Quantile Regression for Long Memory Testing: A Case of Realized Volatility

Abstract

In this paper we derive a quantile regression approach to formally test for long memory in time series. We propose both individual and joint quantile tests which are useful to determine the order of integration along the di¤erent percentiles of the conditional distribution and, therefore, allow to address more robustly the overall hypothesis of fractional integration. The null distributions of these tests obey standard laws (e.g., standard normal) and are free of nuisance parameters. The …nite sample validity of the approach is established through Monte Carlo simulations, showing, for instance, large power gains over several alternative procedures under non-Gaussian errors. An empirical application of the testing procedure on di¤erent measures of daily realized volatility is presented. Our analysis reveals several interesting features, but the main …nding is that the suitability of a long-memory model with a constant order of integration around 0.4 cannot be rejected along the di¤erent percentiles of the distribution, which provides strong support to the existence of long memory in realized volatility from a completely new perspective.

Information in daily data volatility measurements

“…Second, as is widely recognized, the time series of daily volatility measures exhibit strong long‐memory‐like persistence (Demetrescu, Rubia, & Rodrigues, 2018; Hassler, Rodrigues, & Rubia, 2016; Wenger, Leschinski, & Sibbertsen, 2017). Recent research has shown that inference with highly persistent regressors can be unreliable even when using heteroskedasticity and autocorrelation consistent (HAC) covariance (Müller, 2014).…”

Multivariate fractional integration tests allowing for conditional heteroskedasticity with an application to return volatility and trading volume

“…Specifically, to account for a non-zero deterministic mean in the level of the series we use the demeaning process described in Robinson (1994); Demetrescu et al (2008) and Hassler et al (2016). Hence, to account for the nonzero means in (B.1) we regress the differences (1 − L) d i + y it := t−1 j=0 λ j (d i ) y it−j on the variable h t,d i := t−1 j=0 λ j (d i ) , t = 2, ..., T, with {λ j (d i )} as defined in (??)…”

“…In the univariate setting, a number of hypothesis tests on the fractional exponent have been proposed; see, among others, Robinson (1994), Tanaka (1999), Breitung and Hassler (2002), Nielsen (2004b), Demetrescu et al (2008), Hassler et al (2009Hassler et al ( , 2016 and Cavaliere et al (2017). In the context of a vector series, one could perform such univariate fractional integration tests separately on each element of the vector.…”

ARFIMA Reference Forecasts for Worldwide CO2 Emissions and the Need for Large and Frontloaded Decarbonization Policies

“…If 0.5 < < 1, the process is non-stationary with a time-dependent variance, but the series retains its mean-reverting property. Finally, if ≥ 1 , the process is non-stationary and non-mean-reverting, i.e., the effects of random shocks are permanent (for details see, for example, Granger & Joyeux, 1980;Granger, 1980Granger, , 1981Sowell, 1992aSowell, , 1992bBaillie, 1996;Palma, 2007;Hassler et al, 2016;Belbute & Pereira, 2015).…”