A conditional variance tale from an emerging economy's freely floating exchange rate

Abstract

This article studies daily return and volatility dynamics in the exchange rate of an emerging market economy Turkey over the recent floating period. We use Generalized Autoregressive Conditional Heteroscedastic (GARCH) and Fractionally Integrated GARCH (FIGARCH) models with various error distributions. Findings show that a parsimonious FIGARCH model with an asymmetric error distribution characterizes the daily Turkish Lira (TL) returns against US dollar and euro considerably well. We find statistically significant asymmetry and peakedness in conditional returns and time-varying volatility with long-range dependence in conditional volatility. Long memory finding is robust to different specifications for the conditional returns as well as possible shifts in the return and volatility dynamics over sub-periods. Results in the article show that despite the decline in volatility over the course of the recent float, TL returns are still wild compared to developed economies exchange rates during the same period. Findings have implications for exchange rate regime choice, policy and risk management in Turkey and other emerging market economies.

Notes

¹ For a technical definition of long memory in the context of volatility, see Baillie et al. (1996) and Davidson (2004). The GARCH models have short memory as such shocks have ‘less’ persistent effects or ‘short-lived effects’ on the conditional volatility. The FIGARCH process implies a slow hyperbolic rate of decay for the autocorrelations of volatility process, which is a characteristic of long memory processes. As Davidson (2004) shows, FIGARCH model possesses more memory than GARCH and integrated GARCH models.

² Obstfeld and Rogoff (1995) and Mussa et al. (2000) are examples of advocates of free floating, while Reinhart (2000) and Calvo and Reinhart (2002) tend to argue the usefulness of a pegged exchange rate regime for the emerging economies. Tavlas (2003) provides a review of exchange rate systems, emphasizing the choice of exchange rate regime for an emerging economy.

³ For excellent accounts of transformation process in the aftermath of the deep crisis in Turkey, see Ardıç and Selçuk (2006) and Basçı et al. (2007) and references in these articles.

⁴ The FIGARCH model has been used extensively in modelling volatility dynamics and long memory in commodities, equities and exchange rate returns in a number of recent articles. In addition to Baillie et al. (1996), examples include Morana and Beltratti (2004), Baillie et al. (2000), Brunetti and Gilbert (2000), Kiliç (2004, 2007, 2008) among others.

⁵ For details of statistical properties of NIG distribution, see Barndorff-Nielsen (1978).

⁶ We used Berndt–Hall–Hall–Hausman (BHHH) algorithm with numerical derivatives in Gauss to maximize the likelihood functions. In each case, different starting values for the parameters are used to check the global maximum. The results were robust to different initial values. Following Conrad and Haag (2006), we have also checked the necessary and sufficient conditions for the nonnegativity of conditional variance process for the FIGARCH models. All estimated models satisfied the conditions stated in Conrad and Haag (2006). These results are available on request.

⁷ The PIT is defined as , where f(u) is the probability density function for the random variable x. As shown in Diebold et al. (1998), if f(·) is the correct distribution, then z_t ∼ U(0, 1) and therefore z_t and its power transformations should be independent and identically distributed (i.i.d.) as well. See Forsberg and Bollerslev (2002) and Kiliç (2007) for applications of this approach in checking for the adequacy of estimated GARCH and FIGARCH models with different error distributions.

⁸ In order to examine AR and MA components in the conditional returns, following Ardıç and Selçuk (2006), we have estimated ARMA(2,1) models with GARCH and FIGARCH effects on the conditional volatility. Estimation results show that ARMA terms are usually statistically insignificant. Beyond the statistical significance, a major issue with respect to estimated ARMA (2,1) models is the potential over parametrization. Estimated AR and MA parameters in most cases are in the same order with opposite signs suggesting root cancellations (see also Hamilton (1994, pp. 60, 61) on over parametrizations in ARMA models). Moreover, log-likelihood values are not very different from the values reported in Tables 2 and 3. Diagnostic tests, log-likelihood and information criteria show that pure FIGARCH models usually outperform ARMA (2, 1) – GARCH/FIGARCH models in several fronts. To conserve space, we do not report these results. Full estimation results can be obtained upon request.

⁹ It should also be noted that estimated values for a are uniform across GARCH and FIGARCH specifications for each currency and do not change much whether we have restricted b = 0 or not in the NIG distribution. Results with b = 0 in NIG distribution can be obtained upon request.

¹⁰ In addition, following Diebold et al. (1998), Forsberg and Bollerslev (2002) and Kiliç (2007), we have obtained empirical quantile (QQ-plot) plots for the PITs from the FIGARCH models with normal, Student's t and NIG distributions. Careful inspection of the plots shows that FIGARCH–NIG models outperform alternatives as the quantiles for the PITs of residuals from FIGARCH–NIG are almost indistinguishable from the quantiles of an uniform distribution for both return series. For the estimated models to be correctly conditionally calibrated, the corresponding sequence of PITs should be i.i.d. through time with an uniform distribution as shown in Diebold et al. (1998). To conserve space, we do not display these plots which can be obtained upon request.

¹¹ We have also obtained histograms for the simulated LR statistics under each null hypotheses. These plots can be obtained upon request.

¹² A FIGARCH(1, d, 1)-NIG model found to fit these major currencies better than the alternatives. Since the estimated conditional SDs were qualitatively similar, we have plotted results only for the dollar–euro returns. Complete results can be obtained upon request.

¹³ We re-estimated FIGARCH models model with normal, t and NIG errors for the period 23 February 2001 to 13 February 2006 and left observations for the period 14 February 2006 to 13 February 2008 for forecasting.

¹⁴ Based on a binomial approximation, a 95% confidence interval for the quantile predictions can be computed as where refers to the empirical size and n is the number of 1-day ahead quantile predictions. Note that n = 255 and 52 for 1- and 5-day ahead VaRs, respectively.

¹⁵ Not reported for space considerations, we have also estimated GARCH and FIGARCH models with ARMA(2, 1) for the conditional return process over the subperiods. Consistent with Ardıç and Selçuk (2006), results suggest the presence of some ARMA effects especially for the initial subperiod. ARMA components in the conditional returns tend to weaken over the subsequent periods however, especially under the FIGARCH–NIG specification for the conditional variance. This finding might be partly due to small sample size over the subperiods and/or partly due to the fact that NIG model allows us to model explicitly both asymmetry and kurtosis in the distribution of the returns. Findings may also be consistent with the idea that as the experience of a country under the float deepens over time, the information content of past exchange rate returns decline. This would be expected especially under the inflation targeting policy short-term interest rates increasingly used by the Central Bank of Turkey to respond to deviations of inflation from the targeted path (see also Basçı et al., 2007).

¹⁶ As of January 2008, current account deficit is more than 7% of real output, one of the highest among emerging economies, see the Commercial Banks Review and Training (CBRT) web page.