Search results
1 – 10 of 20Xiaohu Wang, Weilin Xiao and Jun Yu
This chapter derives asymptotic properties of the least squares (LS) estimator of the autoregressive (AR) parameter in local to unity processes with errors being fractional…
Abstract
This chapter derives asymptotic properties of the least squares (LS) estimator of the autoregressive (AR) parameter in local to unity processes with errors being fractional Gaussian noise (FGN) with the Hurst parameter
Details
Keywords
The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency…
Abstract
The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter
Details
Keywords
Ngai Hang Chan and Wilfredo Palma
Since the seminal works by Granger and Joyeux (1980) and Hosking (1981), estimations of long-memory time series models have been receiving considerable attention and a number of…
Abstract
Since the seminal works by Granger and Joyeux (1980) and Hosking (1981), estimations of long-memory time series models have been receiving considerable attention and a number of parameter estimation procedures have been proposed. This paper gives an overview of this plethora of methodologies with special focus on likelihood-based techniques. Broadly speaking, likelihood-based techniques can be classified into the following categories: the exact maximum likelihood (ML) estimation (Sowell, 1992; Dahlhaus, 1989), ML estimates based on autoregressive approximations (Granger & Joyeux, 1980; Li & McLeod, 1986), Whittle estimates (Fox & Taqqu, 1986; Giraitis & Surgailis, 1990), Whittle estimates with autoregressive truncation (Beran, 1994a), approximate estimates based on the Durbin–Levinson algorithm (Haslett & Raftery, 1989), state-space-based maximum likelihood estimates for ARFIMA models (Chan & Palma, 1998), and estimation of stochastic volatility models (Ghysels, Harvey, & Renault, 1996; Breidt, Crato, & de Lima, 1998; Chan & Petris, 2000) among others. Given the diversified applications of these techniques in different areas, this review aims at providing a succinct survey of these methodologies as well as an overview of important related problems such as the ML estimation with missing data (Palma & Chan, 1997), influence of subsets of observations on estimates and the estimation of seasonal long-memory models (Palma & Chan, 2005). Performances and asymptotic properties of these techniques are compared and examined. Inter-connections and finite sample performances among these procedures are studied. Finally, applications to financial time series of these methodologies are discussed.
Borus Jungbacker and Siem Jan Koopman
In this chapter, we aim to measure the actual volatility within a model-based framework using high-frequency data. In the empirical finance literature, it is widely discussed that…
Abstract
In this chapter, we aim to measure the actual volatility within a model-based framework using high-frequency data. In the empirical finance literature, it is widely discussed that tick-by-tick prices are subject to market micro-structure effects such as bid-ask bounces and trade information. These market micro-structure effects become more and more apparent as prices or returns are sampled at smaller and smaller time intervals. An increasingly popular measure for the variability of spot prices on a particular day is realised volatility that is typically defined as the sum of squared intra-daily log-returns. Recent theoretical results have shown that realised volatility is a consistent estimator of actual volatility, but when it is subject to micro-structure noise and the sampling frequency increases, the estimator diverges. Parametric and nonparametric methods can be adopted to account for the micro-structure bias. Here, we measure actual volatility using a model that takes account of micro-structure noise together with intra-daily volatility patterns and stochastic volatility. The coefficients of this model are estimated by maximum likelihood methods that are based on importance sampling techniques. It is shown that such Monte Carlo techniques can be employed successfully for our purposes in a feasible way. As far as we know, this is a first attempt to model the basic components of the mean and variance of high-frequency prices simultaneously. An illustration is given for three months of tick-by-tick transaction prices of the IBM stock traded at the New York Stock Exchange.
WILLIAM A. BARNETT, A. RONALD GALLANT, MELVIN J. HINICH, JOCHEN A. JUNGEILGES and DANIEL T. KAPLAN