Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model

Jiang, Feiyu; Li, Dong; Zhu, Ke

doi:10.1016/j.jeconom.2020.10.007

Cited by 5 publications

(7 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, when n > 1, φ is not adaptive any more caused by the term Υ(x) unless Σ(x) 1/4 ⊗ Σ(x) −1/4 ≡ I n (e.g., Σ(x) = τ (x)I n with τ (x) > 0 for x ∈ (0, 1)). See also the similar findings for the BEKK volatility model in Jiang et al (2021). Therefore, when n > 1, if there exists cross-sectional dependence between any two elements of y t , the estimation of Σ t should have the impact on the asymptotic distribution of φ.…”

Section: A Semiparametric Matrix Modelmentioning

confidence: 54%

Testing and Modelling for the Structural Change in Covariance Matrix Time Series With Multiplicative Form

Jiang¹,

Liu²,

Li³

et al. 2023

STAT SINICA

Self Cite

View full text Add to dashboard Cite

We first construct a new generalized Hausman test for detecting the structural change in a multiplicative form of covariance matrix time series model. This generalized Hausman test is asymptotically pivotal, and it has non-trivial power in detecting a broad class of alternatives. Moreover, we propose a new semiparametric covariance matrix time series model, which has a time-varying long run component to take the structural change into account, and a BEKKtype short run component to capture the temporal dependence. A two-step estimation procedure is proposed to estimate this semiparametric model, and the asymptotics of the related estimators are established. Finally, the importance of the generalized Hausman test and the semiparametric model is illustrated by simulations and an application to realized covariance matrix data.1. Introduction. Matrix-variate observations are often encountered in statistical applications with structured information. An important example is the realized covariance (RCOV) matrix, which is calculated from intraday high-frequency returns and able to enhance the prediction ability for the covariance matrix of the underly-Keywords and phrases: Covariance matrix time series model; Profiled quasi maximum likelihood estimation; Realized covariance matrix; Semiparametric time series model; Structural change testing.

show abstract

Section: A Semiparametric Matrix Modelmentioning

confidence: 54%

Testing and Modelling for the Structural Change in Covariance Matrix Time Series With Multiplicative Form

Jiang¹,

Liu²,

Li³

et al. 2023

STAT SINICA

Self Cite

View full text Add to dashboard Cite

show abstract

“…Next, we give five technical lemmas, whose proofs are given in the supplementary material (Jiang et al (2019)). Lemma A.1 captures the error from the nonparametric estimation.…”

Section: Appendix: Proofsmentioning

confidence: 99%

“…Combining with the results in Lemmas A.10-A.12 below, by (A.4) it follows that Proof of Theorem 2.3. See the supplementary material in Jiang et al (2019).…”

Section: By Condition (2) and The Factmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model

Jiang

Zhu

2019

Preprint

Self Cite

View full text Add to dashboard Cite

This paper considers a semiparametric generalized autoregressive conditional heteroscedastic (S-GARCH) model. For this model, we first estimate the time-varying long run component by the kernel estimator, and then estimate the non-time-varying parameters in short run component by the quasi maximum likelihood estimator (QMLE). We show that the QMLE is asymptotically normal with the parametric convergence rate. Next, we provide a consistent Bayesian information criterion for order selection. Furthermore, we construct a Lagrange multiplier test for linear parameter constraint and a portmanteau test for model checking, and obtain their asymptotic null distributions. Our entire statistical inference procedure works for the non-stationary data with two important features: first, our QMLE and two tests are adaptive to the unknown form of the long run component; second, our QMLE and two tests share the same efficiency and testing power as those in variance target method when the S-GARCH model is stationary. Engle (1982) and Bollerslev (1986), the generalized autoregressive conditional heteroscedastic (GARCH) model is perhaps the most influential one to capture and forecast the volatility of economic and financial return data. Introduction. Since the seminal work ofHowever, the GARCH model is often used under the stationarity assumption. Due to

show abstract

“…The assumption that a nonstationary part could drive volatility, has recently permeated in standard ARCH (stationary) models as well. Specifically, [13] and [4] propose using splines, [22] use the Fourier Flexible form of [14] in their periodic volatility model, [20] consider the generalized GARCH model and, in a series of papers [1] and [2], suggest to model volatility as a linear combination of logistic functions.…”

mentioning

confidence: 99%

Choosing between persistent and stationary volatility

2022

View full text Add to dashboard Cite

This paper suggests a multiplicative volatility model where volatility is decomposed into a stationary and a non-stationary persistent part. We provide a testing procedure to determine which type of volatility is prevalent in the data. The persistent part of volatility is associated with a nonstationary persistent process satisfying some smoothness and moment conditions. The stationary part is related to stationary conditional heteroskedasticity. We outline theory and conditions that allow the extraction of the persistent part from the data and enable standard conditional heteroskedasticity tests to detect stationary volatility after persistent volatility is taken into account. Monte Carlo results support the testing strategy in small samples. The empirical application of the theory supports the persistent volatility paradigm, suggesting that stationary conditional heteroskedasticity is considerably less pronounced than previously thought.

show abstract

Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model

Cited by 5 publications

References 41 publications

Testing and Modelling for the Structural Change in Covariance Matrix Time Series With Multiplicative Form

Testing and Modelling for the Structural Change in Covariance Matrix Time Series With Multiplicative Form

Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model

Choosing between persistent and stationary volatility

Contact Info

Product

Resources

About