Statistical modeling of Tamil nadu annual rainfall

The annual rainfall data for a period of 63 years (1950-2012) of Tamil Nadu have been analyzed for climatologically pattern and trend. Climate change for a region can be analyzed only on a long–term average. Detecting climate change with seasonal variability is difficult, thus we have considered the annual rainfall to analyze any change in the climatic trend of Tamil Nadu and forecast the rainfall for the year 2013. The non parametric Mann-Kendall test is used for trend analysis. This resulted with h=0 and p-value = 0.4609 for an alpha value of 0.05. These values do not give us sufficient evidence to reject the null hypothesis (no trend) for the Tamil Nadu annual rainfall series. This result has led us to estimate the stationarity of the rainfall data. Dickey fuller unit root test was done to study the stationarity in the rainfall data. The result h=1 resulted in rejection the presence of stationatiry in the data series. Thus the rainfall data is a non-stationary series. With these preliminary statistical analysis attempt was made to predict the annual rainfall for the year 2013 for Tamil Nadu on a monthly basis. The Box-Jenkins time series seasonal ARIMA (Auto Regression Integrated Moving Average) approach was used for the forecast of annual rainfall on monthly scales. Past years data was used to formulate the seasonal ARIMA model and in determination of model parameters.