Penalty of model misspecification in time series dominated with trend

  • Authors

    • Ogbonna Chukwudi Justin Alex Ekwueme Federal University Ndufu-Alike, Ikwo
    • Nweke Chijioke Joel Federal University of Technology, Owerri
    • Ojide Kelechi Charity Alex Ekwueme Federal University Ndufu-Alike, Ikwo.
    2019-11-05
    https://doi.org/10.14419/ijams.v7i1.29731
  • Deterministic, Mis-Specification, Spectrum, Stochastic, Trend.

  • Abstract

    Model specification is consequential in mathematical science and statistics in particular. This work seeks to ascertain the consequences of model mis-specification in the analysis of a time series dominated by trend. It further discusses the statistical properties of various types of trend as well as when they are combine with AR (1) and MA (1) process. It recommends the use of spectrum analysis in detection of trend type in a given series.Illustrations were carried out using simulated series. The results from the simulated series was in harmony with the theoretical results.

     

     

  • References

    1. [1] Ademola, O. P. (2007). Fuzzy-wavelet method for time series analysis. University of Surrey Guildford, Surrey GU2 7XH, UK. (PhD thesis).

      [2] Box, G.E.P. and Pierce, D.A. (1970). Distributions of residual autocorrelations in autoregressive moving average time series models. Journal of American Statistical Association, (65), 1509-1526.https://doi.org/10.1080/01621459.1970.10481180.

      [3] Box, G.E.P., Jenkins, G. M. and Reinsel, G. C. (1994). Time Series Analysis: Forecasting and Control (3rd Edition). Prentice-Hall, Inc, Englewood Cliffs.

      [4] Chandler, R. E. and Scott, E. M. (2011), Statistical Methods for Trend Detection and Analysis in the Environmental Sciences. John Wiley and Sons Ltd, USA.https://doi.org/10.1002/9781119991571.

      [5] Chatfield, C. (2004). The analysis of time series: An Introduction, (6th Edition), Chapman & Hall/CRC Press Company Boca, New York Washington, D.C.

      [6] Dickey, D.A. and Fuller, W.A. (1979). Distribution of the estimates for autoregressive time series with a unit root. Journal of the American Statistical Association,74 (366), 427-431.https://doi.org/10.1080/01621459.1979.10482531.

      [7] Granger, C. W. J. (1994). Forecasting in Economics.Time Series Prediction: Forecasting the Future and Understanding the Past. N. A. Gershenfeld and A. S. Weigend (eds.) Reading, MA: Addison-Wesley.

      [8] Gujarati, D. N. (2004). Basic Econometrics. (4th Edition). The McGraw−Hill Companies, New York.

      [9] Hamilton, J, D. (1994). Time Series Analysis. Princeton University Press Princeton, New Jersey.

      [10] Heino, B. N. (2005), Non-Stationary Time Series and Unit Root Tests, Unpublished Note on Econometric Fall.

      [11] Kwiatkowski, D., Philips, P.C.B., Schmitt, P. and Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, (54),159-178.https://doi.org/10.1016/0304-4076(92)90104-Y.

      [12] Ljung, G. M. and Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65 (2), 297-303.https://doi.org/10.1093/biomet/65.2.297.

      [13] Nelson, C. R. and Plosser, C. I. (1982). Trends and random walks in macroeconomic time series: Some evidence and implications. Journal of Monetary Economics.139-162.https://doi.org/10.1016/0304-3932(82)90012-5.

      [14] Nelson, M., Hill, T., Remus, T. and O’Connor, M. (1999). Time series forecasting using neural networks: Should the data be deseasonalized first? Journal of Forecasting,18, 359–367.https://doi.org/10.1002/(SICI)1099-131X(199909)18:5<359::AID-FOR746>3.0.CO;2-P.

      [15] Ogbonna, C.J., Nweke, C.J., Nwogu E. C. and Iwueze, I.S. (2016). Wavelet Transform as an Alternative to Power Transformation in Time Series Analysis. Bulletin of Mathematical Sciences and Applications Vol. 17, pp 57-74, SciPress Ltd., Switzerland.https://doi.org/10.18052/www.scipress.com/BMSA.17.57.

      [16] Phillips, P. C. and Perron, P. (1988). Testing for a unit root in time series regression. Biometrika.75(2), 335-346.https://doi.org/10.1093/biomet/75.2.335.

      [17] Robinson, P. M. (2003), Time Series with Long Memory, Advanced Texts in Econometrics, Oxford Univ. Press, New York.

      [18] Ruey, S.T. (1988). Outliers, level shift and variance changes in time series. Journal of Forecasting, 7, 1-20.https://doi.org/10.1002/for.3980070102.

      [19] Said, S. E. and Dickey, D. A. (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.

      [20] Stefan, L., Tomas, V. and Eduard, B. (2011). Unit root and stationary testing with empiricalapplication on industrial production of Central Eastern Europe countries. Munich personal repec Archive No. 29648.

      [21] Tse, R. Y. C. (1997). An application of the ARIMA model to real-estate prices in Hong Kong. Journal of Property Finance, 8 (2) 152-163.https://doi.org/10.1108/09588689710167843.

      [22] Wei, W. S. (1990). Time Series Analysis: Univariate and Multivariate Methods (2nd Edition). Pearson Addison-Wesley Publishing Company, Inc. USA.

      [23] Zhang, B. L., Coggins, R., Jabri, M.A., Dersch, D. and Flower, B. (2001). Multiresolution forecasting for future trading using wavelet decompositions. Institute of electrical and Electronic Engineers Transactions on Neural Networks,12(4), 765-775.https://doi.org/10.1109/72.935090.

      [24] Zhang, G. P. and Qi, M. (2005). Neural network forecasting for seasonal and trend time series. European Journal of Operational Research, 160(2), 501-514.https://doi.org/10.1016/j.ejor.2003.08.037.

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  • How to Cite

    Chukwudi Justin, O., Chijioke Joel, N., & Kelechi Charity, O. (2019). Penalty of model misspecification in time series dominated with trend. International Journal of Advanced Mathematical Sciences, 7(1), 6-15. https://doi.org/10.14419/ijams.v7i1.29731