Quantitative Estimation of Periodicities in Lyari River Flow Routing

Authors: Rana Khalid Naeem, Asif Mansoor

Abstract:

The hydrologic time series data display periodic structure and periodic autoregressive process receives considerable attention in modeling of such series. In this communication long term record of monthly waste flow of Lyari river is utilized to quantify by using PAR modeling technique. The parameters of model are estimated by using Frances & Paap methodology. This study shows that periodic autoregressive model of order 2 is the most parsimonious model for assessing periodicity in waste flow of the river. A careful statistical analysis of residuals of PAR (2) model is used for establishing goodness of fit. The forecast by using proposed model confirms significance and effectiveness of the model.

Keywords: Diagnostic checks, Lyari river, Model selection, Monthly waste flow, Periodicity, Periodic autoregressive model.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076460

References:

[1] J.D. Salas, G.Q. Tabios III and P. Bartolini, "Approaches to multivariate modeling of water resources time series," Water Resources Bulletin, vol. 21, pp. 683-708,1985.
[2] J.D. Salas, Analysis and modeling of hydrologic time series. D.R. Maidment, ed., McGraw-Hill, Handbook of Hydrology, 1993, Scetion.19.5-19.9.
[3] G.E.P. Box, G.M. Jenkins, and G. C. Reinsel, Time Series Analysis: Forecasting and Control. India: Pearson Education, 2003.
[4] A.C. Harvey, Forecasting Structural Time Series and Kalman Filter. Cambridge: Cambridge University Press, 1989.
[5] S. Hylleberg, R.F. Engle, C.W.J. Granger, and B. Yoo, "Seasonal integration and cointegration," Journal of Econometrics, vol 44, pp. 215- 238,1990.
[6] P.H. Franses, and R. Paap, Periodic Time Series Models. United Kingdom: Oxford University Press, 2004.
[7] H.L. Hurd, and N.L. Gerr, "Graphical method for determining the presence of periodic autocorrelation," Journal of Time Series Analysis, vol.12, pp. 337-350, 1991.
[8] P. Bloomfield, H.L. Hurd, and R.B. Lund, "Periodic correlation in stratospheric ozone data," Journal of Time Series Analysis, vol.15, pp.127-150,1994.
[9] M. Bentarzi, and M. Hallins, "Locally optimal test against periodical autoregression: Parametric and nonparametric approaches," Econometric Theory, vol.12, pp. 88-112, 1996.
[10] H. Akaike, "Fitting autoregressive model models for prediction," Annals of the Institute of Statistical Mathematics, vol. 21, pp. 243-247, 1969.
[11] G. Schwarz, "Estimating the dimension of a model," Annals of Statistics, vol.6, pp. 461-464,1978.