New R package arfurimaaparch for Estimation of ARFURIMA-APARCH Model and Big Data Analytics

Authors

  • Sanusi Alhaji Jibrin Department of Statistics, Kano University of Science and Technology Wudil, Kano-State.
  • Hassan Imafidor Ibrahim Department of Statistics, Federal Polytechnic Kaltungo, Gombe State

DOI:

https://doi.org/10.56471/slujst.v4i1&2.264

Keywords:

Fractional unit root differencing, R, arfurimaaparch package, ARFURIMA-APARCH model and big data analytics

Abstract

This paper introduces the R package arfurimaaparch version 0.1.0 for time series computations, big data analytics and estimation of Autoregressive Fractional Unit Root Integral Moving Average-Asymmetric Power Autoregressive Conditional Heteroscedasticity (ARFURIMA-APARCH) model. The fdr, arfurimaaparch, arfurimaaparchforecast, arfurimaaparchdiagnostic and arfurimaaparch.sim are the main functions of the package. An improved version of the arfurima package version 1.1.0 of Jibrin and Rahman (2019) for implementing Monte Carlo simulation is also presented. Daily Nigeria all share index and West Texas Intermediate (WTI) crude oil prices for the period 26th January 2004 to 31st December 2018 were used to explained the usage of the packages. When the arfurimaaparch package is compared with other long memory packages, It would produce better stationary process after transformation, appropriate fractional differencing values in the interval of , minimum Akaike Information Criteria values, larger log-likelihood values, minimum p-values of the ARFURIMA-APARCH parameters estimates and large p-values of the Ljung-Box, ARCH-LM and Jarque-Bera test. Findings show that both R packages and their functions are robust, simple and user-friendly. As conclusion, the R packages are suitable, good and reliable for time series analysis computations, statistical analysis and big data analytics.     

References

Beran, J. (1999). SEMIFAR models, a semiparametric fractional frame work for modelling trends, long-range dependence and nonstationarity. Preprint, University of Konstanz.

Beran, J., Whitcher, B. and Maechler, M., (2020). Longmemo: Statistics for long memory

processes. R package version 1.1-2. http://CRAN.R-project.org/package=longmemo

Borchers, H. W. (2021). pracma: Practical Numerical Math Functions. R package version 2.3.6.

https://CRAN.R-project.org/package=pracma

Box, G. E. P. and Jenkins, G. M. (1976).Time series analysis, forecasting and control,revised ed., Holden-Day.

Boubaker, H., Canarella, G., Gupta, R. and Miller M.S. (2016). Time-varying persistence of inflation: Evidence from a wavelet-based approach. Department of Economics, University of Connecticut, Working Paper Series. http://repec.org.

Constantine, W. and Percival, D. (2011). wmtsa: Wavelet Methods for Time Series Analysis. R

package version 1.1-0/r31. https://R-Forge.R-project.org/projects/wmtsa/

Fraley, C., Leisch, F., Maechler, M., Reisen, V. and Lemonte, A. (2012). fracdiff: fractionally differenced ARIMA aka ARFIMA(p,d,q) models. R package version 1.4-2. https://CRAN.R-project.org/package=fracdiff

Genz, A., Bretz, F., Miwa, T., Mi, X. Leisch, F., Scheipl, F. and Hothorn, T. (2021). mvtnorm:

Multivariate Normal and t Distributions. R package version 1.1-3.

http://CRAN.R-project.org/package=mvtnorm

Ghalanos, A. (2022). rugarch: Univariate GARCH models. R package version 1.4-7. https://cran.r project.org/web/packages/rugarch/rugarch/

Granger, C. W. J. and Joyeux, R. (1980). An introduction to long memory time series models and fractional differencing. Journal of Time Series Analysis, 1, pp. 15-39

Hosking, J. R. M. (1981). Fractional differencing.Biometrika, 68, pp. 165-176

Hyndman, R., Athanasopoulos, G., Bergmeir, C., Caceres, G., Chhay, L., O'Hara-Wild, M., Petropoulos, F., Razbash, S., Wang, E. and Yasmeen, F. (2020). forecast: Forecasting functions for time series and linear models. R package version 8.3. https://pkg.robjhyndman.com/forecast/

Jibrin, S.A. & Rahman, R.A. (2019). R package arfurima for fractional unit root integral (FURI) time series, ARFIMA and ARFURIMA models, Proceedings of the International Conference on Mathematical Sciences and Technology 2018 (MathTech2018), Pulau-Penang, Malaysia, AIP Conf. Proc. 2184, 050015- 1–050015-15. https://doi.org/10.1063/1.5136403.

Jibrin, S.A. (2019). Interminable long memory model and its hybrid for time series modeling, Ph.D Thesis, School of Mathematical Sciences, Universiti Sains Malaysia, Pulau-Penang, Malaysia.

Jibrin, S. A., Ibrahim, H. I. and Munkaila, D. (2022). A Novel Hybrid ARFURIMA-APARCH Model

for Modeling Interminable Long Memory and Asymmetric Effect in Time Series, Dutse Journal Of Pure And Applied Sciences,8(1), pp. 1-15

Leschinski, C. (2019). LongMemoryTS: Long Memory Time Series. R package version 0.1.0.

https://CRAN.R-project.org/package=LongMemoryTS

Maechler, M. (2020). fracdiff: Fractionally Differenced ARIMA aka ARFIMA(p,d,q) Models. R

package version 1.5-1. https://CRAN.R-project.org/package=fracdiff

McLeod, A. I., Sabzikar, F. and Meerschaert, M. M. (2016). Parameter estimation for ARTFIMA time series.Journal of Statistical Planning and Inference, 200, pp. 129-145 https://doi.org/10.1016/j.jspi.2018.09.010

Meerschaert, M.M., Sabzikar, F., Phanikumar, M.S. and Zeleke, A. (2014). Tempered fractional time series model for turbulence in geophysical flows.Journal of Statistical Mechanics: Theory and experiment, pp. 1-13

Musa, Y. and Jibrin, S.A. (2021). Time Series Analysis An Introduction, Fasco Publishers, 67

Gbadebo Street Mokola, Ibadan.

Porter-Hudak, S. (1990). An application of the seasonal fractionally differenced model to the monetary aggregates. Journal of the American Statistical Association, 45(410), pp. 338-344.

Pumi, G., Valk, M., Bisognin, C., Bayer, F. M. and Prass, T. S. (2019). Beta autoregressive fractionally integrated moving average models.Journal of Statistical Planning and Inference, 200, pp. 196-212

Rodriguez-Arias, M., Fernandez, J. A., Cabello, J. and Benitez, R. (2020). nlstac: An R Package for Fitting Separable Nonlinear Models. R package version 0.1.0.

https://CRAN.R-project.org/package=nlstac

R Core Team (2020). R: A language and environment for statistical computing. R Foundation for

Statistical Computing, Vienna, Austria. https://www.R-project.org/.

Tsay, R. S., Wood, D. and Lachmann, J. (2022). MTS: All-Purpose Toolkit for Analyzing

Multivariate Time Series (MTS) and Estimating Multivariate Volatility Models. R package version 1.1.1. https://CRAN.R-project.org/package=MTS

Veenstra, J. (2012). Persistence and anti-persistence: Theory and software, Ph.D. thesis, School of Graduate and Postdoctoral Studies, Western University London, Ontario,Canada.

Published

2022-07-20