The effect of non-trading days on volatility forecasts in equity markets
Introduction
Daily time series are probably the most commonly used data in empirical finance. The main advantage of these data is that they usually represent the highest frequency freely available for various datasets. In addition, for many purposes, daily time series can be considered regularly spaced data, and standard time series techniques can be applied to them. However, most financial data exist only for trading days. As we show in this paper, considering this trading gap can significantly improve the performance of models in some cases.
Many time series data exhibit autoregressive properties, meaning that a variable's value today is related to its value tomorrow. If we can more precisely capture this relationship, our models will be more precise. However, in case of daily financial series, data usually exist for weekdays but not for weekends or holidays. Weekends can be considered a break in the data or days with missing data. In either case, the dependence between two consecutive trading days, for example, Wednesday and Thursday, can be intuitively expected to be stronger than the dependence between two trading days separated by a weekend or holiday, for example, Monday and Friday. If we ignore these differences and assume the same dependence throughout the week, we will likely underestimate the dependence between consecutive weekdays and overestimate the dependence between Friday and Monday. We suggest that allowing the autoregressive coefficient to be dependent on whether a weekend separates the two observations sufficiently addresses this issue.
Obviously, this effect does not matter when very little dependence is reflected in the data. In the literature, volatility is understood to have a long memory (Bollerslev and Mikkelsen, 1996). In the empirical part of our paper, we thus focus on volatility. Volatility is not directly observable, but the concept of realized volatility (RV) calculated from high-frequency data (Andersen and Bollerslev, 1998) makes it observable for practical purposes. Models based on RV have been applied to stock markets (e.g., Christoffersen et al., 2010, Bugge et al., 2016), exchange rates (e.g., Andersen et al., 2001, Lyócsa et al., 2016), and commodities (Haugom et al., 2014, Birkelund et al., 2015, Lyócsa and Molnár, 2016). We thus focus on RV.
Long memory and the persistence of market volatility have led previous research to use fractionally integrated time series models (e.g., Bollerslev and Mikkelsen, 1996). However, the most popular model is the heterogeneous autoregressive (HAR) model of Corsi (2009), which captures the long-memory property as accurately as competing models and is easy to implement. We suggest a simple extension of this model, the NT-HAR model (non-trading days HAR), which allows the autoregressive coefficient to be dependent on whether a non-trading period occurs between two observations.
The data that we use in the empirical evaluation of our model are RV series for 21 equity indices around the globe, including equity indices for Brazil, Canada, China, France, Germany, Greece, India, Italy, Japan, Mexico, Singapore, South Korea, Spain, Switzerland, and the U.K.; three indices for U.S.; and one index for the Eurozone. We find that, in most cases, the NT-HAR model outperforms the benchmark HAR model, both in sample and out of sample.
The rest of the paper is organized as follows. Section 2 intuitively explains our model using a simulation example. Section 3 describes the data and the methodology; Section 4 presents the results; and Section 5 concludes.
Section snippets
Illustrative example
Our motivation can be intuitively explained as follows: given the measure of daily market volatility RVi,t, the lagged market volatility RVi,t-1 does not always precede the predicted volatility at time t by one calendar day. On average, in more than one-fifth of the cases (18.56%), the calendar-day difference between two consecutive days on equity markets is equal to or more than 3 (e.g., see column ``nC” in Table 2). One consequence of non-equidistant observations could be that the lagged
Data and volatility estimators
The predictive regression models used in this study are based on modelling-realized measures of daily volatility RVi,t for the ith stock market index for day t. The standard approach in the literature is to employ the RV given bywhere ri,t,j denotes the jth intraday return. N denotes the number of intraday returns given the length of the trading hours and the sampling frequency.
The literature has recently provided several classes of realized estimators of market volatility, which
Results
Table 2 presents the summary statistics of the returns and RVs of the studied equity indices. In general, summary statistics reveal that these time series behave as expected. Autocorrelation in returns is rather low. By contrast, autocorrelation in RV is high. We can also observe that the days with the highest volatilities and those with the highest and lowest returns typically occur during financial crises or other significant market events.
The last column of Table 2 deserves special
Conclusion
Daily financial time series are usually irregularly spaced due to weekends, holidays and other non-trading days. However, standard time series models ignore this issue, which is most pronounced for highly persistent time series. Volatility usually exhibit long memory, and we therefore study this topic in the context of volatility modelling and forecasting. We suggest a simple way to improve volatility models by incorporating information that some observations occurred after weekends or
References (26)
- et al.
Jump-robust volatility estimation using nearest neighbor truncation
J. Econ.
(2012) - et al.
A comparison of implied and realized volatility in the Nordic power forward market
Energy Econ.
(2015) Generalized autoregressive conditional heteroskedasticity
J. Econ.
(1986)- et al.
Modeling and pricing long memory in stock market volatility
J. Econ.
(1996) - et al.
Implied volatility index for the Norwegian equity market
Int. Rev. Financ. Anal.
(2016) Asymptotic inference under heteroskedasticity of unknown form
Comput. Stat. Data Anal.
(2004)- et al.
An automatic Portmanteau test for serial correlation
J. Econ.
(2009) - et al.
Forecasting volatility of the U.S. oil market
J. Bank. Finance
(2014) - et al.
Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes
J. Econom.
(2015) Volatility forecast comparison using imperfect volatility proxies
J. Econom.
(2011)
Optimal combinations of realised volatility estimators
Int. J. Forecast.
Range-based estimation of stochastic volatility models
J. Finance
Deutsche mark-dollar volatility: intraday activity patterns, macroeconomic announcements, and longer run dependencies
J. Finance
Cited by (15)
Stock market volatility forecasting: Do we need high-frequency data?
2021, International Journal of ForecastingFX market volatility modelling: Can we use low-frequency data?
2021, Finance Research LettersVolatility forecasting using related markets’ information for the Tokyo stock exchange
2020, Economic ModellingCitation Excerpt :Takaishi et al. (2012) analyse realised volatilities using high-frequency TSE listed stock data and they avoid the lack of after-hour’s information in volatility estimations by defining two realised volatilities for the morning and afternoon periods of the TSE. Lyócsa and Molnár (2017) and Díaz-Mendoza and Pardo (2020) state that realised volatility significantly decreases after weekends. Wang et al. (2015) study various trading halts in the Chinese stock market, such as overnight returns, lunch break returns; they conclude that negative overnight returns and negative lunch break returns are important in forecasting volatility.
Heterogeneous market hypothesis approach for modeling unbiased extreme value volatility estimator in presence of leverage effect: An individual stock level study with economic significance analysis
2020, Quarterly Review of Economics and FinanceCitation Excerpt :New approaches to incorporate leverage effect in volatility modeling are proposed in Aït-Sahalia, Fan, Laeven, Wang, and Yang (2017)) and Jin (2017). Also, the recent extensions of the HAR model have been suggested in Lyócsa and Molnár (2017) and Lyócsa and Molnár (2018). The volatility forecasting performance of HAR type models in comparison to GARCH-type, ARFIMA-type, and SV-type models is extensively explored in studies such as Dong and Feng (2018); Gong and Lin (2018); Peng, Chen, Mei, and Diao (2018)), etc.
Holidays, weekends and range-based volatility
2020, North American Journal of Economics and FinanceCitation Excerpt :The first-order autocorrelation coefficients range from 0.357 to 0.597 and they are significant and positive at the 1% level in all the measures. Following Lyócsa and Molnár (2017), if we assume the same dependence throughout the week, but we observe and ignore a difference in volatility after the interrupting period, we will underestimate the dependence between weekdays and overestimate the dependence after non-trading periods. Specifically, the in-sample period in our study contains 5791 range-based daily estimates in which there are 51 holidays, 1047 weekends, and 153 long weekends.
Asymmetric volatility in equity markets around the world
2019, North American Journal of Economics and FinanceCitation Excerpt :We therefore also utilize the HAR-RV. Even though various extensions of the HAR model has been suggested in the literature (e.g. Lyócsa and Molnár, 2017, 2018), only some of them include asymmetric volatility effect (e.g. Corsi & Reno, 2009; Haugom, Langeland, Molnár, & Westgaard, 2014). Recently, Linton et al. (2016) suggested that HAR-RV is a simple way to study the asymmetric volatility effect.
- 1
Lyócsa appreciates the support by the Slovak Research and Development Agency under contract No. APVV-14-0357 and by the Slovak Grant Agency under Grant No. 1/0406/17 and Grant No. 1/0257/18.