Department of Economics and Business Economics

Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach

Research output: Working paper

Standard

Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach. / Hounyo, Ulrich; Varneskov, Rasmus T.

Aarhus : Institut for Økonomi, Aarhus Universitet, 2018.

Research output: Working paper

Harvard

Hounyo, U & Varneskov, RT 2018 'Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach' Institut for Økonomi, Aarhus Universitet, Aarhus.

APA

Hounyo, U., & Varneskov, R. T. (2018). Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach. Aarhus: Institut for Økonomi, Aarhus Universitet. CREATES Research Papers, No. 2018-16

CBE

Hounyo U, Varneskov RT. 2018. Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach. Aarhus: Institut for Økonomi, Aarhus Universitet.

MLA

Hounyo, Ulrich and Rasmus T. Varneskov Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach. Aarhus: Institut for Økonomi, Aarhus Universitet. (CREATES Research Papers; Journal number 2018-16). 2018., 55 p.

Vancouver

Hounyo U, Varneskov RT. Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach. Aarhus: Institut for Økonomi, Aarhus Universitet. 2018 Apr 26.

Author

Hounyo, Ulrich ; Varneskov, Rasmus T./ Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach. Aarhus : Institut for Økonomi, Aarhus Universitet, 2018. (CREATES Research Papers; No. 2018-16).

Bibtex

@techreport{5022a72176624623b995efab5180eed7,
title = "Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach",
abstract = "We study inference for the local innovations of It^o semimartingales. Specifically, we construct a resampling procedure for the empirical CDF of high-frequency innovations that have been standardized using a nonparametric estimate of its stochastic scale (volatility) and truncated to rid the effect of {"}large{"} jumps. Our locally dependent wild bootstrap (LDWB) accommodate issues related to the stochastic scale and jumps as well as account for a special block-wise dependence structure induced by sampling errors. We show that the LDWB replicates first and second-order limit theory from the usual empirical process and the stochastic scale estimate, respectively, as well as an asymptotic bias. Moreover, we design the LDWB sufficiently general to establish asymptotic equivalence between it and and a nonparametric local block bootstrap, also introduced here, up to second-order distribution theory. Finally, we introduce LDWB-aided Kolmogorov-Smirnov tests for local Gaussianity as well as local von-Mises statistics, with and without bootstrap inference, and establish their asymptotic validity using the second-order distribution theory. The finite sample performance of CLT and LDWB-aided local Gaussianity tests are assessed in a simulation study as well as two empirical applications. Whereas the CLT test is oversized, even in large samples, the size of the LDWB tests are accurate, even in small samples. The empirical analysis verifies this pattern, in addition to providing new insights about the distributional properties of equity indices, commodities, exchange rates and popular macro finance variables.",
keywords = "Keywords: Bootstrap inference, High-frequency data, It^o semimartingales, Kolmogorov-Smirnov test, Stable processes, von-Mises statistics",
author = "Ulrich Hounyo and Varneskov, {Rasmus T.}",
year = "2018",
month = "4",
day = "26",
language = "English",
publisher = "Institut for {\O}konomi, Aarhus Universitet",
type = "WorkingPaper",
institution = "Institut for {\O}konomi, Aarhus Universitet",

}

RIS

TY - UNPB

T1 - Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach

AU - Hounyo,Ulrich

AU - Varneskov,Rasmus T.

PY - 2018/4/26

Y1 - 2018/4/26

N2 - We study inference for the local innovations of It^o semimartingales. Specifically, we construct a resampling procedure for the empirical CDF of high-frequency innovations that have been standardized using a nonparametric estimate of its stochastic scale (volatility) and truncated to rid the effect of "large" jumps. Our locally dependent wild bootstrap (LDWB) accommodate issues related to the stochastic scale and jumps as well as account for a special block-wise dependence structure induced by sampling errors. We show that the LDWB replicates first and second-order limit theory from the usual empirical process and the stochastic scale estimate, respectively, as well as an asymptotic bias. Moreover, we design the LDWB sufficiently general to establish asymptotic equivalence between it and and a nonparametric local block bootstrap, also introduced here, up to second-order distribution theory. Finally, we introduce LDWB-aided Kolmogorov-Smirnov tests for local Gaussianity as well as local von-Mises statistics, with and without bootstrap inference, and establish their asymptotic validity using the second-order distribution theory. The finite sample performance of CLT and LDWB-aided local Gaussianity tests are assessed in a simulation study as well as two empirical applications. Whereas the CLT test is oversized, even in large samples, the size of the LDWB tests are accurate, even in small samples. The empirical analysis verifies this pattern, in addition to providing new insights about the distributional properties of equity indices, commodities, exchange rates and popular macro finance variables.

AB - We study inference for the local innovations of It^o semimartingales. Specifically, we construct a resampling procedure for the empirical CDF of high-frequency innovations that have been standardized using a nonparametric estimate of its stochastic scale (volatility) and truncated to rid the effect of "large" jumps. Our locally dependent wild bootstrap (LDWB) accommodate issues related to the stochastic scale and jumps as well as account for a special block-wise dependence structure induced by sampling errors. We show that the LDWB replicates first and second-order limit theory from the usual empirical process and the stochastic scale estimate, respectively, as well as an asymptotic bias. Moreover, we design the LDWB sufficiently general to establish asymptotic equivalence between it and and a nonparametric local block bootstrap, also introduced here, up to second-order distribution theory. Finally, we introduce LDWB-aided Kolmogorov-Smirnov tests for local Gaussianity as well as local von-Mises statistics, with and without bootstrap inference, and establish their asymptotic validity using the second-order distribution theory. The finite sample performance of CLT and LDWB-aided local Gaussianity tests are assessed in a simulation study as well as two empirical applications. Whereas the CLT test is oversized, even in large samples, the size of the LDWB tests are accurate, even in small samples. The empirical analysis verifies this pattern, in addition to providing new insights about the distributional properties of equity indices, commodities, exchange rates and popular macro finance variables.

KW - Keywords: Bootstrap inference, High-frequency data, It^o semimartingales, Kolmogorov-Smirnov test, Stable processes, von-Mises statistics

M3 - Working paper

BT - Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -