Subscribe Now Subscribe Today
Research Article
 

Effect of the Logarithmic Transformation on the Trend-cycle Component



Iheanyi S. Iwueze and Anthony C. Akpanta
 
Facebook Twitter Digg Reddit Linkedin StumbleUpon E-mail
ABSTRACT

In this study we present some solutions to the problems encountered when a time series multiplicative model is linearized by taking the natural logarithm of the observed series. Problems associated with the trend-cycle component, with a view to achieving no alteration (if possible) to the fundamental nature of the original data, are discussed for a class of trending curves which includes the linear, quadratic and exponential growth curves. Necessary and sufficient conditions are derived for the parameters of the linear and quadratic curves. Numerical examples are given to illustrate the results obtained.

Services
Related Articles in ASCI
Similar Articles in this Journal
Search in Google Scholar
View Citation
Report Citation

 
  How to cite this article:

Iheanyi S. Iwueze and Anthony C. Akpanta , 2007. Effect of the Logarithmic Transformation on the Trend-cycle Component. Journal of Applied Sciences, 7: 2414-2422.

DOI: 10.3923/jas.2007.2414.2422

URL: https://scialert.net/abstract/?doi=jas.2007.2414.2422

REFERENCES
1:  Bartlett, M.S., 1947. The use of transformations. Biometrica, 3: 39-52.
Direct Link  |  

2:  Bond, T.G. and C.M. Fox, 2001. Applying the Rasch Model. In: Fundamental Measurement in the Human Sciences, Mahwah, N.J. (Ed.). Lawrence Erlbaum Assoc. Inc., USA.

3:  Box, G., G. Jenkins and C. Reinsel, 1994. Time Series Analysis: Forecasting and Control. 3rd Edn., Prentice Hall, New Jersey, ISBN-13: 978-0130607744.

4:  Chaddha, A.L. and S.S. Chitgopekar, 1971. A generalization of the logistic curves and long-range forecasts. Bell J. Busin. Manage. Sci., 2: 542-560.
Direct Link  |  

5:  Chatfield, C., 1980. The Analysis of Time Series: An Introduction. 2nd Edn., Chapman and Hall, London.

6:  Dolby, J.L., 1963. A quick method for choosing a transformation. Technometrics, 5: 317-325.

7:  Draper, N.R. and H. Smith, 1981. Applied Regression Analysis. John Wiley and Sons Inc., New York.

8:  Hoerl, A.E., 1954. Chemical Business Handbook. McGraw-Hill, New York.

9:  Iwueze, I.S. and E.C. Nwogu, 2004. Buys-Ballot estimates for time series decomposition. Global J. Math. Sci., 3: 83-98.
Direct Link  |  

10:  Iwueze, I.S. and A.C. Akpanta, 2006. Stochastic modeling of inflation in Nigeria. Global J. Math. Sci., 33: 83-98.

11:  Iwueze, I.S., 2007. Some implications of truncating the N(1, σ2) distribution to the left at zero. J. Applied Sci., 7: 189-195.
CrossRef  |  Direct Link  |  

12:  Levenbach, H. and B.C. Reuter, 1976. Forecasting trending time series with relative growth rate models. Technometrics, 18: 261-272.

13:  Osborne, J., 2002. Notes on the use of data transformations. J. Practic. Assess. Res. Evalu., 8: 1-7.
Direct Link  |  

14:  Tuckwell, H.C., 1988. Elementary Applications of Probability Theory. Chapman and Hall, London.

15:  Wei, W.W., 1989. Time Series Analysis: Univariate and Multivariate Methods. Addison-Wesley Publishing Company, Inc., Redwood City, California.

©  2021 Science Alert. All Rights Reserved