American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2016, 4(4), 118-125
DOI: 10.12691/ajams-4-4-4
Open AccessArticle

Arma Type Modeling of Certain Non-stationary Time Series in Calabar


1Department of Mathematics and Statistics, Cross River University of Technology, Calabar, Nigeria

Pub. Date: August 22, 2016

Cite this paper:
B.O. EKPENYONG. Arma Type Modeling of Certain Non-stationary Time Series in Calabar. American Journal of Applied Mathematics and Statistics. 2016; 4(4):118-125. doi: 10.12691/ajams-4-4-4


Divergently different time series are considered in this article. The monthly passengers traffic at Cross lines limited, Calabar from 1990 to 2015 and monthly incidence of tuberculosis diseases at University of Calabar Teaching Hospital based from 1990-2015. The research adopted the statistical models based on time series analysis by Box and Jenkins methodology via the autocorrelation and the partial autocorrelation functions which showed that the two series are not stationary. Logarithm transformation was used to stabilize the variances of the two series and the residual autocorrelation and the partial autocorrelation functions is made stationary. Both regular and seasonal differencing was applied to the two-transformed set of data to obtain stationary series. The study employed ARIMA model on the classes of the two series, and the parameters of the identified model were estimated by the use of SPSS. The two models so chosen were ARMA (2,1,0) x (1,1,1)12 for passengers’ traffic and ARMA (1,0,1) x (1,1,2)12 for tuberculosis cases and forecasts was done for 12 months for the two series. The adequacy of the model was achieved and model fit for passengers traffic yields R-square, RMSE and MAPE of 0.876, 9.137, and 27.479 respectively and for tuberculosis cases yields R-square, RMSE and MAPE of 0.614, 6.785 and 26.522 respectively, recommendation and conclusion was made for the area of study.

ARMA non-stationary time series modeling passenger’s traffic tuberculosis diseases

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[1]  Hamilton, James.D.(1994). “The series analysis new Jersey”, United Kingdom Princeton University press.
[2]  Bhat, U,N. G.K.Miller (2002) “Estimation of the coefficient variation for unobservable services in time series” j. math. Sc. Society math. Sc. i. delhi, india.
[3]  Onwukwe C.E and Nwafor G. O. (2014). “A Multivariate Time Series Modeling of Major Economic Indicators in Nigeria” American journal of applied mathematics and statistics,vol.2, No.6 376-385.
[4]  Box G.E.F. and G.M, Jenkins.(1976) “time series analysis :forecasting and control rev. ed.”San Franciso holden – day.
[5]  Mcleod, A.I and P.R. Holanda sales (1983) “An algorithm for approximate likelihood calculation of ARMA and seasonal ARMA models”, journal of the royal statistical society (series G) 32,211-224.
[6]  Abraham. B. and j. Ledolter (1983). “Statistical methods for forecasting.” New York: wiley.
[7]  Granger, C.W.J. and Paul Newbold (1974). “Spurious regressions in econometrics” journal of econometrics 2:111;20
[8]  Myers, Raymond H. (1990) “Classical and modern regression with applications” 2nd ed. Boston:Duxbury press.
[9]  Anderson Brain D.O and John B. Moore (1979) “optimal filtering. Eaglewood cliffs,”N.J. : Prentice – hall.
[10]  Box G. E. P and Tidwell, A. (1962). “Transformations of independent variable” technometrics 4,431-550.
[11]  Hoerl, E,A. (1954) “Fitting curves to data” Chemical business handbook.
[12]  Dolby J. L. (1963)“A quick method of choosing transformation” Technometrics 5,317-325.
[13]  Turkey, T.W. (1961) “Discussion, emphasizing the connection between analysis of variance and spectrum analysis” Technometrics 3:1-29.
[14]  Box G.E.P and D.R. Cox (1964) “An analysis of transformation” Journal of royal statistical society B26; 211-243.
[15]  Federal ministry of health (2002) “A guide for community health extension workers: providing support to TB patients and communities at TB (DOTS) treatment centre.”