International Journal on Advanced Science, Engineering and Information Technology, Vol. 8 (2018) No. 4, DOI:10.18517/ijaseit.8.4.3107

Natural Cubic Spline Model for Estimating Volatility

Farida -, Nifatamah Makaje, Phattrawan Tongkumchum, Aniruth Phon-On, Jetsada Laipaporn

Abstract

Volatility measures the dispersion of returns for a market variable since a good estimation of the volatility is an appropriate starting point for assessing investment risks and monetary policy making. The well-known method for volatility estimation is the GARCH (1,1) model. However, the recursive term in this model makes finding the derivatives of the likelihood function mathematically intractable. This paper, therefore, presents the natural cubic spline model to estimate the volatility by fitting it to the absolute returns of the data. The Maximum Likelihood method was used to estimate the parameters and a simple algebra was used to find its derivatives. The damped Newton-Raphson method was then used to maximize the likelihood function with the R programming software. The proposed method was illustrated using crude oil price data from West Texas Intermediate and it showed similar results with the well-known GARCH (1,1) model. The natural cubic spline can therefore, be an alternative for estimating the volatility of any financial time series data, even though it was applied to one data set.

 

Keywords:

volatility; natural cubic spline model; the damped Newton-Raphson method; maximum likelihood method; GARCH (1,1) model

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