Search Results

Finite mixture modeling of censored data using the multivariate Student-t distribution,
Víctor H. Lachos, Edgar J. López Moreno, Kun Chen and Celso Rômulo Barbosa Cabral, in Journal of Multivariate Analysis (2017)
Keywords: Censored data; Detection limit; EM-type algorithms; Finite mixture models; Multivariate Student-t;

Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices,
Eckhard Platen and Renata Rendek, from Quantitative Finance Research Centre, University of Technology, Sydney (2007)
Keywords: diversified world stock index; growth optimal portfolio; log-return distribution; Student-t distribution; generalized hyperbolic distribution; likelihood ratio test

Forecasting volatility under fractality, regime-switching, long memory and student-t innovations,
Thomas Lux and Leonardo Morales-Arias, from Kiel Institute for the World Economy (IfW Kiel) (2009)
Keywords: Multiplicative volatility models, long memory, Student-t innovations, international volatility forecasting

Forecasting volatility under fractality, regime-switching, long memory and student-t innovations,
Thomas Lux and Leonardo Morales-Arias, in Computational Statistics & Data Analysis (2010)
Keywords: Multiplicative volatility models Long memory Student-t innovations International volatility forecasting

Local influence in null intercept measurement error regression under a student_t model,
Filidor Labra, Reiko Aoki and Heleno Bolfarine, in Journal of Applied Statistics (2005)
Keywords: Influence diagnostic, student_t model, likelihood displacement, pretest/post-test data, measurement error models,

A Skewed Student-t Value-at-Risk Approach for Long Memory Volatility Processes in Japanese Financial Markets,
Seong-Min Yoon and Sang-Hoon Kang, in East Asian Economic Review (2007)
Keywords: Value-at-Risk; Japanese Financial Markets; Volatility; Asymmetry; Long Memory; Skewed Student-t Distribution

Preliminary test Liu estimators based on the conflicting W, LR and LM tests in a regression model with multivariate Student-t error,
Hu Yang and Jianwen Xu, in Metrika: International Journal for Theoretical and Applied Statistics (2011)
Keywords: Preliminary test estimator, Liu estimator, Multivariate Student-t , Mean square error,

Adaptive Mixture of Student-t distributions as a Flexible Candidate Distribution for Efficient Simulation: the R Package AdMit,
David Ardia, Lennart F. Hoogerheide and Herman van Dijk, from Tinbergen Institute (2008)
Keywords: adaptive mixture; Student-t distributions; importance sampling; independence chain Metropolis-Hasting algorithm; Bayesian; R software

RATS programs to replicate Hansen's GARCH models with time-varying t-densities,
Tom Doan, from Boston College Department of Economics
Keywords: ARCH-GARCH with student-t errors

The R Package MitISEM: Mixture of Student-t Distributions using Importance Sampling Weighted Expectation Maximization for Efficient and Robust Simulation,
Nalan Baştürk, Lennart Hoogerheide, Anne Opschoor and Herman van Dijk, from Tinbergen Institute (2012)
Keywords: finite mixtures, Student-t distributions, Importance Sampling, MCMC, Metropolis-Hastings algorithm, Expectation Maximization, Bayesian inference, R software

Maximum likelihood estimation of high-dimensional Student-t copulas,
Mark Trede, in Statistics & Probability Letters (2020)
Keywords: Student t-copula; Maximum likelihood estimation; Iterative algorithm;

A new representation of Student's t as a function of independent t's, with a generalization to the matrix t,
James M. Dickey, in Journal of Multivariate Analysis (1976)
Keywords: Student's t matrix t inference

From Skews to a Skewed-t,
Cyriel de Jong and Ronald Huisman, from Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam (2000)
Keywords: implied distribution, implied volatility, options, skewness, student-t

Latent Autoregressive Student- t Prior Process Models to Assess Impact of Interventions in Time Series,
Patrick Toman, Nalini Ravishanker, Nathan Lally and Sanguthevar Rajasekaran, in Future Internet (2023)
Keywords: Gaussian process regression; Student-t process; impact of interventions; IoT sensor data; time series analysis; variational inference

An expectation maximization algorithm for the hidden markov models with multiparameter student-t observations,
Emna Ghorbel and Mahdi Louati, in Computational Statistics (2024)
Keywords: Hidden markov models, Expectation maximization algorithm, Forward-backward programming algorithm, Multiparameter t’distribution, Wishart distribution, Riesz distribution

Confidence intervals for the power of Student's t-test,
Joanna Tarasinska, in Statistics & Probability Letters (2005)
Keywords: Student's t-test Power of the test Confidence interval

Describing n-day returns with Student’s t-distributions,
Daniel T. Cassidy, in Physica A: Statistical Mechanics and its Applications (2011)
Keywords: Student’s t-distribution; Truncation; Self-convolution; European options;

A mixture autoregressive model based on Student’s t–distribution,
Mika Meitz, Daniel Preve and Pentti Saikkonen, from City University of Hong Kong, Department of Economics and Finance, Global Research Unit (2018)
Keywords: Conditional heteroskedasticity; mixture model; regime switching; Student’s t–distribution

Exact Distribution of the Product of N Student’s t RVs,
Saralees Nadarajah, in Methodology and Computing in Applied Probability (2012)
Keywords: Meijer G function, Product of random variables, Student’s t distribution

On the Lp-quantiles for the Student t distribution,
Mauro Bernardi, Valeria Bignozzi and Lea Petrella, in Statistics & Probability Letters (2017)
Keywords: Generalised quantiles; Expectiles; Quantiles; Truncated moments; Student t distribution;

Application of Generalized Student’s T-Distribution In Modeling The Distribution of Empirical Return Rates on Selected Stock Exchange Indexes,
Purczyńskiz Jan and Bednarz-Okrzyńska Kamila, in Folia Oeconomica Stetinensia (2014)
Keywords: Student’s t-distribution, generalized Student’s t-distribution, stimation of distribution parameters

Computing percentage points of the largest among Student's t random variables,
Nadarajah Saralees, in Monte Carlo Methods and Applications (2008)
Keywords: Student's t distribution, multivariate normal distribution, multivariate t distribution, R

The product t density distribution arising from the product of two Student’s t PDFs,
Saralees Nadarajah, in Statistical Papers (2009)
Keywords: Bayesian statistics, Decision sciences, Physics, Product t density distribution, Student’s t distribution,

On the density of the sum of two independent Student t-random vectors,
C. Berg and C. Vignat, in Statistics & Probability Letters (2010)
Keywords: Student t-distributions Convolution Infinite divisibility

A generalized class of estimators in linear regression models with multivariate-t distributed error,
R. Karan Singh, Sheela Misra and S. K. Pandey, in Statistics & Probability Letters (1995)
Keywords: Linear regression model Multivariate Student-t distribution Generalized dominance condition Bias and risk

On the characteristic function for asymmetric Student t distributions,
Saralees Nadarajah, Stephen Chan and Emmanuel Afuecheta, in Economics Letters (2013)
Keywords: Asymmetric Student t distribution; Characteristic function; Hypergeometric function;

Skewed distributions generated by the Student's t kernel,
Nadarajah Saralees, in Monte Carlo Methods and Applications (2008)
Keywords: Characteristic function, moments, Student's t distribution, skewed distributions

A hybrid approach based on the Gaussian process with t-observation model for short-term wind speed forecasts,
Jianming Hu, Jianzhou Wang and Liqun Xiao, in Renewable Energy (2017)
Keywords: Gaussian process regression with the Student-t observation model; Expectation propagation (EP) algorithm; Wind speed forecasting;

DSGE-SVt: An Econometric Toolkit for High-Dimensional DSGE Models with SV and t Errors,
Siddhartha Chib, Minchul Shin and Fei Tan, in Computational Economics (2023)
Keywords: DSGE models, Bayesian inference, Marginal likelihood, Tailored proposal densities, Random blocks, Student-t shocks, Stochastic volatility

DSGE-SVt: An Econometric Toolkit for High-Dimensional DSGE Models with SV and t Errors,
Siddhartha Chib, Minchul Shin and Fei Tan, from Federal Reserve Bank of Philadelphia (2021)
Keywords: Bayesian inference; Marginal likelihood; Tailored proposal densities; Random blocks; Student-t shocks; Stochastic volatility.

The Distribution of Cross Sectional Momentum Returns When Underlying Asset Returns Are Student’s t Distributed,
Oh Kang Kwon and Stephen Satchell, in JRFM (2020)
Keywords: cross sectional momentum; student’s t distribution; investment strategy

On the T-test,
S.Y. Novak, in Statistics & Probability Letters (2022)
Keywords: Hypothesis testing; T-test; Student’s statistic;

TPLVM: Portfolio Construction by Student’s t -Process Latent Variable Model,
Yusuke Uchiyama and Kei Nakagawa, in Mathematics (2020)
Keywords: student’s t-process; latent variable model; factor model; Portfolio theory; global stock markets

Pricing European options with a log Student’s t-distribution: A Gosset formula,
Daniel T. Cassidy, Michael J. Hamp and Rachid Ouyed, in Physica A: Statistical Mechanics and its Applications (2010)
Keywords: Econophysics; Financial risk; European options; Fat-tailed distributions; Student’s t-distribution;

Student’s t mixture models for stock indices. A comparative study,
Till Massing and Arturo Ramos, in Physica A: Statistical Mechanics and its Applications (2021)
Keywords: Stock index returns; Goodness-of-fit; Student’s t distribution; Mixture distributions;

On Asymptotic and Strict Monotonicity of a Sharper Lower Bound for Student’s t Percentiles,
Allan Gut and Nitis Mukhopadhyay, in Methodology and Computing in Applied Probability (2010)
Keywords: Asymptotic monotonicity, Gamma function, Percentiles, Standard normal, Strict monotonicity, Student’s t-distribution

Modeling and forecasting exchange rate volatility in Bangladesh using GARCH models: a comparison based on normal and Student’s t-error distribution,
S. M. Abdullah, Salina Siddiqua, Muhammad Shahadat Hossain Siddiquee and Nazmul Hossain, in Financial Innovation (2017)
Keywords: Exchange rate, Volatility, ARCH, GARCH, Student’s t, Error distribution

Bivariate Student t distributions with variable marginal degrees of freedom and independence,
W.T. Shaw and K.T.A. Lee, in Journal of Multivariate Analysis (2008)
Keywords: Bivariate Student Correlation Degrees of freedom Dependence Independence Multivariate Student Student distribution t distribution.

Welch’s t test is more sensitive to real world violations of distributional assumptions than student’s t test but logistic regression is more robust than either,
David Curtis, in Statistical Papers (2024)
Keywords: Welch’s t test, Student’s t test, Likelihood ratio test, Logistic regression, Psoriasis

A tail quantile approximation formula for the student t and the symmetric generalized hyperbolic distribution,
Stephan Schlüter and Matthias J. Fischer, from Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics (2009)
Keywords: Generalized hyperbolic distribution, Quantile approximation, Student t distribution

Student's t- and r-distributions: Unified derivation from an entropic variational principle,
AndréM.C. de Souza and Constantino Tsallis, in Physica A: Statistical Mechanics and its Applications (1997)
Keywords: Generalized entropy; Viriational principle; Student's t-distribution; r-distribution;

Note: t for Two (Clusters),
Stanley L. Sclove, in Journal of Classification (2019)
Keywords: Cluster analysis, Student’s t, Unequal variances

Robust stochastic frontier analysis: a Student’s t-half normal model with application to highway maintenance costs in England,
Phill Wheat, Alexander Stead and William Greene, in Journal of Productivity Analysis (2019)
Keywords: Stochastic frontier analysis, Robust analysis, Student's t, Outliers, Wrong Kurtosis

Dirichlet Process Prior for Student’s t Graph Variational Autoencoders,
Yuexuan Zhao and Jing Huang, in Future Internet (2021)
Keywords: neural network; Bayesian nonparametric; Graph variational auto-encoder; Student’s t distribution; Dirichlet process; network representation learning

On a Sharper Lower Bound for a Percentile of a Student’s t Distribution with an Application,
Nitis Mukhopadhyay, in Methodology and Computing in Applied Probability (2010)
Keywords: Average sample size, Central t-distribution, Compare percentiles, Confidence intervals, Diagnostics, Fixed-width confidence intervals, Jensen’s inequality, Non-central t-distribution, Oversampling percentage, Pilot sample size, Simulations, Standard normal, Student’s t-distribution, Two-stage sampling

Modelling income distribution using the log Student’s t distribution: New evidence for European Union countries,
Francisco Javier Callealta Barroso, Carmelo García-Pérez and Mercedes Prieto-Alaiz, in Economic Modelling (2020)
Keywords: Log Student’s t distribution; Parametric modelling; Income distribution; EU countries;

On the linear combination of the Gaussian and student’s t random field and the integral geometry of its excursion sets,
Ola Ahmad and Jean-Charles Pinoli, in Statistics & Probability Letters (2013)
Keywords: Gaussian random field; Student’s t random field; Excursion sets; Minkowski functionals; Euler–Poincaré characteristic;

From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t -Distribution Case,
Julia Adamska, Łukasz Bielak, Joanna Janczura and Agnieszka Wyłomańska, in Mathematics (2022)
Keywords: multivariate random variables; product; Pareto distribution; Student’s t distribution; heavy tails; transaction value; electricity

Bayesian student-t,
S.T. Boris Choy, Wai-yin Wan and Chun-man Chan, from Emerald Group Publishing Limited (2008)

Spillover Risks on Cryptocurrency Markets: A Look from VAR-SVAR Granger Causality and Student’s-t Copulas,
Toan Luu Duc Huynh, in JRFM (2019)
Keywords: Bitcoin; cryptocurrency; spillover risks; Copulas; Student’s-t

Modeling cryptocurrencies volatility using GARCH models: a comparison based on Normal and Student's T-Error distribution,
Shazia Salamat, Niu Lixia, Sobia Naseem, Muhammad Mohsin, Muhammad Zia-ur-Rehman and Sajjad Ahmad Baig, in Entrepreneurship and Sustainability Issues (2020)
Keywords: cryptocurrency, GARCH models, normal distribution, student's T distribution

A two-regime threshold model with conditional skewed Student t distributions for stock returns,
Daniele Massacci, in Economic Modelling (2014)
Keywords: Threshold model; Skewed Student t distribution; Stock returns; Value at risk;

A VaR assuming Student t distribution not significantly different from a VaR assuming normal distribution,
Su Xu, in Risk Management (2017)
Keywords: VaR, Student t distribution, Normal distribution, Adjustment factor, Sigma threshold

The evaluation of college students' entrepreneurship education performance using the t-test method,
Naiqi Chen and Yumei Wu, in International Journal of Data Science (2024)
Keywords: entrepreneurship education; T-test method; analytical hierarchy process; college students; education performance.

Spearman rank correlation of the bivariate Student t and scale mixtures of normal distributions,
Andréas Heinen and Alfonso Valdesogo Robles, in Journal of Multivariate Analysis (2020)
Keywords: Rank correlation; Rank-based estimation; Scale mixture of normals; Student t; Spearman’s rho;

The Odd Log-Logistic Student t Distribution: Theory and Applications,
Altemir Silva Braga, Gauss M. Cordeiro, Edwin M. M. Ortega and Giovana O. Silva, in Journal of Agricultural, Biological and Environmental Statistics (2017)
Keywords: Log-logistic distribution, Maximum likelihood estimation, Moment, Regression model, Student t distribution

Student’s-t process with spatial deformation for spatio-temporal data,
Fidel Ernesto Castro Morales, Dimitris N. Politis, Jacek Leskow and Marina Silva Paez, in Statistical Methods & Applications (2022)
Keywords: Student’s-t process, Spatio-temporal modeling, Spatial deformation, Markov Chain Monte Carlo, Heavy tails

A generalised Student’s t-distribution,
Ioannis Papastathopoulos and Jonathan A. Tawn, in Statistics & Probability Letters (2013)
Keywords: Generalised t-distribution; Symmetric short-tailed; Shape parameter; Liver toxicity;

Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student’s t-distribution,
Jouchi Nakajima and Yasuhiro Omori, in Computational Statistics & Data Analysis (2012)
Keywords: Generalized hyperbolic skew Student’s t-distribution; Markov chain Monte Carlo; Mixing distribution; State space model; Stochastic volatility; Stock returns;

Preliminary test ridge regression estimators with student’s t errors and conflicting test-statistics,
B. M. Golam Kibria and A. K. Md. E. Saleh, in Metrika: International Journal for Theoretical and Applied Statistics (2004)
Keywords: Dominance, Lagrangian Multiplier, Likelihood Ratio Test, MSE, Ridge Regression, Students t , Superiority, Wald Test, 62J07, 62F03,

Bayesian Estimation of a Skew-Student-t Stochastic Volatility Model,
C. A. Abanto-Valle, V. H. Lachos and Dipak K. Dey, in Methodology and Computing in Applied Probability (2015)
Keywords: Markov chain Monte Carlo, Non-Gaussian and nonlinear state space models, Skew-Student-t, Stochastic volatility, Value-at-risk

Self-normalized deviation inequalities with application to t-statistic,
Xiequan Fan, in Statistics & Probability Letters (2017)
Keywords: Self-normalized deviations; Student’s t-statistic; Exponential inequalities;

A dependent bivariate t distribution with marginals on different degrees of freedom,
M. C. Jones, in Statistics & Probability Letters (2002)
Keywords: Bivariate distribution Spherical symmetry Student's t distribution

Multivariate measurement error models using finite mixtures of skew-Student t distributions,
Celso Rômulo Barbosa Cabral, Víctor Hugo Lachos and Camila Borelli Zeller, in Journal of Multivariate Analysis (2014)
Keywords: Measurement error model; Finite mixtures; EM algorithm; Skew-normal distribution; Skew-Student t distribution; Comparative calibration;

Testing densities with financial data: an empirical comparison of the Edgeworth-Sargan density to the Student's t,
Ignacio Mauleón and Javier Perote, in The European Journal of Finance (2000)
Keywords: Densities Comparison Edgeworth-SARGAN Student T Distributions Financial Data Testing Moment Existence,

Bayesian Analysis of Student t Linear Regression with Unknown Change-Point and Application to Stock Data Analysis,
Jin-Guan Lin, Ji Chen and Yong Li, in Computational Economics (2012)
Keywords: Bayesian method, Student t regression model, Variance change-point, Gibbs sampler,

Sample Kurtosis, GARCH-t and the Degrees of Freedom Issue,
Maria S. Heracleous, from European University Institute (2007)
Keywords: Student’s t distribution, Degree of freedom, Kurtosis coefficient, GARCH t model

GRAN2: Gauss procedure to generate t-distributed random numbers,
Carlos Urzúa, from Tecnológico de Monterrey, Campus Ciudad de México (2007)
Keywords: t distribution, Student's t random numbers, pseudo-random numbers, t variates, GAUSS

A simple and trustworthy asymptotic t test in difference-in-differences regressions,
Cheng Liu and Yixiao Sun, in Journal of Econometrics (2019)
Keywords: Basis functions; Difference-in-differences; Fixed-smoothing asymptotics; Heteroscedasticity and autocorrelation; Student’s t distribution; t test;

Beta-t-(E)GARCH,
Andrew Harvey and Tirthankar Chakravarty, from Faculty of Economics, University of Cambridge (2008)
Keywords: Conditional heteroskedasticity; leverage; robustness; score; Student's t; volatility.

A curious property of the derivatives of the Cauchy density,
Peter Hall, J. Steven Marron and D. M. Titterington, in Statistics & Probability Letters (1996)
Keywords: Cauchy quantiles Decagon Density estimation Student-t

On the Marshall–Olkin transformation as a skewing mechanism,
F.J. Rubio and Mark Steel, in Computational Statistics & Data Analysis (2012)
Keywords: Moment; Skewness measure; Student-t; Tail behaviour;

Variational inference for Bayesian panel VAR models,
Lucas Ter Steege, from European Central Bank (2024)
Keywords: panel-VAR, student-t distribution, variational Bayes

Stochastic Volatility Model with Leverage and Asymmetrically Heavy-tailed Error Using GH Skew Student's t-distribution,
Jouchi Nakajima and Yasuhiro Omori, from Institute of Economic Research, Hitotsubashi University (2010)
Keywords: generalized hyperbolic skew Student's t-distribution, Markov chain Monte Carlo, Mixing distribution, State space model, Stochastic volatility, Stock returns

On the sum of t and Gaussian random variables,
Guy P. Nason, in Statistics & Probability Letters (2006)
Keywords: Sum of Gaussian and Student's t Characteristic function Wavelet shrinkage Error function

Un modelo Tgarch con una distribución t de student asimétrica y las hipótesis de racionalidad de los inversionistas bursátiles en Latinoamérica,
Arturo Lorenzo Valdés and Antonio Ruiz-Porras, in Archivos Revista Economía y Política. (2014)
Keywords: Distribución de Densidad, t de Student Asimétrica, TGARCH, Rendimientos Bursátiles, Latinoamérica.

Un modelo TGARCH con una distribución t de Student asimétrica y las hipotesis de racionalidad de los inversionistas bursátiles en Latinoamérica,
Arturo Lorenzo-Valdes and Antonio Ruiz-Porras, from University Library of Munich, Germany (2014)
Keywords: Density Distribution; Asymmetric t-Student; TGARCH; Stock Market Returns; Latin America

Efficient recursive computational algorithms for multivariate t and multivariate unified skew-t distributions with applications to inference,
Mehdi Amiri, Yaser Mehrali, Narayanaswamy Balakrishnan and Ahad Jamalizadeh, in Computational Statistics (2022)
Keywords: Hazard function, Multivariate Student’s t distribution, Multivariate unified skew-t distribution, Orthant probability, Order statistics, Recurrence relation

Minimal Variance Hedging of Options with Student-t Underlying,
K. Pinn, from arXiv.org (1999)

Bayesian Inference in the Non-Central Student-T Model,
E.G. Tsionas, from Athens University of Economics and Business (2000)
Keywords: ECONOMIC MODELS ; STATISTICS

Minimal variance hedging of options with student-t underlying,
Klaus Pinn, in Physica A: Statistical Mechanics and its Applications (2000)

Predictivistic characterizations of multivariate student-t models,
Rosangela H. Loschi, Pilar L. Iglesias and Reinaldo B. Arellano-Valle, in Journal of Multivariate Analysis (2003)
Keywords: Invariant distributions Conjugate prior distributions Pearson type II distribution de Finetti style theorems

Theoretical properties of Bayesian Student-t linear regression,
Philippe Gagnon and Yoshiko Hayashi, in Statistics & Probability Letters (2023)
Keywords: Built-in robustness; Conflict resolution; Efficiency; Large-sample asymptotics;

Bayesian Inference in the Non-Central Student-T Model,
Mike Tsionas, from Athens University of Economics and Business, Department of International and European Economic Studies (2000)
Keywords: ECONOMIC MODELS ; STATISTICS

Objective Bayesian analysis for the Student-t regression model,
T. C. O. Fonseca, M. A. R. Ferreira and H. S. Migon, in Biometrika (2014)

Objective Bayesian analysis for the Student-t regression model,
Thaís C. O. Fonseca, Marco A. R. Ferreira and Helio S. Migon, in Biometrika (2008)

Modelling Oil Price Volatility with the Beta-Skew-t-EGARCH Framework,
Afees Salisu, in Economics Bulletin (2016)
Keywords: Oil price; Volatility; Student's t; Skewness; Leverage; Persistence

Scaling of Lévy–Student processes,
Oliver Grothe and Rafael Schmidt, in Physica A: Statistical Mechanics and its Applications (2010)
Keywords: Student’s t-distributions; Lévy processes; Convolutions; High-frequency asset returns;

Influence assessment in censored mixed-effects models using the multivariate Student’s-t distribution,
Larissa A. Matos, Dipankar Bandyopadhyay, Luis M. Castro and Victor H. Lachos, in Journal of Multivariate Analysis (2015)
Keywords: Censored data; Case-deletion diagnostics; ECM algorithm; Linear mixed-effects model; Multivariate Student’s-t distribution; Non-linear mixed-effects model;

Extreme co-movements and dependencies in volatility of exchange rate among US dollar and emerging currencies: a GAS-GARCH-student-t model,
Aida Sy, Abdelkader Derbali and Manel Ben Ayeche, in African Journal of Accounting, Auditing and Finance (2015)
Keywords: GAS-GARCH-student-t model; exchange rates; US dollar; emerging currencies; extreme co-movements; extreme dependencies; exchange rate volatility; conditional heteroscedasticity; emerging economies.