Mixed-scale Jump Regressions with Bootstrap Inference

Jia Li, Viktor S Todorov, George Tauchen, Rui Chen

Research output: Working paper

Abstract

We develop an efficient mixed-scale estimator for jump regressions using high-frequency asset returns. A fine time scale is used to accurately identify the locations of large rare jumps in the explanatory variables such as the price of the market portfolio. A coarse scale is then used in the estimation in order to attenuate the effect of trading frictions in the dependent variable such as the prices of potentially less liquid assets. The proposed estimator has a non-standard asymptotic distribution that cannot be made asymptotically pivotal via studentization. We propose a novel bootstrap procedure for feasible inference and justify its asymptotic validity. We show that the bootstrap provides an automatic higher-order asymptotic approximation by accounting for the sampling variation in estimates of nuisance quantities that are used in efficient estimation. The Monte Carlo analysis indicates good finite-sample performance of the general specification test and confidence intervals based on the bootstrap. We apply the method to a high-frequency panel of Dow stock prices together with the market index defined by the S&P 500 index futures over the period 2007–2014. We document remarkable temporal stability in the way that stocks react to market jumps. However, this relationship for many of the stocks in the sample is significantly noisier and more unstable during sector-specific jump events.
Original languageEnglish (US)
Number of pages39
StatePublished - Jan 2 2016

Fingerprint

Bootstrap inference
Jump
Bootstrap
Estimator
Asset returns
Confidence interval
Stock prices
Nuisance
Time scales
Finite sample
Approximation
Monte Carlo analysis
Assets
Market portfolio
Asymptotic distribution
Sampling
Efficient estimation
Inference
Market index
Friction

Cite this

@techreport{b9096b7eed27449d8bb1a874d81fb077,
title = "Mixed-scale Jump Regressions with Bootstrap Inference",
abstract = "We develop an efficient mixed-scale estimator for jump regressions using high-frequency asset returns. A fine time scale is used to accurately identify the locations of large rare jumps in the explanatory variables such as the price of the market portfolio. A coarse scale is then used in the estimation in order to attenuate the effect of trading frictions in the dependent variable such as the prices of potentially less liquid assets. The proposed estimator has a non-standard asymptotic distribution that cannot be made asymptotically pivotal via studentization. We propose a novel bootstrap procedure for feasible inference and justify its asymptotic validity. We show that the bootstrap provides an automatic higher-order asymptotic approximation by accounting for the sampling variation in estimates of nuisance quantities that are used in efficient estimation. The Monte Carlo analysis indicates good finite-sample performance of the general specification test and confidence intervals based on the bootstrap. We apply the method to a high-frequency panel of Dow stock prices together with the market index defined by the S&P 500 index futures over the period 2007–2014. We document remarkable temporal stability in the way that stocks react to market jumps. However, this relationship for many of the stocks in the sample is significantly noisier and more unstable during sector-specific jump events.",
author = "Jia Li and Todorov, {Viktor S} and George Tauchen and Rui Chen",
year = "2016",
month = "1",
day = "2",
language = "English (US)",
type = "WorkingPaper",

}

Mixed-scale Jump Regressions with Bootstrap Inference. / Li, Jia; Todorov, Viktor S; Tauchen, George; Chen, Rui.

2016.

Research output: Working paper

TY - UNPB

T1 - Mixed-scale Jump Regressions with Bootstrap Inference

AU - Li, Jia

AU - Todorov, Viktor S

AU - Tauchen, George

AU - Chen, Rui

PY - 2016/1/2

Y1 - 2016/1/2

N2 - We develop an efficient mixed-scale estimator for jump regressions using high-frequency asset returns. A fine time scale is used to accurately identify the locations of large rare jumps in the explanatory variables such as the price of the market portfolio. A coarse scale is then used in the estimation in order to attenuate the effect of trading frictions in the dependent variable such as the prices of potentially less liquid assets. The proposed estimator has a non-standard asymptotic distribution that cannot be made asymptotically pivotal via studentization. We propose a novel bootstrap procedure for feasible inference and justify its asymptotic validity. We show that the bootstrap provides an automatic higher-order asymptotic approximation by accounting for the sampling variation in estimates of nuisance quantities that are used in efficient estimation. The Monte Carlo analysis indicates good finite-sample performance of the general specification test and confidence intervals based on the bootstrap. We apply the method to a high-frequency panel of Dow stock prices together with the market index defined by the S&P 500 index futures over the period 2007–2014. We document remarkable temporal stability in the way that stocks react to market jumps. However, this relationship for many of the stocks in the sample is significantly noisier and more unstable during sector-specific jump events.

AB - We develop an efficient mixed-scale estimator for jump regressions using high-frequency asset returns. A fine time scale is used to accurately identify the locations of large rare jumps in the explanatory variables such as the price of the market portfolio. A coarse scale is then used in the estimation in order to attenuate the effect of trading frictions in the dependent variable such as the prices of potentially less liquid assets. The proposed estimator has a non-standard asymptotic distribution that cannot be made asymptotically pivotal via studentization. We propose a novel bootstrap procedure for feasible inference and justify its asymptotic validity. We show that the bootstrap provides an automatic higher-order asymptotic approximation by accounting for the sampling variation in estimates of nuisance quantities that are used in efficient estimation. The Monte Carlo analysis indicates good finite-sample performance of the general specification test and confidence intervals based on the bootstrap. We apply the method to a high-frequency panel of Dow stock prices together with the market index defined by the S&P 500 index futures over the period 2007–2014. We document remarkable temporal stability in the way that stocks react to market jumps. However, this relationship for many of the stocks in the sample is significantly noisier and more unstable during sector-specific jump events.

M3 - Working paper

BT - Mixed-scale Jump Regressions with Bootstrap Inference

ER -