Structural breaks in volatility: the case of UK sector returns

Abstract

Evidence in favour of long memory has recently been questioned by tests that allow for structural breaks. This article tests for periodic breaks in the unconditional variance of stock return data on eight UK sectors, as well as the market index. Using the modified Iterative Cumulative Sum of Squares (ICSS) algorithm, we observe breaks in seven sectors and the index series. The breaks range from two or three for basic materials and industrials, to five and more for financials, technology and the telecoms sector. Hence, the more traditional stocks exhibit fewer breaks than the newer sectors. The implications of such breaks are numerous, in terms of volatility dynamics and forecasting and portfolio management. With respect to volatility dynamics, further analysis reveals that accounting for breaks substantially reduces the degree of persistence over a Generalized Autoregressive Conditional Heteroscedastic (GARCH) model that maintains a constant unconditional variance. Moreover, the mean to which volatility reverts is time varying; as such, failure to account for breaks will lead to severe forecast errors. Regarding portfolio management, there is substantial evidence of sector specific volatility breaks. Hence, estimation of a market model over the whole sample will lead to errors in both the riskiness of individual sectors and the ability to take advantage of possible above market returns.

Keywords:

• volatility
• GARCH model
• structural breaks
• persistence
• market model

JEL Classification::

• C22
• G11
• G12

Notes

¹ Also see Kim and Kon (1999) and Granger and Hyung (2004). Intuitively, over-estimating the degree of persistence in volatility by failing to account for structural breaks is related to the argument made by Perron (1989) in the context of unit root testing: failure to account for periodic breaks in the mean (or linear trend) of a stationary series can lead one to over-estimate the degree of persistence in the series and fail to reject the null hypothesis of a unit root (Type II error).

² In the context of exchange rate return volatility forecasting, West and Cho (1995) speculate that the forecasting performance of GARCH models could be improved by allowing for structural breaks in the unconditional variance.

³ Malik (2003) investigated five major exchange rates from January 1990 to September 2000 and found lower persistence in volatility if the standard GARCH model is augmented with the determined breakpoints in volatility. Rapach and Strauss (2008) investigate the empirical importance of structural breaks for GARCH models of exchange rate volatility employing both in-sample and out-of-sample tests. They find significant evidence of structural breaks in the unconditional variance in seven of eight US dollar exchange rate return series over the period 1980 to 2005, implying an unstable GARCH process for these exchange rate series. They also find that the parameters of a GARCH(1,1) model of these series vary significantly over subsamples defined by the structural breaks.

⁴ This Section draws heavily from Rapach et al. (2009).

⁵ The size distortions increase with the sample size.

⁶ Note that it is not necessary that just because the market is a finite average of all sectors, it should exhibit breaks at every point that each of the single component exhibit breaks. In finite samples one will get different results.