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Year 2024, Volume: 45 Issue: 3, 618 - 628, 30.09.2024

Ayoade Adewole

https://doi.org/10.17776/csj.1467360

Abstract

References

  • [1] Adewole A.I., Statistical Modelling and Forecasting of Temperature and Rainfall in Ijebu Ode Nigeria Using SARIMA, FNAS Journal of Scientific Innovations, 5(2) (2023) 55-68.
  • [2] Baillie R.T., Bollerslev T., and Mikkelsen H.O., Fractionally integrated generalized autoregressive conditional Heteroskedasticity, Journal of Econometrics, 74 (1996) 3–30.
  • [3] Beran J., Statistics for Long-Memory Processes, Chapman and Hall Publishing Inc., New York, (1995).
  • [4] Granger C.W.J., Joyeux R., an Introduction to Long-Memory Time Series Models and Fractional Differencing, Journal of Time Series Analysis, 1 (1980) 15-29.
  • [5] Hosking J.R.M., Fractional Differencing, Biometrika, 68 (1981) 165-176.
  • [6] Robinson P.M., Log-periodogram regression of time-series with long-range dependence, The Annals of Statistics, 23 (1995) 1048–1072.
  • [7] Paul R.K., Gurung B., Paul A.K., Modelling and Forecasting of Retail Price of Arhar Dal in Karnal, Haryana, Indian Journal of Agricultural Science, 85(1) (2015a) 69-72.
  • [8] Engle R.F. Autoregressive conditional heteroscedasticity with estimates of the Variance of U.K. inflation, Econometrica, 50 (1982) 987-1008.
  • [9] Bollerslev T., Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31 (1986) 307-327.
  • [10] Taylor S. J., Modeling Financial Time Series, New York, Wiley, (1986).
  • [11] Fung, H.G., Lo W.C., Peterson J.E., Examining the Dependence in Intra-Day Stock Index Futures, the Journal of Futures Markets, 14 (1994) 405-419.
  • [12] Adewole A.I., On the Hybrid of ARIMA and GARCH Model in Modeling Volatilities in Nigeria Stock Exchange. Bima Journal of Science and Technology, 8(1A) (2024) 169-180.
  • [13] Reisen V.A., Sarnaglia A.J.Q., Reis J., L’Evy-Leduc N.C., Santos J.M., Modeling and Forecasting Daily Average PM10 Concentrations by a Seasonal Long-Memory Model with Volatility, Environmental Modeling and Software, 51 (2014) 286-295.
  • [14] Adewole A.I. The Performance of ARIMA and ARFIMA in Modeling the Exchange Rate of Nigeria Currency to other Currencies. Al- Bahir Journal for Engineering and Pure Sciences, 4 (2) (2024)142-155.
  • [15] Tong H., Nonlinear Time Series Analysis, International Encyclopedia of Statistical Science, Springer, Berlin, Heidelberg, (2011) 955-958.
  • [16] Narayan P.K., Liu R., Westerlund J. A., Garch Model for Testing Market Efficiency. Journal of International Financial Markets, Institutions and Money, 41 (2016) 121-138.
  • [17] Bollerslev T., Mikkelsen H.O., Modeling and pricing long memory in stock market volatility, Journal of Econometrics, 73 (1) (1996) 151-184.
  • [18] Bordignon S., Caporin M., Lisi F. A., seasonal fractionally integrated GARCH model, working paper, University of Padova, Italy (2004).
  • [19] Paul R.K., Forecasting Wholesale Price of Pigeon Pea Using Long Memory Time-Series Models, Agricultural Economics Research Review, 27 (2) (2014) 167-176.
  • [20] Paul R.K., Samanta S., Gurung B., Monte Carlo simulation for comparison of different estimators of Long Memory parameter: An application of ARFIMA model for forecasting price, Model Assisted Statistics and Application, 10 (2) (2015b) 116-127.
  • [21] Davidson J., Moment and memory properties of linear conditional heteroscedasticity models, and a new model. Journal of Business and Economic Statistics, 22 (2004) 16-29.
  • [22] Kang S. H., Yoon S. M., Dual Long Memory Properties with Skewed and Fat-Tail Distribution, International Journal of Business and Information, 7 (2) (2012) 225-249.
  • [23] Slaveya Z., ARFIMA-FIGARCH, HYGARCH and FIAPARCH Models of Exchange Rates, Journal of the Union of Scientists, 7 (2) (2018) 142-153.
  • [24] Umar A. G., Dikko H. G, Garba J., Tasi’u M. A., Study of Nigeria Monthly Stock Price Index using ARTFIMA-FIGARCH Hybrid Model, UMYU Scientifica, 2 (4) (2023) 114 – 121.
  • [25] Skare M., Stjepanović S., A Fractionally Integrated Model for the Croatian Aggregate Output (Gdp) Series, Ekonomska Istraživanja, 26 (2) (2013) 1–34.
  • [26] Caporale, Guglielmo M., Škare, M., Long memory in UK real GDP, 1851- 2013: An ARFIMA-FIGARCH Analysis, DIW Discussion Papers, Deutsches Institut für Wirtschaftsforschung (DIW), Berlin 1395 (2014).
  • [27] Aliyu M. A., Dikko H. G., Danbaba U. A., Statistical modeling for forecasting volatility in Naira per Dollar Exchange rate using ARFIMA-GARCH and ARFIMA FIGARCH models, World scientific Journal, 176 (2022) 27–42.
  • [28] Tayafi M., Ramanathan T.V., An overview of FIGARCH and related time-series models, Australian Journal of Statistics, 141 (2012) 175-196.
  • [29] Granger, C.W.J., Long memory relationships and the aggregation of dynamic models, Journal of Econometrics, 14 (1980) 227-238.
  • [30] Engle R.F., Bollerslev T., Modelling the persistence of conditional variances, Econometric Reviews, 5(1) (1986) 1-50.
  • [31] Box, G.E.P and Jenkins, M, Time Series analysis forecasting and control. Holden –Day Inc (1976).

Modeling Long Memory Volatilities of Nigeria Selected Macro Economic Variables with Arfima and Arfima Figarch

Year 2024, Volume: 45 Issue: 3, 618 - 628, 30.09.2024

Ayoade Adewole

https://doi.org/10.17776/csj.1467360

Abstract

The research delved into analysing the stochastic characteristics of Nigeria's Real GDP, the exchange rate of the Naira to US Dollar, and the inflation rate employing Autoregressive fractionally integrated moving average (ARFIMA) and the Autoregressive Fractionally Integrated Moving Average Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity (FIGARCH) modelling approach. The ability of the hybrid formation of ARFIMA-FIGARCH model with Nigeria macroeconomic variables in modeling the periodicity of long memory volatilities was examined. ARIMA GARCH method of modeling was also employed in analyzing the volatilities of Nigeria selected macroeconomic variables to enrich the study. The efficiency of ARFIMA, ARFIMA FIGARCH and ARIMA GARCH models were evaluated with the forecast evaluation measurements. Results revealed that ARFIMA FIGARCH and ARIMA GARCH models are more adequate in modeling the Inflation rate and the exchange rate while ARFIMA present more adequacies in modeling the RGDP. This result revealed evidence of high volatilities in Nigeria Inflation and the exchange rate of Naira to US dollar

Keywords

: Volatilities Long Memory Macroeconomic variables Arfima Figarch

References

  • [1] Adewole A.I., Statistical Modelling and Forecasting of Temperature and Rainfall in Ijebu Ode Nigeria Using SARIMA, FNAS Journal of Scientific Innovations, 5(2) (2023) 55-68.
  • [2] Baillie R.T., Bollerslev T., and Mikkelsen H.O., Fractionally integrated generalized autoregressive conditional Heteroskedasticity, Journal of Econometrics, 74 (1996) 3–30.
  • [3] Beran J., Statistics for Long-Memory Processes, Chapman and Hall Publishing Inc., New York, (1995).
  • [4] Granger C.W.J., Joyeux R., an Introduction to Long-Memory Time Series Models and Fractional Differencing, Journal of Time Series Analysis, 1 (1980) 15-29.
  • [5] Hosking J.R.M., Fractional Differencing, Biometrika, 68 (1981) 165-176.
  • [6] Robinson P.M., Log-periodogram regression of time-series with long-range dependence, The Annals of Statistics, 23 (1995) 1048–1072.
  • [7] Paul R.K., Gurung B., Paul A.K., Modelling and Forecasting of Retail Price of Arhar Dal in Karnal, Haryana, Indian Journal of Agricultural Science, 85(1) (2015a) 69-72.
  • [8] Engle R.F. Autoregressive conditional heteroscedasticity with estimates of the Variance of U.K. inflation, Econometrica, 50 (1982) 987-1008.
  • [9] Bollerslev T., Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31 (1986) 307-327.
  • [10] Taylor S. J., Modeling Financial Time Series, New York, Wiley, (1986).
  • [11] Fung, H.G., Lo W.C., Peterson J.E., Examining the Dependence in Intra-Day Stock Index Futures, the Journal of Futures Markets, 14 (1994) 405-419.
  • [12] Adewole A.I., On the Hybrid of ARIMA and GARCH Model in Modeling Volatilities in Nigeria Stock Exchange. Bima Journal of Science and Technology, 8(1A) (2024) 169-180.
  • [13] Reisen V.A., Sarnaglia A.J.Q., Reis J., L’Evy-Leduc N.C., Santos J.M., Modeling and Forecasting Daily Average PM10 Concentrations by a Seasonal Long-Memory Model with Volatility, Environmental Modeling and Software, 51 (2014) 286-295.
  • [14] Adewole A.I. The Performance of ARIMA and ARFIMA in Modeling the Exchange Rate of Nigeria Currency to other Currencies. Al- Bahir Journal for Engineering and Pure Sciences, 4 (2) (2024)142-155.
  • [15] Tong H., Nonlinear Time Series Analysis, International Encyclopedia of Statistical Science, Springer, Berlin, Heidelberg, (2011) 955-958.
  • [16] Narayan P.K., Liu R., Westerlund J. A., Garch Model for Testing Market Efficiency. Journal of International Financial Markets, Institutions and Money, 41 (2016) 121-138.
  • [17] Bollerslev T., Mikkelsen H.O., Modeling and pricing long memory in stock market volatility, Journal of Econometrics, 73 (1) (1996) 151-184.
  • [18] Bordignon S., Caporin M., Lisi F. A., seasonal fractionally integrated GARCH model, working paper, University of Padova, Italy (2004).
  • [19] Paul R.K., Forecasting Wholesale Price of Pigeon Pea Using Long Memory Time-Series Models, Agricultural Economics Research Review, 27 (2) (2014) 167-176.
  • [20] Paul R.K., Samanta S., Gurung B., Monte Carlo simulation for comparison of different estimators of Long Memory parameter: An application of ARFIMA model for forecasting price, Model Assisted Statistics and Application, 10 (2) (2015b) 116-127.
  • [21] Davidson J., Moment and memory properties of linear conditional heteroscedasticity models, and a new model. Journal of Business and Economic Statistics, 22 (2004) 16-29.
  • [22] Kang S. H., Yoon S. M., Dual Long Memory Properties with Skewed and Fat-Tail Distribution, International Journal of Business and Information, 7 (2) (2012) 225-249.
  • [23] Slaveya Z., ARFIMA-FIGARCH, HYGARCH and FIAPARCH Models of Exchange Rates, Journal of the Union of Scientists, 7 (2) (2018) 142-153.
  • [24] Umar A. G., Dikko H. G, Garba J., Tasi’u M. A., Study of Nigeria Monthly Stock Price Index using ARTFIMA-FIGARCH Hybrid Model, UMYU Scientifica, 2 (4) (2023) 114 – 121.
  • [25] Skare M., Stjepanović S., A Fractionally Integrated Model for the Croatian Aggregate Output (Gdp) Series, Ekonomska Istraživanja, 26 (2) (2013) 1–34.
  • [26] Caporale, Guglielmo M., Škare, M., Long memory in UK real GDP, 1851- 2013: An ARFIMA-FIGARCH Analysis, DIW Discussion Papers, Deutsches Institut für Wirtschaftsforschung (DIW), Berlin 1395 (2014).
  • [27] Aliyu M. A., Dikko H. G., Danbaba U. A., Statistical modeling for forecasting volatility in Naira per Dollar Exchange rate using ARFIMA-GARCH and ARFIMA FIGARCH models, World scientific Journal, 176 (2022) 27–42.
  • [28] Tayafi M., Ramanathan T.V., An overview of FIGARCH and related time-series models, Australian Journal of Statistics, 141 (2012) 175-196.
  • [29] Granger, C.W.J., Long memory relationships and the aggregation of dynamic models, Journal of Econometrics, 14 (1980) 227-238.
  • [30] Engle R.F., Bollerslev T., Modelling the persistence of conditional variances, Econometric Reviews, 5(1) (1986) 1-50.
  • [31] Box, G.E.P and Jenkins, M, Time Series analysis forecasting and control. Holden –Day Inc (1976).
There are 31 citations in total.

Details

Primary Language English
Subjects Applied Statistics
Journal Section Natural Sciences
Authors

Ayoade Adewole 0000-0002-5416-9202

Publication Date September 30, 2024
Submission Date April 10, 2024
Acceptance Date August 20, 2024
Published in Issue Year 2024Volume: 45 Issue: 3

Cite

APA Adewole, A. (2024). Modeling Long Memory Volatilities of Nigeria Selected Macro Economic Variables with Arfima and Arfima Figarch. Cumhuriyet Science Journal, 45(3), 618-628. https://doi.org/10.17776/csj.1467360
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