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This paper introduces the vulgarized network autoregressive process with Gaussian and Student-t random noises. The processes relate the time-varying series of a given variable to the immediate past of the same phenomenon with the inclusion of its neighboring variables and networking structure. The generalized network autoregressive process would be fully spelt-out to contain the aforementioned random noises with their embedded parameters (the autoregressive coefficients, networking nodes, and neighboring nodes) and subjected to monthly prices of ten (10) edible cereals. Global-α of Generalized Network Autoregressive (GNAR) of order lag two, the neighbor at the time lags two and the neighbourhood nodal of zero, that is GNAR (2, [2,0]) was the ideal generalization for both Gaussian and student-t random noises for the prices of cereals, a model with two autoregressive parameters and network regression parameters on the first two neighbor sets at time lag one. GNAR model with student-t random noise produced the smallest BIC of -39.2298 compared to a BIC of -18.1683 by GNAR by Gaussian. The residual error via Gaussian was 0.9900 compared to the one of 0.9000 by student-t. Additionally, GNAR MSE for error of forecasting via student-t was 15.105% less than that of the Gaussian. Similarly, student-t-GNAR MSE for VAR was 1.59% less than that of the Gaussian-GNAR MSE for VAR. Comparing the fitted histogram plots of both the student-t and Gaussian processes, the two histograms produced a symmetric residual estimate for the fitted GNAR model via student-t and Gaussian processes respectively, but the residuals via the student-t were more evenly symmetric than those of the Gaussian. In a contribution to the network autoregressive process, the GNAR process with Student-t random noise generalization should always be favored over Gaussian random noise because of its ability to absolve contaminations, spread, and ability to contain time-varying network measurements.

Abstract Conventional δ‐generalised labelled multi‐Bernoulli filter (δ‐GLMB) cannot deal with the problem of the heavy‐tailed process noise and measurement noise. In order to solve this problem, an adaptive δ‐GLMB approach based on minimising Kullback‐Leibler Divergence (KLD) is proposed in this study. The inverse wishart and Student‐t mixture is used to approximate the joint posterior distribution of process noise covariance and measurement noise covariance together with multi‐target state, and the multi‐target state and noise parameters are jointly estimated by minimising the KLD. The simulation results show that the proposed approach is robust to multi‐target tracking for condition with heavy‐tailed process noise covariance and measurement noise covariance. Accurate target number and target state estimation are obtained by effectively estimating the process noise covariance and measurement noise covariance.

The paper summarizes the design and implementation of a passenger traffic prediction model, based on Gaussian Process Regression (GPR). Passenger traffic analysis is the present day requirement for proper bus scheduling and traffic management to improve the efficiency and passenger comfort. Bayesian analysis uses statistical modelling to recursively estimate new data from existing data. GPR is a fully Bayesian process model, which is developed using PyMC3 with Theano as backend. The passenger data is modelled as a Poisson process so that the prior for designing the GP regression model is a Gamma distributed function. It is observed that the proposed GP based regression method outperforms the existing methods like Student-t process model and Kernel Ridge Regression (KRR) process. [ABSTRACT FROM AUTHOR]

GARCH-X(1, 1) model specifies that conditional variance follows an AR(1) process and includes a past exogenous variable. This study proposes a new class from that model by allowing a more general (non-linear) variance function to follow an AR(1) process. The functions applied to the variance equation include exponential, Tukey’s ladder, and Yeo–Johnson transformations. In the framework of normal and student-t distributions for return errors, the empirical analysis focuses on two stock indices data in developed countries (FTSE100 and SP500) over the daily period from January 2000 to December 2020. This study uses 10-minute realized volatility as the exogenous component. The parameters of considered models are estimated using the adaptive random walk metropolis method in the Monte Carlo Markov chain algorithm and implemented in the Matlab program. The 95% highest posterior density intervals show that the three transformations are significant for the GARCHX(1, 1) model. In general, based on the Akaike information criterion, the GARCH-X(1, 1) model that has return errors with student-t distribution and variance transformed by Tukey’s ladder function provides the best data fit. In forecasting value-at-risk with the 95% confidence level, the Christoffersen’s independence test suggest that non-linear models is the most suitable for modeling return data, especially model with the Tukey’s ladder transformation. [ABSTRACT FROM AUTHOR]

Conventional δ‐generalised labelled multi‐Bernoulli filter (δ‐GLMB) cannot deal with the problem of the heavy‐tailed process noise and measurement noise. In order to solve this problem, an adaptive δ‐GLMB approach based on minimising Kullback‐Leibler Divergence (KLD) is proposed in this study. The inverse wishart and Student‐t mixture is used to approximate the joint posterior distribution of process noise covariance and measurement noise covariance together with multi‐target state, and the multi‐target state and noise parameters are jointly estimated by minimising the KLD. The simulation results show that the proposed approach is robust to multi‐target tracking for condition with heavy‐tailed process noise covariance and measurement noise covariance. Accurate target number and target state estimation are obtained by effectively estimating the process noise covariance and measurement noise covariance. [ABSTRACT FROM AUTHOR]

Numerous variants of the basic Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have been proposed to provide good volatility estimating and forecasting. Most of the study does not work Excel’s Solver to estimate GARCH-type models. The first purpose of this study is to provide the capability analyze of the GRG non-linear method built in Excel’s Solver to estimate the GARCH models in comparison to the adaptive random walk Metropolis method in Matlab by own codes. The second contribution of this study is to evaluate some characteristics and performance of the GARCH-M(1,1), GJR(1,1), and log-GARCH(1,1) models with Normal and Student-t error distributions that fitted to financial data. Empirical analyze is based on the application of models and methods to the DJIA, S&P500, and S&P CNX Nifty stock indices. The first empirical result showed that Excel’s Solver’s Generalized Reduced Gradient (GRG) non-linear method has capability to estimate the econometric models. Second, the GJR(1,1) models provide the best fitting, followed by the GARCH-M(1,1), GARCH(1,1), and log-GARCH(1,1) models. This study concludes that Excel’s Solver’s GRG non-linear can be recommended to the practitioners that do not have enough knowledge in the programming language in order to estimate the econometrics models. It also suggests to incorporate a risk premium in the return equation and an asymmetric effect in the variance equation.

Investors are becoming more sensitive about returns and losses, especially when the investments are exposed to downside risk potential in the financial markets. Despite the computational intensity of the downside risk measures, they are very widely applied to construct a portfolio and evaluate performance in terms of the investors’ loss aversion. Value-at-risk (VaR) has emerged as an industry standard to analyze the market downside risk potential. The approaches used to measure VaR vary from the standard approaches to more recently introduced highly sophisticated volatility models. In this paper, the standard approaches (student-t-distribution, log normal, historical simulation) and sophisticated volatility models (EWMA, GARCH (1,1)) both have been used to estimate the VaR of mutual funds in the Saudi Stock Exchange between June 2017 and June 2020. The VaR approaches have been subjected to conditional coverage backtest to identify the model that is the best at predicting VaR. The empirical coverage probability of the models reveals that EWMA was able to capture VaR better than the other models at a higher significance level followed by GARCH (1,1).

The research had two objectives. First, it compared the performance of the Generalized Autoregressive Conditional Heteroscedasticity (1,1) (GARCH) and Quadratic GARCH (1,1) (QGARCH)) models based on the fitting to real data sets. The model assumed that return error follows four different distributions: Normal (Gaussian), Student-t, General Error Distribution (GED), and Skew GED (SGED). Maximum likelihood estimation was usually employed in estimating the GARCH model, but it might not be easily applied to more complicated ones. Second, it provided two ways to evaluate the considered models. The models were estimated using the Generalized Reduced Gradient (GRG) Non-Linear method in Excel’s Solver and the Adaptive Random Walk Metropolis (ARWM) in the Scilab program. The real data in the empirical study were Financial Times Stock Exchange Milano Italia Borsa (FTSEMIB) and Stoxx Europe 600 indices over the daily period from January 2000 to December 2017 to test the conditional variance process and see whether the estimation methods could adapt to the complicated models. The analysis shows that GRG Non-Linear in Excel’s Solver and ARWM methods have close results. It indicates a good estimation ability. Based on the Akaike Information Criterion (AIC), the QGARCH(1,1) model provides a better fitting than the GARCH(1,1) model on each distribution specification. Overall, the QGARCH(1,1) with SGED distribution best fits both data.

Investors are becoming more sensitive about returns and losses, especially when the investments are exposed to downside risk potential in the financial markets. Despite the computational intensity of the downside risk measures, they are very widely applied to construct a portfolio and evaluate performance in terms of the investors' loss aversion. Value-at-risk (VaR) has emerged as an industry standard to analyze the market downside risk potential. The approaches used to measure VaR vary from the standard approaches to more recently introduced highly sophisticated volatility models. In this paper, the standard approaches (student-t-distribution, log normal, historical simulation) and sophisticated volatility models (EWMA, GARCH (1,1)) both have been used to estimate the VaR of mutual funds in the Saudi Stock Exchange between June 2017 and June 2020. The VaR approaches have been subjected to conditional coverage backtest to identify the model that is the best at predicting VaR. The empirical coverage probability of the models reveals that EWMA was able to capture VaR better than the other models at a higher significance level followed by GARCH (1,1). [ABSTRACT FROM AUTHOR]

Cardiac disease is one of the major causes for death all over the world. Heart rate variability (HRV) is a significant parameter that used in assessing Autonomous Nervous System (ANS) activity. Generally, the 2D Poincare′ plot and 3D Poincaré plot of the HRV signals reflect the effect of different external stimuli on the ANS. Meditation is one of such external stimulus, which has different techniques with different types of effects on the ANS. Chinese Chi-meditation and Kundalini yoga are two different effective meditation techniques. The current work is interested with the analysis of the HRV signals under the effect of these two based on meditation techniques. The 2D and 3D Poincare′ plots are generally plotted by fitting respectively an ellipse/ellipsoid to the dense region of the constructed Poincare′ plot of HRV signals. However, the 2D and 3D Poincaré plots sometimes fail to describe the proper behaviour of the system. Thus in this study, a three-dimensional frequency-delay plot is proposed to properly distinguish these two famous meditation techniques by analyzing their effects on ANS. This proposed 3D frequency-delay plot is applied on HRV signals of eight persons practicing same Chi-meditation and four other persons practising same Kundalini yoga. To substantiate the result for larger sample of data, statistical Student t-test is applied, which shows a satisfactory result in this context. The experimental results established that the Chi-meditation has large impact on the HRVcompared to the Kundalini yoga.

Monte Carlo (MC) techniques are widely applied to check a design on its robustness and for estimating the production yield of integrated circuits. Using standard random MC and the sample yield for estimation, a very large number of samples is required for accurate verification, especially if a high yield is desired. This can make MC extremely time consuming, but if the data follows a normal Gaussian distribution a much faster yield prediction is possible by using the well-known C\text {PK} method. We extended this specification-distance-based scheme for the far more difficult general non-normal case by three different means, ending up in a new generalized process capability index named C\text {GPK} . First, we apply parametric modeling only to the specification-sided distribution part. This way any difficulties in distribution parts that actually have little yield impact do not degrade the model fit anymore. Second, to improve the parametric model we introduce a new tail parameter t . Third, to allow modeling of difficult asymmetrical, multimodal or flat distributions we also introduce a new reference location parameter instead of using the mean. An advantage of improving MC this way is that—in opposite to many other MC enhancements (like importance sampling)—the performance of the C\text {GPK} is not negatively impacted by design complexity. We described the formulation of the C\text {GPK} and derived confidence intervals using an advanced bootstrap scheme. We verified the performance against the sample yield and C\text {PK} for a representative set of distributions, including real production data and MC data from the design of a CMOS operational amplifier and other circuits. [ABSTRACT FROM AUTHOR]

The application of stochastic volatility (SV) models in the option pricing literature usually assumes that the market has sufficient option data to calibrate the model’s risk-neutral parameters. When option data are insufficient or unavailable, market practitioners must estimate the model from the historical returns of the underlying asset and then transform the resulting model into its risk-neutral equivalent. However, the likelihood function of an SV model can only be expressed in a high-dimensional integration, which makes the estimation a highly challenging task. The Bayesian approach has been the classical way to estimate SV models under the data-generating (physical) probability measure, but the transformation from the estimated physical dynamic into its risk-neutral counterpart has not been addressed. Inspired by the generalized autoregressive conditional heteroskedasticity (GARCH) option pricing approach by Duan in 1995, we propose an SV model that enables us to simultaneously and conveniently perform Bayesian inference and transformation into risk-neutral dynamics. Our model relaxes the normality assumption on innovations of both return and volatility processes, and our empirical study shows that the estimated option prices generate realistic implied volatility smile shapes. In addition, the volatility premium is almost flat across strike prices, so adding a few option data to the historical time series of the underlying asset can greatly improve the estimation of option prices.

There is a dramatically increase in institutional investors ownership of Chinese stock market from 2003. In this paper, we improve the MS-GARCH model to analyze the daily returns data, and provide empirical evidence on the impact of sub-owned shares reform and institutional investors in stock market. We find that Chinese stock market transform form low volatility state to high volatility state after the sub-owned shares reform. The results also prove that different funds have vary effects on the volatility of the stock market, and the adjusting of interest rate and reserve ratio could also affect the the volatility of the stock market. According to the comparison between two models, MS-GARCH model is much better than single-regime GARCH model in goodness-of-fit and forecasting performance. [ABSTRACT FROM AUTHOR]

This paper examines local influence assessment in generalized autoregressive conditional heteroscesdasticity models with Gaussian and Student-t errors, where influence is examined via the likelihood displacement. The analysis of local influence is discussed under three perturbation schemes: data perturbation, innovative model perturbation and additive model perturbation. For each case, expressions for slope and curvature diagnostics are derived. Monte Carlo experiments are presented to determine the threshold values for locating influential observations. The empirical study of daily returns of the New York Stock Exchange composite index shows that local influence analysis is a useful technique for detecting influential observations; most of the observations detected as influential are associated with historical shocks in the market. Finally, based on this empirical study and the analysis of simulated data, some advice is given on how to use the discussed methodology. [ABSTRACT FROM PUBLISHER]

We present a quasi-analytic perturbation expansion for multivariate N-dimensional Gaussian integrals. The perturbation expansion is an infinite series of lower-dimensional integrals (one-dimensional in the simplest approximation). This perturbative idea can also be applied to multivariate Student-t integrals. We evaluate the perturbation expansion explicitly through 2nd order, and discuss the convergence, including enhancement using Padé approximants. Brief comments on potential applications in finance are given, including options, models for credit risk and derivatives, and correlation sensitivities. [ABSTRACT FROM AUTHOR]