
Tianqi Ao ◽  
Ting Chen
Keyword(s):  
Marginal Distribution ◽  
Standardized Precipitation Index ◽  
Meteorological Drought ◽  
Copula Function ◽  
Distribution Functions ◽  
Joint Probability Distribution ◽  
Drought Risk ◽  
Monthly Precipitation ◽  
Copula Functions ◽  
Minjiang River

Based on the Standardized Precipitation Index (SPI) and copula function, this study analyzed the meteorological drought in the upper Minjiang River basin. The Tyson polygon method is used to divide the research area into four regions based on four meteorological stations. The monthly precipitation data of four meteorological stations from 1966 to 2016 were used for the calculation of SPI. The change trend of SPI1, SPI3 and SPI12 showed the historical dry-wet evolution phenomenon of short-term humidification and long-term aridification in the study area. The major drought events in each region are counted based on SPI3. The results show that the drought lasted the longest in Maoxian region, the occurrence of minor drought events was more frequent than the other regions. Nine distribution functions are used to fit the marginal distribution of drought duration (D), severity (S) and peak (P) estimated based on SPI3, the best marginal distribution is obtained by chi-square test. Five copula functions are used to create a bivariate joint probability distribution, the best copula function is selected through AIC, the univariate and bivariate return periods were calculated. The results of this paper will help the study area to assess the drought risk.

scholarly journals Penerapan Metode GARCH-Vine Copula untuk Estimasi Value at Risk (VaR) pada Portofolio

2018 ◽  
Vol 7 (2) ◽  
pp. 63-77 ◽  
Author(s):  
Herida Okta Pintari ◽  
Retno Subekti
Keyword(s):  
At Risk ◽  
Linear Correlation ◽  
Value At Risk ◽  
Marginal Distribution ◽  
Measurement Instrument ◽  
Copula Function ◽  
Copula Functions ◽  
Non Linear ◽  
Vine Copula ◽  
T Distribution

Salah satu alat ukur yang digunakan untuk menghitung risiko portofolio adalah Value at Risk (VaR). Beberapa metode pengukuran VaR mengasumsikan return berdistribusi normal dan ukuran dependensi antar saham menggunakan korelasi linear. Faktanya, asumsi normalitas pada data finansial jarang terpenuhi dan terdapat indikasi adanya heteroskedastisitas. Selain itu, kebergantungan antar saham yang non-linear tidak sesuai apabila diukur dengan korelasi linear. Penyimpangan ini menyebabkan tidak validnya estimasi VaR. Tujuan dari penelitian ini adalah untuk mengetahui penerapan metode GARCH-Vine Copula untuk estimasi VaR pada portofolio. Vine Copula adalah fungsi distribusi multivariat yang menggabungkan distribusi marginal return univariat dalam portofolio, dan dapat menggambarkan struktur kebergantungan non-linearnya. Vine Copula dapat dilakukan dengan menentukan dekomposisi Vine Copula dan fungsi keluarga copulanya. Dekomposisi Vine Copula dilakukan dengan menggunakan C-Vine dan D-Vine Copula. Kemudian dengan menggunakan fungsi copula keluarga Archimedean, yaitu Clayton, Gumbel, dan Frank dapat ditentukan distribusi bersamanya. Pembentukan distribusi marginal menggunakan model GARCH berdistribusi Student-t digunakan untuk mengatasi adanya heteroskedastisitas. Hasil penerapan dari tiga saham perbankan, yaitu BBNI, BBRI, dan BMRI periode 26 Agustus 2013 hingga 20 November 2017 diperoleh model D-Vine Copula dengan fungsi copula Frank adalah model terbaik untuk memodelkan data, dengan nilai VaR sebesar 1,86%, 2,56%, dan 4,49% dari dana investasi pada tingkat kepercayaan 90%, 95%, dan 99%. [One of the measurement instrument that are used to calculate the risk of portfolio is Value at Risk (VaR). Several methods of measuring VaR assumes normal and the size of dependencies return between the stock using a linear correlation. Basically, the assumption normal in financial data is violated and the possibility of heteroscedasticity is indicated. In addition, dependences non-linear is not appropriate when measured with a linear correlation. This deviation causes invalidity VaR estimation. The purpose of this research is to know the application of GARCH-Vine Copula method for estimation of VaR on portfolio. Vine Copula is a multivariate distribution function that combines the univariate marginal distribution of return in portfolio, and it can describe the structure of dependencies non-linear. Vine Copula can be done by determining the decomposition of Vine Copula and its copula family function. Vine Copula decomposition is using C-Vine and D-Vine Copula. Then by using the copula function of the Archimedean family, namely Clayton, Gumbel, and Frank can be determined the joint distribution. The facts, the formation of the marginal distribution of GARCH model using the student-t distribution used to overcome the presence of heteroscedasticity. The result of the application of these stocks namely BBNI, BBRI, and BMRI from 26 August 2013 to 20 November 2017 has shown model D-Vine Copula copula functions with Frank is the best one to model the data. So, the VaR estimation at 90%, 95%, and 99% confidence levels are 1,86%, 2,56%, and 4,49% respectively of the invested funds.]

scholarly journals Modeling of Lake Malombe Annual Fish Landings and Catch per Unit Effort (CPUE)

Forecasting ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 39-55
Author(s):  
Rodgers Makwinja ◽  
Seyoum Mengistou ◽  
Emmanuel Kaunda ◽  
Tena Alemiew ◽  
Titus Bandulo Phiri ◽  
...  
Keyword(s):  
Time Series ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Series Data ◽  
Efficiency Coefficient ◽  
Arima Models ◽  
Catch Per Unit Effort ◽  
Annual Fish ◽  
Unit Effort ◽  
The Mean

Forecasting, using time series data, has become the most relevant and effective tool for fisheries stock assessment. Autoregressive integrated moving average (ARIMA) modeling has been commonly used to predict the general trend for fish landings with increased reliability and precision. In this paper, ARIMA models were applied to predict Lake Malombe annual fish landings and catch per unit effort (CPUE). The annual fish landings and CPUE trends were first observed and both were non-stationary. The first-order differencing was applied to transform the non-stationary data into stationary. Autocorrelation functions (AC), partial autocorrelation function (PAC), Akaike information criterion (AIC), Bayesian information criterion (BIC), square root of the mean square error (RMSE), the mean absolute error (MAE), percentage standard error of prediction (SEP), average relative variance (ARV), Gaussian maximum likelihood estimation (GMLE) algorithm, efficiency coefficient (E2), coefficient of determination (R2), and persistent index (PI) were estimated, which led to the identification and construction of ARIMA models, suitable in explaining the time series and forecasting. According to the measures of forecasting accuracy, the best forecasting models for fish landings and CPUE were ARIMA (0,1,1) and ARIMA (0,1,0). These models had the lowest values AIC, BIC, RMSE, MAE, SEP, ARV. The models further displayed the highest values of GMLE, PI, R2, and E2. The “auto. arima ()” command in R version 3.6.3 further displayed ARIMA (0,1,1) and ARIMA (0,1,0) as the best. The selected models satisfactorily forecasted the fish landings of 2725.243 metric tons and CPUE of 0.097 kg/h by 2024.

scholarly journals An edge-cloud collaboration architecture for pattern anomaly detection of time series in wireless sensor networks

2021 ◽  
Author(s):  
Cong Gao ◽  
Ping Yang ◽  
Yanping Chen ◽  
Zhongmin Wang ◽  
Yue Wang
Keyword(s):  
Time Series ◽  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Anomaly Detection ◽  
Estimation Method ◽  
Feature Representation ◽  
Sensor Data ◽  
Wireless Sensor ◽  
Data Sets ◽  
Edge Node

AbstractWith large deployment of wireless sensor networks, anomaly detection for sensor data is becoming increasingly important in various fields. As a vital data form of sensor data, time series has three main types of anomaly: point anomaly, pattern anomaly, and sequence anomaly. In production environments, the analysis of pattern anomaly is the most rewarding one. However, the traditional processing model cloud computing is crippled in front of large amount of widely distributed data. This paper presents an edge-cloud collaboration architecture for pattern anomaly detection of time series. A task migration algorithm is developed to alleviate the problem of backlogged detection tasks at edge node. Besides, the detection tasks related to long-term correlation and short-term correlation in time series are allocated to cloud and edge node, respectively. A multi-dimensional feature representation scheme is devised to conduct efficient dimension reduction. Two key components of the feature representation trend identification and feature point extraction are elaborated. Based on the result of feature representation, pattern anomaly detection is performed with an improved kernel density estimation method. Finally, extensive experiments are conducted with synthetic data sets and real-world data sets.

scholarly journals A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Mark Levene
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Marginal Distribution ◽  
Hypothesis Test ◽  
Data Sets ◽  
Test Statistic ◽  
Sample Test ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

scholarly journals SARIMA Approach to Generating Synthetic Monthly Rainfall in the Sinú River Watershed in Colombia

Atmosphere ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 602
Author(s):  
Luisa Martínez-Acosta ◽  
Juan Pablo Medrano-Barboza ◽  
Álvaro López-Ramos ◽  
John Freddy Remolina López ◽  
Álvaro Alberto López-Lambraño
Keyword(s):  
Time Series ◽  
Water Resources ◽  
Autocorrelation Function ◽  
Information Criterion ◽  
Monthly Rainfall ◽  
Statistical Characteristics ◽  
Rainfall Time Series ◽  
River Watershed ◽  
Statistical Measures ◽  
Sarima Models

Seasonal Auto Regressive Integrative Moving Average models (SARIMA) were developed for monthly rainfall time series. Normality of the rainfall time series was achieved by using the Box Cox transformation. The best SARIMA models were selected based on their autocorrelation function (ACF), partial autocorrelation function (PACF), and the minimum values of the Akaike Information Criterion (AIC). The result of the Ljung–Box statistical test shows the randomness and homogeneity of each model residuals. The performance and validation of the SARIMA models were evaluated based on various statistical measures, among these, the Student’s t-test. It is possible to obtain synthetic records that preserve the statistical characteristics of the historical record through the SARIMA models. Finally, the results obtained can be applied to various hydrological and water resources management studies. This will certainly assist policy and decision-makers to establish strategies, priorities, and the proper use of water resources in the Sinú river watershed.

ON DEFAULT CORRELATION AND PRICING OF COLLATERALIZED DEBT OBLIGATION BY COPULA FUNCTIONS

2006 ◽  
Vol 05 (03) ◽  
pp. 483-493 ◽  
Author(s):  
PING LI ◽  
HOUSHENG CHEN ◽  
XIAOTIE DENG ◽  
SHUNMING ZHANG
Keyword(s):  
Credit Derivatives ◽  
Copula Function ◽  
Dependence Structure ◽  
Default Correlation ◽  
Specific Kind ◽  
Copula Functions ◽  
Recovery Rates ◽  
Collateralized Debt Obligation ◽  
Collateralized Debt ◽  
Debt Obligation

Default correlation is the key point for the pricing of multi-name credit derivatives. In this paper, we apply copulas to characterize the dependence structure of defaults, determine the joint default distribution, and give the price for a specific kind of multi-name credit derivative — collateralized debt obligation (CDO). We also analyze two important factors influencing the pricing of multi-name credit derivatives, recovery rates and copula function. Finally, we apply Clayton copula, in a numerical example, to simulate default times taking specific underlying recovery rates and average recovery rates, then price the tranches of a given CDO and then analyze the results.

scholarly journals Learning from Nighttime Observations of Gas Flaring in North Dakota for Better Decision and Policy Making

2021 ◽  
Vol 13 (5) ◽  
pp. 941
Author(s):  
Rong Lu ◽  
Jennifer L. Miskimins ◽  
Mikhail Zhizhin
Keyword(s):  
Time Series ◽  
North Dakota ◽  
Policy Making ◽  
Nearest Neighbor ◽  
Negative Binomial ◽  
Infrared Imaging ◽  
Gaussian Mixture Models ◽  
Data Gathering ◽  
Gaussian Mixture ◽  
Estimation Errors

In today’s oil industry, companies frequently flare the produced natural gas from oil wells. The flaring activities are extensive in some regions including North Dakota. Besides company-reported data, which are compiled by the North Dakota Industrial Commission, flaring statistics such as count and volume can be estimated via Visible Infrared Imaging Radiometer Suite nighttime observations. Following data gathering and preprocessing, Bayesian machine learning implemented with Markov chain Monte Carlo methods is performed to tackle two tasks: flaring time series analysis and distribution approximation. They help further understanding of the flaring profiles and reporting qualities, which are important for decision/policy making. First, although fraught with measurement and estimation errors, the time series provide insights into flaring approaches and characteristics. Gaussian processes are successful in inferring the latent flaring trends. Second, distribution approximation is achieved by unsupervised learning. The negative binomial and Gaussian mixture models are utilized to describe the distributions of field flare count and volume, respectively. Finally, a nearest-neighbor-based approach for company level flared volume allocation is developed. Potential discrepancies are spotted between the company reported and the remotely sensed flaring profiles.

scholarly journals Parametric and Semiparametric Estimations of Bivariate Truncated Type I Generalized Logistic Models driven from Copulas

2017 ◽  
Vol 7 (1) ◽  
pp. 72 ◽  
Author(s):  
Lamya A Baharith
Keyword(s):  
Logistic Models ◽  
Real Data ◽  
Information Criterion ◽  
Logistic Distribution ◽  
Type I ◽  
Copula Functions ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Generalized Logistic Distribution ◽  
Weibull Models

Truncated type I generalized logistic distribution has been used in a variety of applications. In this article, a new bivariate truncated type I generalized logistic (BTTGL) distributional models driven from three different copula functions are introduced. A study of some properties is illustrated. Parametric and semiparametric methods are used to estimate the parameters of the BTTGL models. Maximum likelihood and inference function for margin estimates of the BTTGL parameters are compared with semiparametric estimates using real data set. Further, a comparison between BTTGL, bivariate generalized exponential and bivariate exponentiated Weibull models is conducted using Akaike information criterion and the maximized log-likelihood. Extensive Monte Carlo simulation study is carried out for different values of the parameters and different sample sizes to compare the performance of parametric and semiparametric estimators based on relative mean square error.

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