Applications of the Natural Cubic Spline Function to Estimate Financial Volatilities and Time-varying Correlations of the ASEAN-5 Financial Time Series

Abstract

This thesis introduced methods to investigate financial stability and financial integration in ASEAN. The natural cubic spline function with quantile knots was applied to financial time series, including the stock market indexes, the bilateral exchange rates to the United States dollar, and the effective exchange rates during two decades from January 1, 2001 to December 31, 2020 of the ASEAN-5, including Thailand, Singapore, Malaysia, Indonesia, and the Philippines. Initially, this study estimated financial volatilities of the investigated series by applying the natural cubic spline function with 22 quantile knots, that had an approximately one trading-year interval between them. The results showed that during the global financial crisis the estimated natural cubic spline volatilities dramatically increased, reflecting an instability in time of crisis. In addition, the Monte Carlo simulation demonstrated that the natural cubic spline volatility revealed more precise volatility’s pattern than the smoothing GARCH (1,1) volatility method introduced in previous study. To investigate the financial integration in this region, this study alternatively estimated time-varying correlation coefficients of the ASEAN-5 stock indexes with a new method based on the indirect covariance concept and the natural cubic spline volatility. The estimated time-varying correlation coefficients consequently exhibited that in time of the global financial crisis these five stock market indexes were more likely to change in the same direction and after the declaration of the ASEAN Economic Community blueprints in 2007, these stock market indexes had stronger linkages, indicating the emerging financial integration in this region. Moreover, the simulation showed that the time-varying correlation coefficients estimated following this method, better in revealing varying patterns of time-varying correlation coefficients than the other three estimators, consisting of the backward rolling correlation coefficient estimator, the centered rolling correlation coefficient estimator, and the dynamic conditional correlation model. This thesis also investigated the use of model selection criteria in selecting a number of quantile knots for the natural cubic spline function in the financial volatility estimation. The simulation presented that the Generalized Cross-Validation was a superior criterion than the other three candidates including the Akaike’s Information Criteria, the Bayesian Information Criteria, and the modified Generalized Cross-Validation. Then, the volatilities of the bilateral exchange rates and the effective exchange rates of the ASEAN-5 were estimated by the natural cubic spline function with a number of quantile knots selected by the Generalized Cross-Validation. The results showed that the bilateral exchange rate generally had higher volatility than the effective exchange rate, reflecting the influence of the United Stated dollar on the stability of the bilateral exchange rates and volatility of bilateral exchange rate was impacted by its concurrent adopted exchange rate policy. Applying the natural cubic spline function for estimating financial volatility and time-varying correlation coefficients was found practical to investigate financial stability and financial integration in the ASEAN and could be broadly adopted for estimating financial volatility and time-varying correlation coefficients of the other financial time series as well.