Quantile Double Autoregression

Zhu, Qianqian; Li, Guodong

doi:10.1017/s026646662100030x

Cited by 7 publications

(13 citation statements)

References 54 publications

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“…Assumption 3 is commonly required for QR processes whose coefficients are functions of a uniform random variable; see Assumption A.3 in Koenker and Xiao (2006) for quantile AR models and Assumption 4 in Zhu and Li (2022) for quantile double AR models.…”

Section: Self-weighted Estimationmentioning

confidence: 99%

“…By assuming that the AR coefficients are functions of a standard uniform random variable, the quantile AR model in Koenker and Xiao (2006) allows for asymmetric dynamic structures across quantile levels; see, e.g., Ferreira (2011) and Baur et al (2012) for various empirical applications of this model. There have been many extensions of the quantile AR model, such as the quantile self-exciting threshold AR model (Cai and Stander, 2008), the threshold quantile AR model (Galvao et al, 2011), and the quantile double AR model (Zhu and Li, 2022). However, as far as we know, the approach of Koenker and Xiao (2006) has not been explored for GARCH-type models.…”

Section: Introductionmentioning

confidence: 99%

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Quantile autoregressive conditional heteroscedasticity

Zhu

Tan

Yao

et al. 2023

Journal of the Royal Statistical Society Series B: Statistical Methodology

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This article proposes a novel conditional heteroscedastic time series model by applying the framework of quantile regression processes to the ARCH(∞) form of the GARCH model. This model can provide varying structures for conditional quantiles of the time series across different quantile levels, while including the commonly used GARCH model as a special case. The strict stationarity of the model is discussed. For robustness against heavy-tailed distributions, a self-weighted quantile regression (QR) estimator is proposed. While QR performs satisfactorily at intermediate quantile levels, its accuracy deteriorates at high quantile levels due to data scarcity. As a remedy, a self-weighted composite quantile regression estimator is further introduced and, based on an approximate GARCH model with a flexible Tukey-lambda distribution for the innovations, we can extrapolate the high quantile levels by borrowing information from intermediate ones. Asymptotic properties for the proposed estimators are established. Simulation experiments are carried out to access the finite sample performance of the proposed methods, and an empirical example is presented to illustrate the usefulness of the new model.

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Section: Self-weighted Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantile autoregressive conditional heteroscedasticity

Zhu

Tan

Yao

et al. 2023

Journal of the Royal Statistical Society Series B: Statistical Methodology

Self Cite

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“…To capture the time-varying volatility, it is necessary to take the conditional heteroscedasticity into account when a linear model is fitted to financial time series. Among existing conditional heteroscedastic models, the double-autoregressive (DAR) models (Ling, 2004) have recently attracted growing attention, see Cai et al (2013), Li et al (2015), Xu and Zhao (2021), Zhu and Li (2022) and among others. Because it has two novel properties.…”

Section: Introductionmentioning

confidence: 99%

Non‐crossing quantile double‐autoregression for the analysis of streaming time series data

Jiang,

Kai Choy,

2023

Journal Time Series Analysis

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Many financial time series not only have varying structures at different quantile levels and exhibit the phenomenon of conditional heteroscedasticity at the same time but also arrive in the stream. Quantile double‐autoregression is very useful for time series analysis but faces challenges with model fitting of streaming data sets when estimating other quantiles in subsequent batches. This article proposes a renewable estimation method for quantile double‐autoregression analysis of streaming time series data due to its ability to break with storage barrier and computational barrier. Moreover, the proposed flexible parametric structure of the quantile function enables us to predict any interested quantile value without quantile curve crossing problem or keeping the desirable monotone property of the conditional quantile function. The proposed methods are illustrated using current data and the summary statistics of historical data. Theoretically, the proposed statistic is shown to have the same asymptotic distribution as the standard version computed on an entire data stream with the data batches pooled into one data set, without additional condition. Simulation studies and an empirical example are presented to illustrate the finite sample performance of the proposed methods.

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Section: Introductionmentioning

confidence: 99%

“…Liu, Li, and Kang (2018) investigated the sample path properties of an explosive DAR model. For some recent achievements on the DAR models, we refer to Zhu, Zhang, and Liang (2017), Zhu, Zheng, and Li (2018), Gong and Li (2020), Zhu and Li (2022), among others. Scholars have found that many financial time series exhibit features such as heavy-tailed, large kurtosis, extreme events and multimodal marginals.…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference for a mixture double autoregressive model

Yang

Zhang

et al. 2022

Statistica Neerlandica

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This paper considers a mixture double autoregressive model with two components, which can flexibly capture the features usually exhibited by many financial returns such as heteroscedasticity, large kurtosis and multimodal marginals. Bayesian method based on modern Markov Chain Monte Carlo (MCMC) technology is used to estimate the model parameters. The heteroscedasticity test problem for the underlying process is also addressed by means of Bayes factor. The performances of the proposed methods are evaluated via some simulations. It is shown that the MCMC algorithm is an effective tool to deal with the mixture model. Finally, the proposed model is applied to the S&P500 index data.set.

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Quantile Double Autoregression

Cited by 7 publications

References 54 publications

Quantile autoregressive conditional heteroscedasticity

Quantile autoregressive conditional heteroscedasticity

Non‐crossing quantile double‐autoregression for the analysis of streaming time series data

Bayesian inference for a mixture double autoregressive model

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