Empirical comparison of skewed t-copula models for insurance and financial data

2020 ◽  
Vol 15 (4) ◽  
pp. 351-361
Author(s):  
Liwei Huang ◽  
Arkady Shemyakin
Keyword(s):  
Bayesian Estimation ◽  
Goodness Of Fit ◽  
Model Performance ◽  
Information Criteria ◽  
Stock Index ◽  
Likelihood Method ◽  
Special Importance ◽  
Copula Model ◽  
Technical Problems ◽  
T Copula

Skewed t-copulas recently became popular as a modeling tool of non-linear dependence in statistics. In this paper we consider three different versions of skewed t-copulas introduced by Demarta and McNeill; Smith, Gan and Kohn; and Azzalini and Capitanio. Each of these versions represents a generalization of the symmetric t-copula model, allowing for a different treatment of lower and upper tails. Each of them has certain advantages in mathematical construction, inferential tools and interpretability. Our objective is to apply models based on different types of skewed t-copulas to the same financial and insurance applications. We consider comovements of stock index returns and times-to-failure of related vehicle parts under the warranty period. In both cases the treatment of both lower and upper tails of the joint distributions is of a special importance. Skewed t-copula model performance is compared to the benchmark cases of Gaussian and symmetric Student t-copulas. Instruments of comparison include information criteria, goodness-of-fit and tail dependence. A special attention is paid to methods of estimation of copula parameters. Some technical problems with the implementation of maximum likelihood method and the method of moments suggest the use of Bayesian estimation. We discuss the accuracy and computational efficiency of Bayesian estimation versus MLE. Metropolis-Hastings algorithm with block updates was suggested to deal with the problem of intractability of conditionals.

scholarly journals Type II Topp–Leone Inverted Kumaraswamy Distribution with Statistical Inference and Applications

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1459 ◽  
Author(s):  
Ramadan A. ZeinEldin ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Maximum Likelihood ◽  
Probability Density ◽  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Information Criteria ◽  
Likelihood Method ◽  
Type Ii ◽  
Asymptotic Results ◽  
Kumaraswamy Distribution ◽  
New Distribution

In this paper, we present and study a new four-parameter lifetime distribution obtained by the combination of the so-called type II Topp–Leone-G and transmuted-G families and the inverted Kumaraswamy distribution. By construction, the new distribution enjoys nice flexible properties and covers some well-known distributions which have already proven themselves in statistical applications, including some extensions of the Bur XII distribution. We first present the main functions related to the new distribution, with discussions on their shapes. In particular, we show that the related probability density function is left, right skewed, near symmetrical and reverse J shaped, with a notable difference regarding the right tailed, illustrating the flexibility of the distribution. Then, the related model is displayed, with the estimation of the parameters by the maximum likelihood method and the consideration of two practical data sets. We show that the proposed model is the best one in terms of standard model selection criteria, including Akaike information and Bayesian information criteria, and goodness of fit tests against three well-established competitors. Then, for the new model, the theoretical background on the maximum likelihood method is given, with numerical guaranties of the efficiency of the estimates obtained via a simulation study. Finally, the main mathematical properties of the new distribution are discussed, including asymptotic results, quantile function, Bowley skewness and Moors kurtosis, mixture representations for the probability density and cumulative density functions, ordinary moments, incomplete moments, probability weighted moments, stress-strength reliability and order statistics.

scholarly journals Modeling and Risk Analysis Using Parametric Distributions with an Application in Equity-Linked Securities

2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Sun-Yong Choi ◽  
Ji-Hun Yoon
Keyword(s):  
Risk Analysis ◽  
Goodness Of Fit ◽  
Risk Measures ◽  
Information Criteria ◽  
Stock Index ◽  
Distribution Model ◽  
Goodness Of Fit Test ◽  
Stock Indices ◽  
Management Concepts ◽  
Best Fit

In this study, we model the returns of a stock index using various parametric distribution models. There are four indices used in this study: HSCEI, KOSPI 200, S&P 500, and EURO STOXX 50. We applied 12 distributions to the data of these stock indices—Cauchy, Laplace, normal, Student’s t, skew normal, skew Cauchy, skew Laplace, skew Student’s t, hyperbolic, normal inverse Gaussian, variance gamma, and general hyperbolic—for the parametric distribution model. In order to choose the best-fit distribution for describing the stock index, we used the information criteria, goodness-of-fit test, and graphical tail test for each stock index. We estimated the value-at-risk (VaR), one of the most popular management concepts in the area of risk management, for the return of stock indices. Furthermore, we applied the parametric distributions to the risk analysis of equity-linked securities (ELS) as they are a very popular financial product on the Korean financial market. Relevant risk measures, such as VaR and conditional tail expectation, are calculated using various distributions. For calculating the risk measures, we used Monte Carlo simulations under the best-fit distribution. According to the empirical results, investing in ELS is more risky than investing in securities, and the risk measure of the ELS heavily depends on the type of security.

Formal Comparison of Copula-AR(1)-t-GARCH(1,1) Models for Sub-Indices of the Stock Index WIG

2016 ◽  
Vol 63 (2) ◽  
pp. 123-148
Author(s):  
Justyna Mokrzycka ◽  
Anna Pajor
Keyword(s):  
Model Comparison ◽  
Stock Exchange ◽  
Financial Time Series ◽  
Explanatory Power ◽  
Information Criteria ◽  
Stock Index ◽  
Likelihood Method ◽  
Dependence Structure ◽  
Daily Growth ◽  
Bayesian Model Comparison

Copulas have become one of most popular tools used in modelling the dependencies among financial time series. The main aim of the paper is to formally assess the relative explanatory power of competing bivariate Copula-AR-GARCH models, which differ in assumptions on the conditional dependence structure represented by particular copulas. For the sake of comparison the Copula-AR-GARCH mod-els are estimated using the maximum likelihood method, and next they are informally compared and ranked according to the values of the Akaike (AIC) and of the Schwarz (BIC) information criteria. We apply these tools to the daily growth rates of four sub-indices of the stock index WIG published by the Warsaw Stock Exchange. Our results indicate that the informal use of the information criteria (AIC or BIC) leads to very similar ranks of models as compared to those obtained by the use of the formal Bayesian model comparison.

scholarly journals Container Throughput Forecasting Using Dynamic Factor Analysis and ARIMAX Model

2017 ◽  
Vol 29 (5) ◽  
pp. 529-542 ◽  
Author(s):  
Marko Intihar ◽  
Tomaž Kramberger ◽  
Dejan Dragan
Keyword(s):  
Factor Analysis ◽  
Goodness Of Fit ◽  
Moving Average ◽  
Real Data ◽  
Information Criteria ◽  
Dynamic Factor Analysis ◽  
Forecasting Model ◽  
Dynamic Factor ◽  
Macroeconomic Indicators ◽  
The Impact

The paper examines the impact of integration of macroeconomic indicators on the accuracy of container throughput time series forecasting model. For this purpose, a Dynamic factor analysis and AutoRegressive Integrated Moving-Average model with eXogenous inputs (ARIMAX) are used. Both methodologies are integrated into a novel four-stage heuristic procedure. Firstly, dynamic factors are extracted from external macroeconomic indicators influencing the observed throughput. Secondly, the family of ARIMAX models of different orders is generated based on the derived factors. In the third stage, the diagnostic and goodness-of-fit testing is applied, which includes statistical criteria such as fit performance, information criteria, and parsimony. Finally, the best model is heuristically selected and tested on the real data of the Port of Koper. The results show that by applying macroeconomic indicators into the forecasting model, more accurate future throughput forecasts can be achieved. The model is also used to produce future forecasts for the next four years indicating a more oscillatory behaviour in (2018-2020). Hence, care must be taken concerning any bigger investment decisions initiated from the management side. It is believed that the proposed model might be a useful reinforcement of the existing forecasting module in the observed port.

PARAMETER ESTIMATION ON HURDLE POISSON REGRESSION MODEL WITH CENSORED DATA

2012 ◽  
Vol 57 (1) ◽  
Author(s):  
SEYED EHSAN SAFFAR ◽  
ROBIAH ADNAN ◽  
WILLIAM GREENE
Keyword(s):  
Regression Model ◽  
Count Data ◽  
Poisson Regression ◽  
Goodness Of Fit ◽  
Poisson Model ◽  
Likelihood Method ◽  
Poisson Regression Model ◽  
Response Variable ◽  
The Mean ◽  
Over Dispersion

A Poisson model typically is assumed for count data. In many cases, there are many zeros in the dependent variable and because of these many zeros, the mean and the variance values of the dependent variable are not the same as before. In fact, the variance value of the dependent variable will be much more than the mean value of the dependent variable and this is called over–dispersion. Therefore, Poisson model is not suitable anymore for this kind of data because of too many zeros. Thus, it is suggested to use a hurdle Poisson regression model to overcome over–dispersion problem. Furthermore, the response variable in such cases is censored for some values. In this paper, a censored hurdle Poisson regression model is introduced on count data with many zeros. In this model, we consider a response variable and one or more than one explanatory variables. The estimation of regression parameters using the maximum likelihood method is discussed and the goodness–of–fit for the regression model is examined. We study the effects of right censoring on estimated parameters and their standard errors via an example.

Abstract 353: Performance of SOFA Score to Predict Mortality at Hospital Discharge After Cardiac Arrest

Circulation ◽  
2018 ◽  
Vol 138 (Suppl_2) ◽  
Author(s):  
Anne V Grossestreuer ◽  
Tuyen Yankama ◽  
Ari Moskowitz ◽  
Anthony Mahoney-Pacheco ◽  
Varun Konanki ◽  
...  
Keyword(s):  
Cardiac Arrest ◽  
Hospital Discharge ◽  
Sofa Score ◽  
Statistical Power ◽  
Goodness Of Fit ◽  
Outcome Measure ◽  
Model Performance ◽  
Surrogate Outcome ◽  
Surrogate Outcome Measure ◽  
Good Calibration

Introduction: Cardiac arrest (CA) outcomes, when dichotomized as survival/non-survival, limit statistical power of interventional studies and do not acknowledge hospital-level factors independent of post-CA sequelae. We explored the Sequential Organ Failure Assessment (SOFA) score at 72 hours post-CA as a surrogate outcome measure for mortality. We also assessed methods to account for death <72 hours post-CA in SOFA score computation. Methods: This was a single center retrospective study of post-CA patients from 1/08-12/17. SOFA score components were abstracted at baseline, 24, 48, and 72h post-CA. Thirteen ways of accounting for missing data were assessed. The outcome was mortality at hospital discharge. Model performance was assessed using area under the receiver-operator characteristic (AUC) curves and Hosmer-Lemeshow goodness of fit statistics. Results: Of 847 patients, 528 (62%) had complete baseline SOFA scores and 205 (24%) had complete scores at 72h. Death <72h occurred in 28%; 45% survived to hospital discharge. SOFA score at 72h without accounting for death had an AUC of 0.62. The best performing SOFA model at 72h with good calibration imputed a 20% increase over the last observed SOFA score in patients who expired <72h with an AUC of 0.79 (95% CI: 0.74-0.83). In terms of change in SOFA at 72h from baseline, the best performing model with good calibration imputed death <72h as the highest possible score (AUC: 0.88 [95% CI: 0.84-0.92]). These results were consistent when analyzing in- and out-of-hospital CA separately, although the change from baseline model was not well calibrated in in-hospital arrests. Conclusions: Without consideration of death, SOFA scores at 72 hours post-CA perform poorly. Imputing for early mortality improved the model. If this imputation structure is validated prospectively, SOFA could provide a scoring system to predict death at hospital discharge and serve as a surrogate outcome measure in interventional studies.

scholarly journals Influence of Hydrological Model Selection on Simulation of Moderate and Extreme Flow Events: A Case Study of the Blue Nile Basin

2016 ◽  
Vol 2016 ◽  
pp. 1-28 ◽  
Author(s):  
Charles Onyutha
Keyword(s):  
Model Selection ◽  
Extreme Events ◽  
Goodness Of Fit ◽  
Model Performance ◽  
Flow Conditions ◽  
Nile Basin ◽  
Blue Nile ◽  
Low Flows ◽  
Blue Nile Basin ◽  
Extreme Flow

Five hydrological models were applied based on data from the Blue Nile Basin. Optimal parameters of each model were obtained by automatic calibration. Model performance was tested under both moderate and extreme flow conditions. Extreme events for the model performance evaluation were extracted based on seven criteria. Apart from graphical techniques, there were nine statistical “goodness-of-fit” metrics used to judge the model performance. It was found that whereas the influence of model selection may be minimal in the simulation of normal flow events, it can lead to large under- and/or overestimations of extreme events. Besides, the selection of the best model for extreme events may be influenced by the choice of the statistical “goodness-of-fit” measures as well as the criteria for extraction of high and low flows. It was noted that the use of overall water-balance-based objective function not only is suitable for moderate flow conditions but also influences the models to perform better for high flows than low flows. Thus, the choice of a particular model is recommended to be made on a case by case basis with respect to the objectives of the modeling as well as the results from evaluation of the intermodel differences.

Remaining Useful Life Estimation Based on a Segmental Hidden Markov Model With Continuous Observations

2017 ◽  
Author(s):  
Zhen Chen ◽  
Tangbin Xia ◽  
Ershun Pan
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Goodness Of Fit ◽  
Hidden Markov ◽  
Remaining Useful Life ◽  
Likelihood Method ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Useful Life ◽  
Hidden States

In this paper, a segmental hidden Markov model (SHMM) with continuous observations, is developed to tackle the problem of remaining useful life (RUL) estimation. The proposed approach has the advantage of predicting the RUL and detecting the degradation states simultaneously. As the observation space is discretized into N segments corresponding to N hidden states, the explicit relationship between actual degradation paths and the hidden states can be depicted. The continuous observations are fitted by Gaussian, Gamma and Lognormal distribution, respectively. To select a more suitable distribution, model validation metrics are employed for evaluating the goodness-of-fit of the available models to the observed data. The unknown parameters of the SHMM can be estimated by the maximum likelihood method with the complete data. Then a recursive method is used for RUL estimation. Finally, an illustrate case is analyzed to demonstrate the accuracy and efficiency of the proposed method. The result also suggests that SHMM with observation probability distribution which is closer to the real data behavior may be more suitable for the prediction of RUL.

scholarly journals Two-Parameter Nwikpe (TPAN) Distribution with Application

2021 ◽  
pp. 56-67
Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Real Life ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Data Sets ◽  
Method Of Moment ◽  
Two Parameter ◽  
New Distribution

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established.  The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.

A COMPARISON OF NEURAL NETWORK MODEL SELECTION STRATEGIES FOR THE PRICING OF S&P 500 STOCK INDEX OPTIONS

2007 ◽  
Vol 16 (06) ◽  
pp. 1093-1113 ◽  
Author(s):  
N. S. THOMAIDIS ◽  
V. S. TZASTOUDIS ◽  
G. D. DOUNIAS
Keyword(s):  
Neural Network ◽  
Model Selection ◽  
Network Model ◽  
Neural Network Model ◽  
Information Criteria ◽  
Stock Index ◽  
Statistical Hypothesis ◽  
Neural Network Models ◽  
Index Options ◽  
Pruning Technique

This paper compares a number of neural network model selection approaches on the basis of pricing S&P 500 stock index options. For the choice of the optimal architecture of the neural network, we experiment with a “top-down” pruning technique as well as two “bottom-up” strategies that start with simple models and gradually complicate the architecture if data indicate so. We adopt methods that base model selection on statistical hypothesis testing and information criteria and we compare their performance to a simple heuristic pruning technique. In the first set of experiments, neural network models are employed to fit the entire options surface and in the second they are used as parts of a hybrid intelligence scheme that combines a neural network model with theoretical option-pricing hints.

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