Application of Iterative Approaches in Modeling the Efficiency of ARIMA-GARCH Processes in the Presence of Outliers

Akpan, Emmanuel Alphonsus; Lasisi, K. E.; Adamu, Ali; Rann, Haruna Bakari

doi:10.4236/am.2019.103012

Cited by 3 publications

(2 citation statements)

References 21 publications

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“…E( ) = 0 and variance 1. In practice, is often assumed to follow the standard normal or a standardized student-t distribution while is the standardized residual term that follows autoregressive conditional heteroscedastic (ARCH(q)), generalized autoregressive conditional heteroscedastic (GARCH (q, p)), exponential generalized autoregressive conditional heteroscedastic (EGARCH(q,p)) and Glosten, Jagannathan and Runkle generalized autoregressive conditional heteroscedastic (GJR-GARCH(q,p)) models in (5), (6), (7) and (8), respectively.…”

Section: Standard Garch-type Modelsmentioning

confidence: 99%

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

Moffat

Akpan

2019

AJPAS

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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.

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Section: Standard Garch-type Modelsmentioning

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

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Appraisal of excess Kurtosis through outlier-modified GARCH-type models

Akpan

Lasisi

Moffat

et al. 2021

Communications in Statistics - Simulation and Computation

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White Noise Analysis: A Measure of Time Series Model Adequacy

Moffat¹,

Akpan²

2019

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The purpose of this study is to apply white noise process in measuring model adequacy targeted at confirming the assumption of independence. This ensures that no autocorrelation exists in any time series under consideration, and that the autoregressive integrated moving average (ARIMA) model entertained is able to capture the linear structure in such series. The study explored the share price series of Union bank of Nigeria, Unity bank, and Wema bank obtained from Nigerian Stock Exchange from January 3, 2006 to November 24, 2016 comprising 2690 observations. ARIMA models were used to model the linear dependence in the data while autocorrelation function (ACF), partial autocorrelation function (PACF), and Ljung-Box test were applied in checking the adequacy of the selected models. The findings revealed that ARIMA(1,1,0) model adequately captured the linear dependence in the return series of both Union and Unity banks while ARIMA(2,1,0) model was sufficient for that of Wema bank. Also, evidence from ACF, PACF and Ljung-Box test revealed that the residual series of the fitted models were white noise, thus satisfying the conditions for stationarity.

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Application of Iterative Approaches in Modeling the Efficiency of ARIMA-GARCH Processes in the Presence of Outliers

Cited by 3 publications

References 21 publications

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

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

Appraisal of excess Kurtosis through outlier-modified GARCH-type models

White Noise Analysis: A Measure of Time Series Model Adequacy

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