Abstract:
The quantity of rainfall and its related events have become
more and more uncertain due to climatic variability. The complexity
of the rainfall pattern increases due to the changes of the atmospheric
behavior from time to time. Relatively, few measures have been taken
to perform the modeling of rainfall in the context of long memory.
This paper provides an assessment of such a phenomenon by fitting an
appropriate time series model. A long range dependency model is proposed
to fit weekly rainfall data to explore characteristics of persistence
through an unbounded spectral density. Careful examination of the data
exhibits periodic fluctuations as an additional feature. Since, the rainfall
series exhibits periodic variations and persistence, a seasonal autoregressive
fractionally integrated moving average (SARFIMA) model is fitted.
Parameters of it are estimated using maximum likelihood estimation
(MLE) method. A Monte Carlo simulation was carried out with different
seasonal and non seasonal fractionally differing parameters to measure
the suitability of the method for parameter estimation. Best fitted
model is chosen based on the minimum of the mean absolute error and
the forecasting performance are compared with the result of Seasonal
autoregressive integrated moving average (SARIMA) using an independent
sample as a creative contribution.
