In this chapter we first review the theoretical and empirical work on fractional integration and
cointegration, placing special emphasis on the estimation procedures for fractionally …

Long-memory, or more generally fractal, processes are known to play an important role in
many scientific disciplines and applied fields such as physics, geophysics, hydrology …

Univariate dependencies in market volatility, both objective and risk neutral, are best
described by long-memory fractionally integrated processes. Meanwhile, the ex post …

I explain why at-the-money implied volatility is a biased and inefficient forecast of future
realized volatility using the insights from the empirical option-pricing literature. First, I explain …

This paper proposes two simple tests that are based on certain time domain properties of I
(d) processes. First, if a time series follows an I (d) process, then each subsample of the time …

We propose a new empirical specification of volatility that links volatility to the information
flow, measured as the order flow in the market, and to the price sensitivity to that information …

Provides a simple exposition of the basic time series material, and insights into underlying
technical aspects and methods of proof Long memory time series are characterized by a …

Moving from univariate to bivariate jointly dependent long-memory time series introduces a
phase parameter (γ), at the frequency of principal interest, zero; for short-memory series γ= 0 …

Recent empirical evidence demonstrates the presence of an important long-memory
component in realized asset return volatility. We specify and estimate multivariate models for …

This paper constructs and analyzes various measures of trading costs in US equity markets
covering the period 1926–2015. These measures contain statistically and economically …