Quantitative Estimation of Periodicities in Lyari River Flow Routing
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:60053", author = "Rana Khalid Naeem and Asif Mansoor", title = "Quantitative Estimation of Periodicities in Lyari River Flow Routing", 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.", volume = "2", number = "1", pages = "32-6", }