J. Onyeka-Ubaka - Academia.edu (original) (raw)

Papers by J. Onyeka-Ubaka

Tanzania Journal of Science

A generalized student t distribution technique based on estimation of bilinear generalized autore... more A generalized student t distribution technique based on estimation of bilinear generalized autoregressive conditional heteroskedasticity (BL-GARCH) model is introduced. The paper investigates from empirical perspective, aspects of the model related to the economic and financial risk management and its impacts on volatility forecasting. The purposive sampling technique was applied to select four banks for the study, namely First Bank of Nigeria (FBN), Guaranty Trust Bank (GTB), United Bank for Africa (UBA) and Zenith Bank (ZEB). The four banks are selected, because their daily stock prices are considered to be more susceptible to volatility than those of other banks within the sampled period (January 2007–May 2022). The data collected were analyzed using MATLAB R2008b Software. The results show that the newly introduced generalized student t distribution is the most general of all the useful distributions applied in the BL-GARCH model parameter estimation. It serves as a general dist...

Calcutta Statistical Association Bulletin, 2006

We thoroughly study a very important family of nonlinear timeseries models, viz. Self exciting th... more We thoroughly study a very important family of nonlinear timeseries models, viz. Self exciting threshold autoregressive (SETAR) types of models. A heartening feature of this family is that it is capable of describing cyclical data. As an illustration, SETAR models are then applied to country's lac export data during the period 1900-2000, obtained from Annual reports of Shellac Export Promotion Council, Kolkata. It is shown that fitted model, based on minimum Akaike information criterion (AIC), exhibits a threshold behaviour. Finally, attempts are made to obtain optimal predictor for out-of-sample data based on fitted SETAR model, which is found to be quite satisfactory.

Bayesian GARCH models for Nigeria Covid-19 data

Annals of Mathematics and Computer Science, Dec 2, 2021

Afrika Statistika, 2021

For the first time, a location-scale regression model based on the logarithm of an extended Ralei... more For the first time, a location-scale regression model based on the logarithm of an extended Raleigh Lomax distribution which has the ability to deal and model of any survival data than classical regression model is introduced. We obtain the estimate for the model parameters using the method of maximum likelihood by considering breast cancer data. In addition, normal probability plot of the residual is used to detect the outliers and evaluate model assumptions. We use a real data set to illustrate the performance of the new model, some of its submodels and classical models consider in the study. Also, we perform the statistics AIC, BIC and CAIC to select the most appropriate model among those regression models considered in the study.

A Modified Bl-garch Model for Distributions with Heavy Tails

On Optimal Estimate Functions for Asymmetric GARCH Models

High frequency data exhibit non-constant variance. This paper models the exhibited fluctuations v... more High frequency data exhibit non-constant variance. This paper models the exhibited fluctuations via asymmetric GARCH models. The Maximum Likelihood Estimation (MLE) and Estimating Functions (EF) are used in the estimation of the asymmetric GARCH family models. This EF approach utilizes the third and fourth moments which are common features in financial time series data analysis and does not rely on distributional assumptions of the data. Optimal estimating functions have been constructed as a combination of linear and quadratic estimating functions. The results show that estimates from the estimating functions approach are better than those of the traditional estimation methods such as the MLE especially in cases where distributional assumptions on the data are seriously violated. The implementation of the EF approach to asymmetric GARCH models assuming a generalized student-t distribution innovation reveals the efficiency benefits of the EF approach over the MLE method in parameter...

Several methods which have been adopted to analyze multi-category data yields unsatisfactory resu... more Several methods which have been adopted to analyze multi-category data yields unsatisfactory results because of strict assumptions regarding normality, linearity, and homoscedasticity. As a result, Multinomial logistic regression is considered as an alternative because it does not assume normality, linearity, or homoscedasticity (Hosmer & Lemeshow, (2000)). The study attempted to use Maximum likelihood estimation and predicted probability to model Maternal Health Care Services data based on a set of explanatory variables. Also to determine the indices that affect Mortality rate. The result shows that wealth index has a significant impact on the use of public and private health delivery facilities. Educational level, antenatal care, assistance during delivery and place of residence are also important factors in assessing Maternal Health Care Services. Finally, the study revealed that educated women, who are wealthy, living in urban areas and who received antenatal care services and a...

Nigerian Journal of Basic and Applied Sciences, 2020

Election process and results in many countries have resulted in both political and economic insta... more Election process and results in many countries have resulted in both political and economic instability of that country. Fair and credible election process and results must be evidence-based and statistical proven. This study employed a Bayesian procedure for the validation of election results. Based on Nigerian 2011 and 2015 presidential election results, Bayesian credible intervals were obtained to assess the credibility of Nigeria presidential election results. The study explores Bayesian methods using a Bayesian model called beta-binomial conjugate model to compute posterior probability of electoral votes cast and confirm if these votes are within Bayesian credible intervals. The results obtained showed that election outcomes for the two major political parties in Nigeria 2011 presidential election are not within Bayesian credible bounds while 2015 presidential election results are within computed Bayesian credible bounds. Also, in contrast to frequentist approach, applied Bayes...

International journal of statistics and applications, 2014

A generalized student t distribution technique based on estimation of bilinear generalized autore... more A generalized student t distribution technique based on estimation of bilinear generalized autoregressive conditional heteroskedasticity (BL-GARCH) model is described. The paper investigates from empirical perspective, among other things, aspects related to the economic and financial risk management and to its impact on volatility forecasting. The purposive sampling technique was applied to select four banks (First Bank of Nigeria (FBN), Guaranty Trust Bank (GTB), United Bank for Africa (UBA) and Zenith Bank (ZEB)) daily stock prices, considered to be more susceptible to volatility than other banks within the sampled period (January, 2007- May, 2011). The data collected were analyzed using MATLAB R2008b Software. The results show that the newly introduced generalized student-t distribution is the most general of all the useful distributions applied in the BL-GARCH model parameter estimation. They serve as general distributions for obtaining empirical characteristics such as volatili...

American Journal of Mathematics and Statistics, 2015

This paper emphasizes estimating volatility using historical time series data of volatility indic... more This paper emphasizes estimating volatility using historical time series data of volatility indices at the Nigeria Stock Exchange. The realized volatility that are widely used by financial and risk management practitioners are employed to determine levels of volatility risk. These well-known features of financial data imply dynamic behaviours which can be well captured using regime structures. The analysis shows that the high-low-open-close volatility estimator performed better than the other estimators. The results also show that the pricing dynamic of the pricing model is heavily dependent on the dynamic of the underlying stochastic process whether or not the parameters is time varying.

Some Forecast Asymmetric GARCH Models for Distributions with Heavy Tails

Crude oil prices are inuenced by a number of factors that are far beyond the traditionalsupply a... more Crude oil prices are inuenced by a number of factors that are far beyond the traditionalsupply and demand dynamics such as West Texas Intermediate (WTI), Brent and Dubai. Thehigh frequency crude oil data exhibit non-constant variance. This paper models and forecaststhe exhibited uctuations via asymmetric GARCH models with the three commonly used errordistributions: Student'stdistribution, normal distribution and generalized error distribution(GED). The Maximum Likelihood Estimation (MLE) approach is used in the estimation ofthe asymmetric GARCH family models. The analysis shows that volatility estimates given bythe exponential generalized autoregressive conditional heteroskedasticity (EGARCH) modelexhibit generally lower forecast errors in returns of WTI oil spot price while the asymmetricpower autoregressive conditional heteroskedasticity (APARCH) model exhibits lower forecasterrors in returns of Brent oil spot price, therefore they are more accurate than the estimatesgiven b...

International Journal of Mathematical Analysis and Optimization: Theory and Applications, 2021

Rainfall estimates are important components of water resources applications, especially in agricu... more Rainfall estimates are important components of water resources applications, especially in agriculture, transport constructing irrigation and drainage systems. This paper aims to stochastically model and forecast the rainfall trend and pattern for a city, each purposively selected in five states of the South-Western Region of Nigeria. The data collected from Nigerian Meteorological Agency (NIMET) website are captured with fractional autoregressive integrated moving average (ARFIMA) and seasonal autoregressive integrated moving average (SARIMA) models. The autocorrelation function (ACF) and partial autocorrelation function (PACF) are used for model identification, the models selected are subjected to diagnostic checks for the models adequacy. Several tests: Augmented Dickey Fuller (ADF), Ljung Box and Jarque Bera tests are used for investigating unit root, serial autocorrelation and normality of residuals, respectively; the mean square error, root mean square error and mean absolute ...

Conditional Variance Parameters in Symmetric Models

International Journal of Probability and Statistics, 2014

The parameters and are restricted to be non-negative in GARCH model, which have some consequences... more The parameters and are restricted to be non-negative in GARCH model, which have some consequences for the stationarity condition, and although the disturbances have mean 0, they are clearly not white noise because of their time-varying asymmetric probability density functions. Thus, this stationary process is capable of capturing well known phenomena present in financial markets such as volatility clustering, marginal distributions having heavy tails and thin centres (Leptokurtosis); return series appearing to be almost uncorrelated over time but to be dependent through higher moments. The possibility of having dependence between higher conditional moments, most notably variances, involves examining nonlinear stochastic processes from a more realistic perspective in time series data. This motivates the consideration of nonlinear models. The results obtained through Monte Carlo simulations established the practicability and small sample performance of symmetric models under Gaussian distributions. The results also showed that the corresponding standard errors are very small indicating that estimators are asymptotically unbiased, efficient and consistent at least within the sample.

Time Series Analysis of Empirical Regularities in Nigeria Banking Sector

A time series analysis method based on estimation of exponential generalized autoregressive condi... more A time series analysis method based on estimation of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models is described. The paper investigates from empirical perspective, among other things, aspects related to the occurrence of the IGARCH effect and to its impact on volatility forecasting. The purposive sampling technique was applied to select four banks (First Bank of Nigeria (FBN), Guaranty Trust Bank (GTB), United Bank for Africa (UBA) and Zenith Bank (ZEB)) daily stock prices, considered to be more susceptible to volatility than other banks within the sampled period (January, 2007-May, 2011). The data collected were analyzed using Eview and Matlab R2008b Software. The results show that volatility clustering, leptokurtosis and leverage effect between returns and conditional variances were present in the selected banks stock returns with leverage effect having greater magnitude in UBA than the other three banks.

Afrika Statistika

For the first time, a location-scale regression model based on the logarithm of an extended Ralei... more For the first time, a location-scale regression model based on the logarithm of an extended Raleigh Lomax distribution which has the ability to deal and model of any survival data than classical regression model is introduced. We obtain the estimate for the model parameters using the method of maximum likelihood by considering breast cancer data. In addition, normal probability plot of the residual is used to detect the outliers and evaluate model assumptions. We use a real data set to illustrate the performance of the new model, some of its submodels and classical models consider in the study. Also, we perform the statistics AIC, BIC and CAIC to select the most appropriate model among those regression models considered in the study.

Tanzania Journal of Science

A generalized student t distribution technique based on estimation of bilinear generalized autore... more A generalized student t distribution technique based on estimation of bilinear generalized autoregressive conditional heteroskedasticity (BL-GARCH) model is introduced. The paper investigates from empirical perspective, aspects of the model related to the economic and financial risk management and its impacts on volatility forecasting. The purposive sampling technique was applied to select four banks for the study, namely First Bank of Nigeria (FBN), Guaranty Trust Bank (GTB), United Bank for Africa (UBA) and Zenith Bank (ZEB). The four banks are selected, because their daily stock prices are considered to be more susceptible to volatility than those of other banks within the sampled period (January 2007–May 2022). The data collected were analyzed using MATLAB R2008b Software. The results show that the newly introduced generalized student t distribution is the most general of all the useful distributions applied in the BL-GARCH model parameter estimation. It serves as a general dist...

Calcutta Statistical Association Bulletin, 2006

We thoroughly study a very important family of nonlinear timeseries models, viz. Self exciting th... more We thoroughly study a very important family of nonlinear timeseries models, viz. Self exciting threshold autoregressive (SETAR) types of models. A heartening feature of this family is that it is capable of describing cyclical data. As an illustration, SETAR models are then applied to country's lac export data during the period 1900-2000, obtained from Annual reports of Shellac Export Promotion Council, Kolkata. It is shown that fitted model, based on minimum Akaike information criterion (AIC), exhibits a threshold behaviour. Finally, attempts are made to obtain optimal predictor for out-of-sample data based on fitted SETAR model, which is found to be quite satisfactory.

Bayesian GARCH models for Nigeria Covid-19 data

Annals of Mathematics and Computer Science, Dec 2, 2021

Afrika Statistika, 2021

For the first time, a location-scale regression model based on the logarithm of an extended Ralei... more For the first time, a location-scale regression model based on the logarithm of an extended Raleigh Lomax distribution which has the ability to deal and model of any survival data than classical regression model is introduced. We obtain the estimate for the model parameters using the method of maximum likelihood by considering breast cancer data. In addition, normal probability plot of the residual is used to detect the outliers and evaluate model assumptions. We use a real data set to illustrate the performance of the new model, some of its submodels and classical models consider in the study. Also, we perform the statistics AIC, BIC and CAIC to select the most appropriate model among those regression models considered in the study.

A Modified Bl-garch Model for Distributions with Heavy Tails

On Optimal Estimate Functions for Asymmetric GARCH Models

High frequency data exhibit non-constant variance. This paper models the exhibited fluctuations v... more High frequency data exhibit non-constant variance. This paper models the exhibited fluctuations via asymmetric GARCH models. The Maximum Likelihood Estimation (MLE) and Estimating Functions (EF) are used in the estimation of the asymmetric GARCH family models. This EF approach utilizes the third and fourth moments which are common features in financial time series data analysis and does not rely on distributional assumptions of the data. Optimal estimating functions have been constructed as a combination of linear and quadratic estimating functions. The results show that estimates from the estimating functions approach are better than those of the traditional estimation methods such as the MLE especially in cases where distributional assumptions on the data are seriously violated. The implementation of the EF approach to asymmetric GARCH models assuming a generalized student-t distribution innovation reveals the efficiency benefits of the EF approach over the MLE method in parameter...

Several methods which have been adopted to analyze multi-category data yields unsatisfactory resu... more Several methods which have been adopted to analyze multi-category data yields unsatisfactory results because of strict assumptions regarding normality, linearity, and homoscedasticity. As a result, Multinomial logistic regression is considered as an alternative because it does not assume normality, linearity, or homoscedasticity (Hosmer & Lemeshow, (2000)). The study attempted to use Maximum likelihood estimation and predicted probability to model Maternal Health Care Services data based on a set of explanatory variables. Also to determine the indices that affect Mortality rate. The result shows that wealth index has a significant impact on the use of public and private health delivery facilities. Educational level, antenatal care, assistance during delivery and place of residence are also important factors in assessing Maternal Health Care Services. Finally, the study revealed that educated women, who are wealthy, living in urban areas and who received antenatal care services and a...

Nigerian Journal of Basic and Applied Sciences, 2020

Election process and results in many countries have resulted in both political and economic insta... more Election process and results in many countries have resulted in both political and economic instability of that country. Fair and credible election process and results must be evidence-based and statistical proven. This study employed a Bayesian procedure for the validation of election results. Based on Nigerian 2011 and 2015 presidential election results, Bayesian credible intervals were obtained to assess the credibility of Nigeria presidential election results. The study explores Bayesian methods using a Bayesian model called beta-binomial conjugate model to compute posterior probability of electoral votes cast and confirm if these votes are within Bayesian credible intervals. The results obtained showed that election outcomes for the two major political parties in Nigeria 2011 presidential election are not within Bayesian credible bounds while 2015 presidential election results are within computed Bayesian credible bounds. Also, in contrast to frequentist approach, applied Bayes...

International journal of statistics and applications, 2014

A generalized student t distribution technique based on estimation of bilinear generalized autore... more A generalized student t distribution technique based on estimation of bilinear generalized autoregressive conditional heteroskedasticity (BL-GARCH) model is described. The paper investigates from empirical perspective, among other things, aspects related to the economic and financial risk management and to its impact on volatility forecasting. The purposive sampling technique was applied to select four banks (First Bank of Nigeria (FBN), Guaranty Trust Bank (GTB), United Bank for Africa (UBA) and Zenith Bank (ZEB)) daily stock prices, considered to be more susceptible to volatility than other banks within the sampled period (January, 2007- May, 2011). The data collected were analyzed using MATLAB R2008b Software. The results show that the newly introduced generalized student-t distribution is the most general of all the useful distributions applied in the BL-GARCH model parameter estimation. They serve as general distributions for obtaining empirical characteristics such as volatili...

American Journal of Mathematics and Statistics, 2015

This paper emphasizes estimating volatility using historical time series data of volatility indic... more This paper emphasizes estimating volatility using historical time series data of volatility indices at the Nigeria Stock Exchange. The realized volatility that are widely used by financial and risk management practitioners are employed to determine levels of volatility risk. These well-known features of financial data imply dynamic behaviours which can be well captured using regime structures. The analysis shows that the high-low-open-close volatility estimator performed better than the other estimators. The results also show that the pricing dynamic of the pricing model is heavily dependent on the dynamic of the underlying stochastic process whether or not the parameters is time varying.

Some Forecast Asymmetric GARCH Models for Distributions with Heavy Tails

Crude oil prices are inuenced by a number of factors that are far beyond the traditionalsupply a... more Crude oil prices are inuenced by a number of factors that are far beyond the traditionalsupply and demand dynamics such as West Texas Intermediate (WTI), Brent and Dubai. Thehigh frequency crude oil data exhibit non-constant variance. This paper models and forecaststhe exhibited uctuations via asymmetric GARCH models with the three commonly used errordistributions: Student'stdistribution, normal distribution and generalized error distribution(GED). The Maximum Likelihood Estimation (MLE) approach is used in the estimation ofthe asymmetric GARCH family models. The analysis shows that volatility estimates given bythe exponential generalized autoregressive conditional heteroskedasticity (EGARCH) modelexhibit generally lower forecast errors in returns of WTI oil spot price while the asymmetricpower autoregressive conditional heteroskedasticity (APARCH) model exhibits lower forecasterrors in returns of Brent oil spot price, therefore they are more accurate than the estimatesgiven b...

International Journal of Mathematical Analysis and Optimization: Theory and Applications, 2021

Rainfall estimates are important components of water resources applications, especially in agricu... more Rainfall estimates are important components of water resources applications, especially in agriculture, transport constructing irrigation and drainage systems. This paper aims to stochastically model and forecast the rainfall trend and pattern for a city, each purposively selected in five states of the South-Western Region of Nigeria. The data collected from Nigerian Meteorological Agency (NIMET) website are captured with fractional autoregressive integrated moving average (ARFIMA) and seasonal autoregressive integrated moving average (SARIMA) models. The autocorrelation function (ACF) and partial autocorrelation function (PACF) are used for model identification, the models selected are subjected to diagnostic checks for the models adequacy. Several tests: Augmented Dickey Fuller (ADF), Ljung Box and Jarque Bera tests are used for investigating unit root, serial autocorrelation and normality of residuals, respectively; the mean square error, root mean square error and mean absolute ...

Conditional Variance Parameters in Symmetric Models

International Journal of Probability and Statistics, 2014

The parameters and are restricted to be non-negative in GARCH model, which have some consequences... more The parameters and are restricted to be non-negative in GARCH model, which have some consequences for the stationarity condition, and although the disturbances have mean 0, they are clearly not white noise because of their time-varying asymmetric probability density functions. Thus, this stationary process is capable of capturing well known phenomena present in financial markets such as volatility clustering, marginal distributions having heavy tails and thin centres (Leptokurtosis); return series appearing to be almost uncorrelated over time but to be dependent through higher moments. The possibility of having dependence between higher conditional moments, most notably variances, involves examining nonlinear stochastic processes from a more realistic perspective in time series data. This motivates the consideration of nonlinear models. The results obtained through Monte Carlo simulations established the practicability and small sample performance of symmetric models under Gaussian distributions. The results also showed that the corresponding standard errors are very small indicating that estimators are asymptotically unbiased, efficient and consistent at least within the sample.

Time Series Analysis of Empirical Regularities in Nigeria Banking Sector

A time series analysis method based on estimation of exponential generalized autoregressive condi... more A time series analysis method based on estimation of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models is described. The paper investigates from empirical perspective, among other things, aspects related to the occurrence of the IGARCH effect and to its impact on volatility forecasting. The purposive sampling technique was applied to select four banks (First Bank of Nigeria (FBN), Guaranty Trust Bank (GTB), United Bank for Africa (UBA) and Zenith Bank (ZEB)) daily stock prices, considered to be more susceptible to volatility than other banks within the sampled period (January, 2007-May, 2011). The data collected were analyzed using Eview and Matlab R2008b Software. The results show that volatility clustering, leptokurtosis and leverage effect between returns and conditional variances were present in the selected banks stock returns with leverage effect having greater magnitude in UBA than the other three banks.

Afrika Statistika

For the first time, a location-scale regression model based on the logarithm of an extended Ralei... more For the first time, a location-scale regression model based on the logarithm of an extended Raleigh Lomax distribution which has the ability to deal and model of any survival data than classical regression model is introduced. We obtain the estimate for the model parameters using the method of maximum likelihood by considering breast cancer data. In addition, normal probability plot of the residual is used to detect the outliers and evaluate model assumptions. We use a real data set to illustrate the performance of the new model, some of its submodels and classical models consider in the study. Also, we perform the statistics AIC, BIC and CAIC to select the most appropriate model among those regression models considered in the study.