Modeling fractionally integrated maximum temperature series in India in presence of structural break
- 95 Downloads
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.
We would like to express our sincere thanks to the anonymous reviewers for their valuable suggestions that helped us a lot in improving this manuscript.
Compliance with ethical standards
Conflict of interests
The authors declare that they have no conflict of interests regarding the publication of this paper.
- Aggarwal PK (2009) Vulnerability of Indian agriculture to climate change: current state of knowledge, paper presented at the National Workshop – Review of Implementation of Work Programme towards Indian Network of Climate Change Assessment, October 14. Ministry of Environment and Forests, New Delhi http://moef.nic.in/downloads/others/Vulnerability_PK%20Aggarwal.pdf Google Scholar
- Beran J (1995) Statistics for long memory processes. Chapman & HallGoogle Scholar
- Birthal PS, Negi DS, Kumar S, Aggarwal S, Suresh A, Khan T (2014) How sensitive is Indian agriculture to climate change? Indian Journal of Agricultural Economics 69(4):474–487Google Scholar
- Hurst HE (1951) Long term storage capacity of reservoirs. Trans Am Soc Agric Eng 116:770–799Google Scholar
- Mallows CL (1973) Some comments on Cp. Technometrics 15:661–675Google Scholar
- Malamud BD and Turcotte DL (1999) Advances in geophysics: long range persistence in geophysical time series, self-affine time series: I. Generation and analysis, Dmowska R and Saltzman B (ed.), pp 1–87. Academic press, San DiegoGoogle Scholar
- Mantis HT, Dickey WW (1945) Objective methods of forecasting the daily minimum and maximum temperature. In: Report number 4. Army Air Force, Weather Station, New York University, U.S.Google Scholar
- Nagarajan R (2009) Drought assessment. Springer, The NetherlandGoogle Scholar
- Paul RK, Birthal PS and Khokhar A. (2014) Structural breaks in mean temperature over agro-climatic zones in India. Sci World J. http://dx.doi.org/10.1155/2014/434325
- Paul RK, Birthal PS, Paul AK, Gurung B (2015a) Temperature trend in different agro-climatic zones in India. Mausam 66(4):841–846Google Scholar
- Paul RK, Samanta S, Gurung B (2015b) Monte Carlo simulation for comparison of different estimators of long memory parameter: an application of ARFIMA model for forecasting commodity price. Model Assist Stat Appl 10(2):116–127Google Scholar
- Paul RK (2017) Modelling long memory in maximum and minimum temperature series in India. Mausam 68(2):317–326Google Scholar
- Spreen WC (1956) Empirically determined distributions of hourly temperatures. J Atmos Sci 13:351–355Google Scholar