Modeling fractionally integrated maximum temperature series in India in presence of structural break

In this study, the long memory behaviour of monthly maximum temperature of India for the period 1901 to 2007 is investigated. The correlogram of the series reveals a slow hyperbolic decay, a typical shape for time series having the long memory property. Wavelet transformation is applied to decompose the temperature series into time–frequency domain in order to study the local as well as global variation over different scale and time epochs. Significant increasing trend is found in the maximum temperature series in India. The rate of increase in maximum temperature accelerated after 1960s as compared to the earlier period. Here, an attempt is also made to detect the structural break for seasonally adjusted monthly maximum temperature series. It is found that there is a significant break in maximum temperature during July, 1963. Two-stage forecasting (TSF) approach to deal with the coexistence of long memory and structural change in temperature pattern is discussed thoroughly. The forecast performance of the fitted model is assessed on the basis of relative mean absolute prediction error (RMAPE), sum of squared errors (SSE) and mean squared errors (MSE) for different forecast horizons.