Modelling Conditional Volatility of Saving Rate by a Time-Varying Parameter Model

Authors: Katleho D. Makatjane, Kalebe M. Kalebe

Abstract:

The present paper used time-varying parameters which are based on the score function of a probability density at time t to model volatility of saving rate. We used a scaled likelihood function to update the parameters of the model overtime. Our results revealed high diligence of time-varying since the location parameter is greater than zero. Furthermore, we discovered a leptokurtic condition on saving rate’s distribution. Kapetanios, Shin-Shell Nonlinear Augmented Dickey-Fuller (KSS-NADF) test showed that the saving rate has a nonlinear unit root; therefore, it can be modeled by a generalised autoregressive score (GAS) model. Additionally, value at risk (VaR) and conditional tail expectation (CTE) indicate that 99% of the time people in Lesotho are saving more than spending. This puts the economy in high risk of not expanding. Therefore, the monetary policy committee (MPC) of Lesotho should revise their monetary policies towards this high saving rates risk.

Keywords: Generalized autoregressive score, time-varying, saving rate, Lesotho.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1474469

References:

[1] Ardia, D., K. Boudt, and L. Catania, Generalized Autoregressive Score Models in R: The GAS Package. 2016.
[2] Bernardi, M. and L. Catania, Switching-GAS copula models for systemic risk assessment. arXiv preprint arXiv:1504.03733, 2015.
[3] Chowdhury, S.S.H., A.T. Mollik, and M.S. Akhter, Does predicted macroeconomic volatility influence stock market volatility? Evidence from the Bangladesh capital market. University of Rajshahi, Bangladesh, 2006
[4] Creal, D., S.J. Koopman, and A. Lucas, Generalized autoregressive score models with applications. Journal of Applied Econometrics, 2013. 28(5): p. 777-795.
[5] Angle, R.F. and T. Bollerslev, Modelling the persistence of conditional variances. Econometric reviews, 1986. 5(1): p. 1-50.
[6] Harvey, A.C., Dynamic models for volatility and heavy tails: with applications to financial and economic time series. Vol. 52. 2013: Cambridge University Press.
[7] Hassan, S.A. and F. Malik, Multivariate GARCH modelling of sector volatility transmission. The Quarterly Review of Economics and Finance, 2007. 47(3): p. 470-480.
[8] Huang, C.-S. and C.-K. Huang, Assessing The Relative Performance Of Heavy-Tailed Distributions: Empirical Evidence From The Johannesburg Stock Exchange. Journal of Applied Business Research, 2014. 30(4): p. 1263.
[9] Huang, C.K., C.S. Huang, and J. Hammujuddy, Empirical Analyses of Extreme Value Models for the South African Mining Index. South African Journal of Economics, 2015. 83(1): p. 41-55.
[10] Janus, P., S.J. Koopman, and A. Lucas, Long memory dynamics for multivariate dependence under heavy tails. Journal of Empirical Finance, 2014. 29: p. 187-206.
[11] Kapetanios, G., Y. Shin, and A. Snell Testing for a unit root in the nonlinear STAR framework. Journal of econometrics, 2003. 112(2): p. 359-379.
[12] Lanne, M., Forecasting realized exchange rate volatility by decomposition. International Journal of Forecasting, 2007. 23(2): p. 307-320.
[13] Makatjane, K., D. Xaba, and N. Moroke, Application of Generalized Autoregressive Score Model to Stock Returns. World Academy of Science, Engineering and Technology, International Journal of Social, Behavioral, Educational, Economic, Business and Industrial Engineering, 2017. 11(11): p. 2528-2531.
[14] Makatjane, K.D. and T.J. Makatjane, Factors that associated with the academic performance of First-year students at the National University of Lesotho: structural equation modelling approach. International Journal of Statistics and Applied Mathematics, 2017(1): p. 42-49.
[15] Opschoor, A., et al., New HEAVY models for fat-tailed realized covariances and returns. Journal of Business & Economic Statistics, 2017: p. 1-15.
[16] Rapach, D.E. and J.K. Strauss, Structural breaks and GARCH models of exchange rate volatility. Journal of Applied Econometrics, 2008. 23(1): p. 65-90.
[17] Tsay, R.S., Analysis of financial time series. Vol. 543. 2005: John Wiley & Sons.
[18] Wentzel, D. and E. Mare, Extreme value theory—An application to the South African equity market. Investment Analysts Journal, 2007. 36(66): p. 73-77.