Functional time series analysis of age-specific fertility rates: visualizing the change in the age-pattern of fertility in India

  • Authors

    • Mallika Deb North-Eastern Hill University
    • Tapan Kumar Chakrabarty North-Eastern Hill University
    2016-06-17
    https://doi.org/10.14419/ijasp.v4i2.6182
  • Age-Specific Fertility Rates, Cubic Spline Interpolation Smoothing, Fertility Forecasting, Functional Time Series Analysis, Principal Component.

  • Functional Time Series Analysis (FTSA) is carried out in this article to uncover the temporal variations in the age pattern of fertility in India. Attempt is made to find whether there is any typical age pattern in the nation’s fertility across the reproductive age groups. If so, how do we characterize the role of changing age pattern of fertility across reproductive age groups in the nation’s fertility transition? We have used region-specific (rural-urban) and country level data series on Age-Specific Fertility Rates (ASFRs) available from Sample Registration System (SRS), India during 1971-2013. Findings of this study are very impressive. It is observed that the youngest age group of women in 15-19 years has contributed to the maximum decline in fertility with a substantially accelerated pace during the period of study. The major changes in fertility rates among Indian women dominated by the rural representation occur at the ages after 30. Further, the study also suggests that the future course of demographic transition in India from third phase to the fourth phase of replacement fertility would depend on the degree and pace of decline among the rural women aged below 30 years.

  • References

    1. [1] Besse, P. C and Cardot, H., “Autoregressive Forecasting of Some Functional Climatic Variationsâ€, Scandinavian Journal of Statistics, Vol.27, No.4, (2000), pp.673-687. http://empslocal.ex.ac.uk/people/staff/dbs202/publications/2000/besse.pdf

      [2] Box, G. E. P. and Jenkins, G. M., Time Series Analysis: Forecasting and Control, Holden-Day: Wiley Series in Probability and Statistics, (1976).

      [3] Chakrabarty, T. K., “Forecasting rate of decline in infant mortality in South Asia using random walk approximationâ€, International Journal of Statistics in Medical Research, Vol.3, No.3, (2014), pp.282-290. http://dx.doi.org/10.6000/1929-6029.2014.03.03.7

      [4] Chakrabarty, T. K. and Deb, M., “Is India on the Path to Replacement Fertility soon? Exploring the Role of Rural-Urban Differential Pace and Timing of Fertility Declineâ€, (2015). Forthcoming.

      [5] Ferraty, F. and Vieu, P., Nonparametric functional data analysis: theory and practice, Springer, New York, 2006.

      [6] Green, P. and Silverman, B., Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman and Hall, (1994).

      [7] H¨ormann, S. and Kokoszka, P., “Weakly dependent functional dataâ€, The Annals of Statistics, Vol.38, No.3, (2010), pp.1845-1884. http://projecteuclid.org/euclid.aos/1269452656

      [8] Hyndman, R. J. and Ullah, M. S., “Robust forecasting of mortality and fertility rates: a functional data approachâ€, Computational Statistics and Data Analysis, Vol.51, No.10, (2007), pp.4942-4956. http://www.sciencedirect.com/science/article/pii/S0167947306002453

      [9] Hyndman, R. J. and Booth, H., “Stochastic population forecasts using functional data models for mortality, fertility and migrationâ€, International Journal of Forecasting, Vol.24, No.3, (2008), pp.323-342. http://www.sciencedirect.com/science/article/pii/S0167947306002453

      [10] Hyndman, R. J. and Shang, H. L., “Forecasting functional time seriesâ€, Journal of the Korean Statistical Society, Vol.38, No.3, (2009), pp.199-221. http://www.sciencedirect.com/science/article/pii/S1226319209000398

      [11] Hyndman, R. J. and Shang, H. L., “Rainbow plots, bagplots, and boxplots for functional dataâ€, Journal of Computational and Graphical Statistics, Vol.19, No.1, (2010), pp.29-45. http://www.tandfonline.com/doi/abs/10.1198/jcgs.2009.08158

      [12] Ramsay, J. and Dalzell, C. J., “Some tools for functional data analysisâ€, Journal of the Royal Statistical Society. Series B, Vol.53, No.3, (1991), pp.539-572. http://www.jstor.org/stable/2345586?seq=1#page_scan_tab_contents

      [13] Ramsay, J. O. and Silverman, B. W., Functional Data Analysis, Springer, New York, 1997.

      [14] Ramsay, J. O. and Silverman, B.W., Applied Functional Data Analysis, Springer, New York, 2002.

      [15] Ramsay, J. O. and Silverman, B. W., Functional Data Analysis, Second edition, Springer, New York, 2005.

      [16] Retherford, R. D. and Mishra V. K., “An Evaluation of Recent Estimates of Fertility Trends in Indiaâ€, National Family Health Survey Subject Reports, Vol.19, Mumbai: International Institute for Population Sciences; Honolulu: East-West Center, 2001. http://scholarspace.manoa.hawaii.edu/bitstream/handle/10125/3473/NFHSsubjrpt019.pdf?sequence=1

      [17] RGI (Registrar General of India). Compendium of India’s Fertility and Mortality Indicators, 1971-2013: Based on the Sample Registration System, New Delhi. Office of the Registrar General. http://censusindia.gov.in

      [18] RGI (Registrar General of India). Sample Registration System annual report 49, New Delhi. Office of the Registrar General, 2014. http://censusindia.gov.in

      [19] Shang, H. L., “rainbow: an R package for visualizing functional time seriesâ€, The R Journal, Vol.3, No.2, (2011), pp.54-59. https://journal.r-project.org/archive/2011-2/RJournal_2011-2_Lin~Shang.pdf

      [20] Shang, H. L., “ftsa: An R Package for Analyzing Functional Time Seriesâ€, The R Journal, Vol.5, No.1, (2013), pp.64-72. https://journal.rproject.org/archive/2013-1/shang.pdf

      [21] Shang, H. L. and Hyndman, R. J., “Nonparametric time series forecasting with dynamic updatingâ€, Mathematics and Computers in Simulation, Vol.81, No.7, (2011), pp.1310-1324. http://www.sciencedirect.com/science/article/pii/S037847541000145X

      [22] Spoorenberg, T. and Dommaraju, P., “Regional Fertility Transition in India: An Analysis Using Synthetic Parity Progression Ratiosâ€, International Journal of Population Research, Vol.2012, (2012), pp.1-20. http://dx.doi.org/10.1155/2012/358409

      [23] Yasmeen, F., Waseem, H. F. and Mahmood, Z., “An FDA Approach to Forecast Age-Specific Fertility Rates of Pakistan Region-Wiseâ€, Computer Science and Applications, Vol.1, No.6, (2014), pp.341-348. http://dx.doi.org/10.1155/2012/358409

  • Downloads

    Additional Files