International Journal of Advanced and Applied Sciences
Int. j. adv. appl. sci.
EISSN: 2313-3724
Print ISSN: 2313-626X
Volume 4, Issue 9 (September 2017), Pages: 96-100
Title: Time series modeling of the interaction between deterministic and stochastic trends
Author(s): Imoh Udo Moffat *, Emmanuel Alphonsus Akpan
Affiliation(s):
Department of Mathematics and Statistics, University of Uyo, Uyo, Nigeria
https://doi.org/10.21833/ijaas.2017.09.012
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Abstract:
This study investigated a scenario where both the deterministic and stochastic trends coexist in a single realization. On exploring the monthly internally generated revenue of Akwa Ibom State in Nigeria from January, 2010 to December, 2014, we found that the deterministic trend with ARMA (1, 0) model adequately described the coexistence of both the deterministic and stochastic trends.
© 2017 The Authors. Published by IASE.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Autocorrelation, Deterministic trend, Stochastic trend, Time series
Article History: Received 10 December 2016, Received in revised form 20 July 2017, Accepted 20 July 2017
Digital Object Identifier:
https://doi.org/10.21833/ijaas.2017.09.012
Citation:
Moffat IU and Akpan EA (2017). Time series modeling of the interaction between deterministic and stochastic trends. International Journal of Advanced and Applied Sciences, 4(9): 96-100
http://www.science-gate.com/IJAAS/V4I9/Moffat.html
References:
- Caiado J and Crato N (2005). Discrimination between deterministic trend and stochastic trend processes. In the 14th International Conference on Applied Stochastic Models and Data Analysis: 1419-1424. Available online at: https://mpra.ub.uni-muenchen.de/id/eprint/2076
- Cryer JD and Chan K (2008). Time series analysis with application in R. Springer, New York, USA.
- Dagum EB and Dagum C (2006). Stochastic and deterministic trend models. Statistica, 66(3): 269-280.
- Dagum EB and Luati A (2001). A study of the asymmetric and symmetric weights of Kernel smoothers and their spectral properties. Estadistica, 53(160): 215-258.
- Dickey DA and Fuller WA (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366a): 427-431. https://doi.org/10.1080/01621459.1979.10482531
- Fuller WA (2009). Introduction to statistical time series. John Wiley and Sons, Hoboken, New Jersey, USA.
- Hamilton JD (1994). Time series analysis. Princeton University Press, Princeton, New Jersey, USA.
- Harvey AC (1985). Trends and cycles in macroeconomic time series. Journal of Business and Economic Statistics, 3(3): 216-227. https://doi.org/10.1080/07350015.1985.10509453
- MacKinnon JG (1996). Numerical distribution functions for unit root and cointegration tests. Journal of Applied Econometrics, 11(6):601-618. https://doi.org/10.1002/(SICI)1099-1255(199611)11:6<601::AID-JAE417>3.0.CO;2-T
- Moffat IU (2007). On the intervention analysis and robust regression of time series outliers. Unpublished Ph.D. Dissertation, Rivers State University of Science and Technology, Port Harcourt, Nigeria.
- Nelson CR and Plosser CR (1982). Trends and random walks in macroeconmic time series: some evidence and implications. Journal of Monetary Economics, 10(2): 139-162. https://doi.org/10.1016/0304-3932(82)90012-5
- Qi M and Zhang PG (2008). Trend time series modeling and forecasting with neural network. IEEE Transaction on Neural Networks, 19(15): 808-816. PMid:18467210
- Rao BB (2010). Deterministic and stochastic trends in the time series models: A guide for the applied economist. Applied Economics, 42(17): 2193-2202. https://doi.org/10.1080/00036840701765494
- Said SE and Dickey DA (1984). Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika, 71(3): 599-607. https://doi.org/10.1093/biomet/71.3.599
- Watson MW (1986). Univariate detrending methods with stochastic trends. Journal of Monetary Economics, 18(1): 49-75. https://doi.org/10.1016/0304-3932(86)90054-1
- Wei WW (2006). Time series analysis: Univariate and multivariate methods. Pearson Addison Wesley, Boston, USA.