Modelling long memory in maximum and minimum temperature series in India

Abstract

Time series analysis of weather data can be a very valuable tool to investigate its variability pattern and, maybe, even to predict short- and long-term changes in the time series. In this study, the long memory behaviour of monthly minimum and maximum temperature of India for the period 1901 to 2007 by means of fractional integration techniques has been investigated. The results show that the time series can be specified in terms of autoregressive fractionally integrated moving average (ARFIMA) process. Both the series were found to be integrated with orders of integration smaller than 0.5 ensuring the long memory stationarity. Wavelet methodology in frequency domain with Haar wavelet filter was applied in order to see the oscillation at different scale and at different time epochs of the series. Multiresolution analysis (MRA) was carried out to explore the local as well as global variations in both the temperature series over the years. The variability in minimum temperature is found to be more than maximum temperature. Though there is no clear significance trend in the temperature series in the long run, but there are pockets of change in the temperature pattern. The predictive ability of ARFIMA model was investigated in terms of relative mean absolute percentage error.