Identification of Heteroscedasticity in the Presence of Outliers in Discrete-Time Series

Akpan, Emmanuel Alphonsus; Lasisi, K. E.; Adamu, Ali

doi:10.9734/arjom/2018/42517

Cited by 3 publications

(6 citation statements)

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“…where, is the sample size, = ℎ and is the sample autocorrelation coefficient [21] (K = 1, 2, ….) LB is asymptotically a Chi-squared random variable with m-p-q degrees of freedom [22,23]. The decision: if LB is less than critical value of , then we do not reject the null hypothesis.…”

Section: Model Verificationmentioning

confidence: 98%

Selection of Linear Time Series Model on the Basis of Out-of-Sample Prediction Criteria

Henry

Lasisi

Akpan

et al. 2019

AJPAS

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Background: In linear time series, the in-sample model selection and the out-of-sample model selection are the two common approaches to model selection. However, empirical evidence based on out-of-sample forecast performance is generally considered more trustworthy than evidence based on in-sample performance, which is deficient in providing information about future observations. Aim: The aim of the study is to select the best linear time series model suitable to predict Nigeria exchange rates for the period 2002-2018. Materials and Methods: Data on naira to pound and naira to euro exchange rates from January 2002 to December 2018, comprising of 204 data points were considered. The data were divided into two portions; the first portion which comprises of 192 observations was used for model building while the second portion with 12 observations was used for out-of-sample prediction evaluation. The Box-Jenkins ARIMA iterative procedure was used in model building while the mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and Theil’s U coefficient were the measures of accuracy adopted in selecting the best out-of sample model. Results: Our results revealed that, based on in-sample model selection, ARIMA (0, 1, 1) and ARIMA (1, 1, 0) were the appropriate models with minimum information criteria. However, on the basis of out-sample forecast performance evaluation criteria, ARIMA (1, 1, 0) and ARIMA (1, 1, 2) were found to be appropriate out-of-sample models with minimum forecast evaluation criteria. In all, our results showed that, the out-of sample models performed better than their in-sample counterparts in their ability to forecast future values. Conclusion: So far, this study revealed that out-of-sample is a better model selection criterion than the in-sample counterpart as evident in its ability to predict future values which is the very essence for modelling in time series.

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Section: Model Verificationmentioning

confidence: 98%

Selection of Linear Time Series Model on the Basis of Out-of-Sample Prediction Criteria

Henry

Lasisi

Akpan

et al. 2019

AJPAS

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“…The GJR-GARCH (q, p) model proposed by Glosten and Reinsel [10]; Akpan, Lasisi and Adamu [8] for more details on the procedures and its application, respectively. )…”

Section: Glosten Jagannathan and Runkle (Gjr-garch) Modelmentioning

confidence: 99%

“…Westfall [8]). Therefore, to completely account for excess kurtosis, it is required that outliers (which are the observations that deviate from the overall pattern of the distribution of the data) be adjusted for.…”

Section: Introductionmentioning

confidence: 99%

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

Akpan¹,

Lasisi²,

Adamu³

et al. 2019

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The study explored both Box and Jenkins, and iterative outlier detection procedures in determining the efficiency of ARIMA-GARCH-type models in the presence of outliers using the daily closing share price returns series of four prominent banks in Nigeria (Skye (Polaris) bank, Sterling bank, Unity bank and Zenith bank) from January 3, 2006 to November 24, 2016. The series consists of 2690 observations for each bank. The data were obtained from the Nigerian Stock Exchange. Unconditional variance and kurtosis coefficient were used as criteria for measuring the efficiency of ARIMA-GARCH-type models and our findings revealed that kurtosis is a better criterion (as it is a true measure of outliers) than the unconditional variance (as it can be depleted or amplified by outliers). Specifically, the strength of this study is in showing the applicability and relevance of iterative methods in time series modeling.

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“…Meanwhile, in Nigeria, model selection in heteroscedastic processes are mainly based on in-sample criteria. For instance, the studies of [28]- [33] rely on the in-sample procedure to select the best fit model. Hence, this study seeks to improve on the work of [28] who applied the in-sample model selection criteria to choose best fitted heteroscedastic models by adopting out-of-sample forecasting approach in selecting heteroscedastic models that would best describe the accuracy and precision of future observations.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, the studies of [28]- [33] rely on the in-sample procedure to select the best fit model. Hence, this study seeks to improve on the work of [28] who applied the in-sample model selection criteria to choose best fitted heteroscedastic models by adopting out-of-sample forecasting approach in selecting heteroscedastic models that would best describe the accuracy and precision of future observations. This work is further organized as follows: materials and methods are treated in Section 2, results and discussion covered in Section 3 and Section 4 takes care of conclusion.…”

Section: Introductionmentioning

confidence: 99%

Selection of Heteroscedastic Models: A Time Series Forecasting Approach

Moffat¹,

Akpan²

2019

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To overcome the weaknesses of in-sample model selection, this study adopted out-of-sample model selection approach for selecting models with improved forecasting accuracies and performances. Daily closing share prices were obtained from Diamond Bank and Fidelity Bank as listed in the Nigerian Stock Exchange spanning from January 3, 2006 to December 30, 2016. Thus, a total of 2713 observations were explored and were divided into two portions. The first which ranged from January 3, 2006 to November 24, 2016, comprising 2690 observations, was used for model formulation. The second portion which ranged from November 25, 2016 to December 30, 2016, consisting of 23 observations, was used for out-of-sample forecasting performance evaluation. Combined linear (ARIMA) and Nonlinear (GARCH-type) models were applied on the returns series with respect to normal and student-t distributions. The findings revealed that ARIMA (2,1,1)-EGARCH (1,1)-norm and ARIMA (1,1,0)-EGARCH (1,1)-norm models selected based on minimum predictive errors throughout-of-sample approach outperformed ARIMA (2,1,1)-GARCH (2,0)-std and ARIMA (1,1,0)-EGARCH (1,1)-std model chosen through in-sample approach. Therefore, it could be deduced that out-of-sample model selection approach was suitable for selecting models with improved forecasting accuracies and performances.

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Identification of Heteroscedasticity in the Presence of Outliers in Discrete-Time Series

Cited by 3 publications

References 0 publications

Selection of Linear Time Series Model on the Basis of Out-of-Sample Prediction Criteria

Selection of Linear Time Series Model on the Basis of Out-of-Sample Prediction Criteria

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

Selection of Heteroscedastic Models: A Time Series Forecasting Approach

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