Semiparametric Estimator of Time Series Conditional Variance

Abstract

We propose a new combined semiparametric estimator, which incorporates the parametric and nonparametric estimators of the conditional variance in a multiplicative way. We derive the asymptotic bias, variance, and normality of the combined estimator under general conditions. We show that under correct parametric specification, our estimator can do as well as the parametric estimator in terms of convergence rates; whereas under parametric mis-specification our estimator can still be consistent. It also improves over the nonparametric estimator of Ziegelman (2002) in terms of bias reduction. The superiority of our estimator is verfied by Monte Carlo simulations and empirical data analysis.

Conditional Duration Models for High‐frequency Data: A Review on Recent Developments

“…() propose another semiparametric autoregressive duration (SACD) model, inspired by the univariate and multivariate volatility works of Mishra et al . () and Long et al . (), respectively.…”

“…An empirical evidence in support of the robust finite sample performance of the SEMI-ACD model is provided by applying it to study the price duration process in the foreign exchange market 21 published over the Reuters' network, specifically, the US dollar to Euro exchange rate data. Dungey et al (2014) propose another semiparametric autoregressive duration (SACD) model, inspired by the univariate and multivariate volatility works of Mishra et al (2010) and Long et al (2011), respectively. The SACD incorporates the parametric and nonparametric estimators of the conditional duration in a multiplicative way and its estimators are consistent.…”

Nonparametric, conditional pricing of higher order multivariate contingent claims

“…As Mishra et al (2006) pointed out, the nonparametric specification may capture some characteristics of the conditional variances that the ARMA-GARCH in (1) missed out. Unlike the problems faced with the estimation of higher order multivariate GARCH, which are mainly convergence issues, the estimation of the nonparametric model in (4) consists of a set of recursive loops, and the only limitation it faces is computational power and time.…”

“…(3). To obtain dynamic nonparametric conditional estimates of all crosspair correlations, we make use of the Nadaraya-Watson (NW) regression, revealed in Long and Ullah (2005) and Mishra et al (2006). The parametric estimates of the standardised residuals of the set of underlying variables are fed in a NW system of equations to be transformed into a joint set of dynamic and nonparametric estimates.…”

“…However, the FHS imposes the restriction on the correlation coefficient matrix of the underlying variable returns to be constant over time, Pritsker (2006). In this study the above restriction is relaxed and, as in Mishra et al (2006), the conditional dynamics of the correlation matrix is modelled in a nonparametric way that aims to avoid any pricing biases that are due to fallacious assumptions about the joint dynamics of the set of underlying variables. This paper is organised as follows: the next section describes the nonparametric multivariate FHS algorithm; Section 3 shows empirically how FHS could be use to price a spread option and an option on the maximum of four assets; Section 4 concluded and summarises the findings.…”