Arma-Arch Modeling Of The Returns Of First Bank Of Nigeria

Akpan, Emmanuel Alphonsus; Moffat, Imoh Udo; Ekpo, Ntiedo Bassey

doi:10.19044/esj.2016.v12n18p257

Cited by 5 publications

(7 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The joint null hypothesis is stated as follows: 0 : 1 = 2 = ⋯ = = 0 against : 1 ≠ 2 ≠ ⋯ ≠ ≠ 0. The decision rule is to reject 0 if Q(m) > 2 , where 2 denotes the 100 (1 -)th percentile of a Chi-squared distribution with m -(p + q) degree of freedom (see for example Akpan, Moffat and Ekpo, 2016).…”

Section: Diagnostic Checking Of the Modelmentioning

confidence: 99%

“…Moreover, the formal tests for the presence of heteroscedasticity (ARCH/GARCH effects) areusually Lagrange Multiplier and Ljung-Box on the squares of the residual series obtained from ARIMA modeling of the return series. Once these ARCH/GARCH effects are identified, then GARCH models could be applied (Akpan, Moffat and Ekpo, 2016;Akpan and Moffat, 2015;Ogum, Beer and Nouyrigat, 2005;Mgbame and Ikhatua, 2014;Atoi, 2014;Onwukwe, Samson and Lipcsey, 2014;Yaya, 2013;Emenike, 2010). Meanwhile, in an attempt to model the asymmetric GARCH, previous studies in Nigeria only extended the fitted GARCH models to the asymmetric ones and thereafter, access the significance of coefficient of leverage effect without prior formal test for the presence of asymmetric GARCH effect and thus created a gap in knowledge by not exploring a formal test in detecting the asymmetric GARCH effect.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Detection and Modeling of Asymmetric GARCH Effects in a Discrete-Time Series

Akpan¹,

Moffat²

2017

IJSP

Self Cite

View full text Add to dashboard Cite

This study traced the patterns of discrete time series over time with respect to GARCH effect and asymmetric GARCH effect. Particularly, we paid attention to the weakness of the GARCH model in modeling the asymmetry of GARCH effect. In order to handle this weakness, we applied the sign and size bias test which comprises sign bias test, negative size bias test, positive size bias test, and Lagrange Multiplier test in order to identify the asymmetric effect in the residual series of the GARCH model. Where the asymmetric effect is present and significant, we fit the asymmetric GARCH models. Exploring the share price returns of Zenith bank plc obtained from the Nigerian Stock Exchange from January 4, 2006 to May 26, 2015, our findings indicated the presence of GARCH effect and was adequately captured by GARCH(0,1) model. Also, the sign and size bias test for asymmetric GARCH effect on the residual series of GARCH(0,1) model showed a joint significance as indicated by the Lagrange Multiplier test. Moreover, the asymmetric GARCH effect was adequately captured by EGARCH(0,1) and TGARCH(0,1) models. In addition, the significance of the size bias test indicated that the size of negative and positive returns has an impact on the predicted heteroscedasticity. Hence, we concluded that GARCH(0,1) model adequately predicted the GARCH effect but failed to capture the asymmetric effect in the share price returns of the discrete series. However, this was complemented by both EGARCH(0,1) and TGARCH(0,1) models with the size of both the negative and positive effects taken into consideration.

show abstract

Section: Diagnostic Checking Of the Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Detection and Modeling of Asymmetric GARCH Effects in a Discrete-Time Series

Akpan¹,

Moffat²

2017

IJSP

Self Cite

View full text Add to dashboard Cite

show abstract

“…The mean equation (3) is modified to obtain GARCH-in-mean model in (11) such that the return series depends on its variance. The specification of GARCH-in-mean model implies that there are serial correlations in the return series (see [14]).…”

Section: Garch-in-mean Modelmentioning

confidence: 99%

“…Lastly, neglecting heteroscedasticity can lead to spurious non-linearity in the conditional mean and difficulty in computing the confidence interval for forecasts (see [2,3,4,5]). Furthermore, details of heteroscedasticity modeling are documented in [6,7,8,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Modeling Heteroscedasticity in the Presence of Serial Correlations in Discrete-time Stochastic Series: A GARCH-in-Mean Approach

Moffat

Akpan

2019

AJPAS

Self Cite

View full text Add to dashboard Cite

Background: In modeling heteroscedasticity of returns, it is often assumed that the series are uncorrelated. In practice, such series with small time periods between observations can be observed to contain significant serial correlations, hence the motivation for this research. Aim: The aim of this research is to assess the existence of serial correlations in the return series of Zenith Bank Plc, which is targeted at identifying their effects on the parameter estimates of heteroscedastic models. Materials and Methods: The data were obtained from the Nigerian Stock Exchange spanning from January 3, 2006, to November 24, 2016, having 2690 observations. The hybridized Autoregressive Integrated Moving Average-Generalized Autoregressive Conditional Heteroscedasticity (ARIMA-GARCH-type) models such as Autoregressive Integrated Moving Average-Generalized Autoregressive Conditional Heteroscedasticity (ARIMA-GARCH), Autoregressive Integrated Moving Average-Exponential Generalized Autoregressive Conditional Heteroscedasticity (ARIMA-EGARCH) and the Autoregressive Integrated Moving Average-Glosten, Jagannathan and Runkle Generalized Autoregressive Conditional Heteroscedastic (ARIMA-GJRGARCH) under normal and student-t distributions were employed to model the conditional variance while the GARCH-in-Mean-GARCH-type model corresponding to the selected ARIMA-GARCH-type model was applied to appraise the possible existence of serial correlations. Results: The findings of this study showed that heteroscedasticity exists and appeared to be adequately captured by ARIMA(2,1,1)-EGARCH(1,1) model under student-t distribution but failed to account for the presence of serial correlations in the series. Meanwhile, its counterpart, GARCH-in-Mean-EGARCH(1,1) model under student-t distribution sufficiently appraised the existence of serial correlations. Conclusion: One remarkable implication is that the estimates of the parameters of ARIMA-GARCH-type model are likely to be biased when the presence of serial correlations is ignored. Also, the application of GARCH-in-Mean-GARCH-type model possibly provides the feedback mechanism or interaction between the variance and mean equations.

show abstract

“…As such, modelling and forecasting the volatility of a financial time series has become an essential area in research.Most financial time series possess volatility and have unique features referred to as stylized financial time series facts, which include the absence of autocorrelations, heavy tails, asymmetry in time scales, volatility clustering, and leverage effect [5]. Linear time series models are not effective for describing the features of a volatility series as they assume the existence of linear dependence in given series [6]. Furthermore, the linear models are built on the homoscedastic assumption which may not necessarily be held in most time-series data as they might be highly time-variant.…”

mentioning

confidence: 99%

Application of Asymmetric-GARCH Type Models to The Kenyan Exchange Rates

Ndege,

Muriithi,

Wagala

2023

EJMATH

View full text Add to dashboard Cite

Modelling and forecasting the volatility of a financial time series has become essential in many economic and financial applications like portfolio optimization and risk management. The symmetric-GARCH type models can capture volatility and leptokurtosis. However, the models fail to capture leverage effects, volatility clustering, and the thick tail property of high-frequency financial time series. The main objective of this study was to apply the asymmetric-GARCH type models to Kenyan exchange to overcome the shortcomings of symmetric-GARCH type models. The study compared the asymmetric Conditional Heteroskedasticity class of models: EGARCH, TGARCH, APARCH, GJR-GARCH, and IGARCH. Secondary data on the exchange rate from January 1993 to June 2021 were obtained from the Central Bank of Kenya website. The best fit model is determined based on parsimony of the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Log-Likelihood criterion, and minimisation of prediction production errors (Mean error [ME] and Root Mean Absolute error [RMAE]). The optimal variance equation for the exchange rates data was APARCH (1,1) - ARMA (3,0) model with a skewed normal distribution (AIC = -4.6871, BIC = -4.5860). Volatility clustering was present in exchange rate data with evidence of the leverage effect. Estimated Kenya’s exchange rate volatility narrows over time, indicating sustained exchange rate stability.

show abstract

Arma-Arch Modeling Of The Returns Of First Bank Of Nigeria

Cited by 5 publications

References 6 publications

Detection and Modeling of Asymmetric GARCH Effects in a Discrete-Time Series

Detection and Modeling of Asymmetric GARCH Effects in a Discrete-Time Series

Modeling Heteroscedasticity in the Presence of Serial Correlations in Discrete-time Stochastic Series: A GARCH-in-Mean Approach

Application of Asymmetric-GARCH Type Models to The Kenyan Exchange Rates

Contact Info

Product

Resources

About