Nonparametric test for a constant beta between Itô semi-martingales based on high-frequency data

Rei, Markus; Todorov, Viktor; Tauchen, George

doi:10.1016/j.spa.2015.02.008

Cited by 39 publications

(8 citation statements)

References 27 publications

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“…We proceed by examining the properties of our new Laplace transform‐based estimators and their associated bootstrap inference for the spot variance, covariance, correlation, and beta. To this end, we generate two processes

false{X_{t}, t \geq 0 false}

and

false{Y_{t}, t \geq 0 false}

in a setting reminiscent of the one in Reiss, Todorov, and Tauchen (2015). Specifically, the series are simulated according to the bivariate dynamics,

d X_{t} = \sqrt{V_{t}} d W_{t} + d L_{t}, d Y_{t} = β_{t} d X_{t} + \sqrt{{\overset{V}{true}}_{t}} d {\tilde{W}}_{t} + d {\tilde{L}}_{t},

d V_{t} = 0.03 (1 - V_{t}) d t + 0.18 \sqrt{V_{t}} d B_{t}, d {\tilde{V}}_{t} = 0.03 (1 - {\tilde{V}}_{t}) d t + 0.18 \sqrt{{\overset{V}{true}}_{t}} d {\tilde{B}}_{t},

where

{false(W, \overset{W}{true}, B, \overset{B}{true} false)}^{'}

is a vector of independent standard Brownian motions; L and

\overset{L}{true}

are two pure‐jump compound Poisson processes with intensity

λ = 4

and jump sizes drawn from

N false(

…”

Section: Simulation Studymentioning

confidence: 99%

Bootstrapping Laplace transforms of volatility

Hounyo

Zhi

Varneskov

2023

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This paper studies inference for the realized Laplace transform (RLT) of volatility in a fixed‐span setting using bootstrap methods. Specifically, since standard wild bootstrap procedures deliver inconsistent inference, we propose a local Gaussian (LG) bootstrap, establish its first‐order asymptotic validity, and use Edgeworth expansions to show that the LG bootstrap inference achieves second‐order asymptotic refinements. Moreover, we provide new Laplace transform‐based estimators of the spot variance as well as the covariance, correlation, and beta between two semimartingales, and adapt our bootstrap procedure to the requisite scenario. We establish central limit theory for our estimators and first‐order asymptotic validity of their associated bootstrap methods. Simulations demonstrate that the LG bootstrap outperforms existing feasible inference theory and wild bootstrap procedures in finite samples. Finally, we illustrate the use of the new methods by examining the coherence between stocks and bonds during the global financial crisis of 2008 as well as the COVID‐19 pandemic stock sell‐off during 2020, and by a forecasting exercise.

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false{X_{t}, t \geq 0 false}

and

false{Y_{t}, t \geq 0 false}

in a setting reminiscent of the one in Reiss, Todorov, and Tauchen (2015). Specifically, the series are simulated according to the bivariate dynamics,

d X_{t} = \sqrt{V_{t}} d W_{t} + d L_{t}, d Y_{t} = β_{t} d X_{t} + \sqrt{{\overset{V}{true}}_{t}} d {\tilde{W}}_{t} + d {\tilde{L}}_{t},

d V_{t} = 0.03 (1 - V_{t}) d t + 0.18 \sqrt{V_{t}} d B_{t}, d {\tilde{V}}_{t} = 0.03 (1 - {\tilde{V}}_{t}) d t + 0.18 \sqrt{{\overset{V}{true}}_{t}} d {\tilde{B}}_{t},

where

{false(W, \overset{W}{true}, B, \overset{B}{true} false)}^{'}

is a vector of independent standard Brownian motions; L and

\overset{L}{true}

are two pure‐jump compound Poisson processes with intensity

λ = 4

and jump sizes drawn from

N false(

…”

Section: Simulation Studymentioning

confidence: 99%

Bootstrapping Laplace transforms of volatility

Hounyo

Zhi

Varneskov

2023

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“…This model is widely used in high-frequency financial econometrics; see [ 8 , 9 , 11 ] in the context of high-dimensional covariance matrix estimation. One restriction of the model Equation ( 7 ) is that the factor loading

is assumed to be constant, but there is empirical evidence that

may be regarded as constant in short time intervals (one week or less); see [ 18 , 43 ] for instance.…”

Section: Factor Structurementioning

confidence: 99%

De-Biased Graphical Lasso for High-Frequency Data

Koike

2020

Entropy

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This paper develops a new statistical inference theory for the precision matrix of high-frequency data in a high-dimensional setting. The focus is not only on point estimation but also on interval estimation and hypothesis testing for entries of the precision matrix. To accomplish this purpose, we establish an abstract asymptotic theory for the weighted graphical Lasso and its de-biased version without specifying the form of the initial covariance estimator. We also extend the scope of the theory to the case that a known factor structure is present in the data. The developed theory is applied to the concrete situation where we can use the realized covariance matrix as the initial covariance estimator, and we obtain a feasible asymptotic distribution theory to construct (simultaneous) confidence intervals and (multiple) testing procedures for entries of the precision matrix.[19] and subsequently built up by, among others, [2,17,20]. Other common methods used in i.i.d. settings have also been investigated in the literature of high-frequency financial econometrics. Hautsch et al. [25] and Morimoto & Nagata [41] formally apply eigenvalue regularization methods based on random matrix theory to high-frequency data. Lam et al. [37] accommodate the non-linear shrinkage estimator of [39] to a high-frequency data setting with the help of the spectral distribution theory for the realized covariance matrix developed in [58]. Brownlees et al. [8] employ the ℓ 1 -penalized Gaussian MLE, which is known as the graphical Lasso, to estimate the precision matrix (the inverse of the covariance matrix) of high-frequency data. The latter approach is closely related to the methodology we will focus on.Despite the recent advances in this topic as above, most studies in this area focus only on point estimation of covariance and precision matrices, and there are little work about interval estimation and hypothesis testing for these objects. A few exceptions are [36,44] and [34]. The first two articles are concerned with continuous-time factor models: Kong & Liu [36] propose a test for the constancy of the factor loading matrix, while Pelger [44] assumes constant loadings and develops an asymptotic distribution theory to make inference for the factors and loadings. Meanwhile, Koike [34] establishes a high-dimensional central limit theorem for the realized covariance matrix which allows us to construct simultaneous confidence regions or carry out multiple testing for entries of the high-dimensional covariance matrix of high-frequency data. The aim of this study is to develop such a statistical inference theory for the precision matrix of high-frequency data. This is naturally motivated by the fact that the precision matrix of asset returns plays an important role in mean-variance analysis of portfolio allocation (see e.g. [16, Chapter 5]). We accomplish this purpose by imposing a sparsity assumption on the precision matrix. Such an assumption has a clear interpretation in connection with Gaussian graphical models: For a Gaussian random v...

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“…For example, Barndorff-Nielsen and Shephard (2004) employed the OLS method by calculating a ratio of the integrated covariance between assets and sys-tematic factors to the integrated variation of systematic factors. See also Andersen et al (2006); Li et al (2017a); Reiß et al (2015). Mykland and Zhang (2009) further computed the market beta as the aggregation of market betas estimated over local blocks.…”

Section: Introductionmentioning

confidence: 99%

Robust Realized Integrated Beta Estimator with Application to Dynamic Analysis of Integrated Beta

Oh¹,

Kim²,

Wang³

2023

Preprint

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In this paper, we develop a robust non-parametric realized integrated beta estimator using high-frequency financial data contaminated by microstructure noises, which is robust to the stylized features, such as the time-varying beta and the dependence structure of microstructure noises. With this robust realized integrated beta estimator, we investigate dynamic structures of integrated betas and find an auto-regressivemoving-average (ARMA) structure. To model this dynamic structure, we utilize the ARMA model for daily integrated market betas. We call this the dynamic realized beta (DR Beta). We further introduce a high-frequency data generating process by filling the gap between the high-frequency-based non-parametric estimator and low-frequency dynamic structure. Then, we propose a quasi-likelihood procedure for estimating the model parameters with the robust realized integrated beta estimator as the proxy. We also establish asymptotic theorems for the proposed estimator and conduct a simulation study to check the performance of finite samples of the estimator. The empirical study with the S&P 500 index and the top 50 large trading volume stocks from the S&P 500 illustrates that the proposed DR Beta model with the robust realized beta estimator

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Nonparametric test for a constant beta between Itô semi-martingales based on high-frequency data

Cited by 39 publications

References 27 publications

Bootstrapping Laplace transforms of volatility

Bootstrapping Laplace transforms of volatility

De-Biased Graphical Lasso for High-Frequency Data

Robust Realized Integrated Beta Estimator with Application to Dynamic Analysis of Integrated Beta

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