Asymptotic Inference for Nearly Nonstationary AR(1) Processes

Chan, Ngai Hang; Wei, Ching-Zong

doi:10.1214/aos/1176350492

Cited by 431 publications

(274 citation statements)

References 13 publications

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“…An alternative way to ensure a smooth transition between the asymptotics for short-memory processes and the unit root limiting theory is the local-to-unity framework (Chan and Wei, 1987;Phillips, 1987). Suppose that the dynamics of implied volatility is described by the near-integrated model where c £ 0 is a fixed constant and e t~i id(0, s 2 ).…”

Section: Near-integrated Ar Modelmentioning

confidence: 99%

Forecasting volatility

Gospodinov

and

Jiang

2006

Journal of Forecasting

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In this paper, we investigate the time series properties of S&P 100 volatility and the forecasting performance of different volatility models. We consider several nonparametric and parametric volatility measures, such as implied, realized and model-based volatility, and show that these volatility processes exhibit an extremely slow mean-reverting behavior and possible long memory. For this reason, we explicitly model the near-unit root behavior of volatility and construct median unbiased forecasts by approximating the finite-sample forecast distribution using bootstrap methods. Furthermore, we produce prediction intervals for the next-period implied volatility that provide important information about the uncertainty surrounding the point forecasts. Finally, we apply intercept corrections to forecasts from misspecified models which dramatically improve the accuracy of the volatility forecasts.

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Section: Near-integrated Ar Modelmentioning

confidence: 99%

Forecasting volatility

Gospodinov

and

Jiang

2006

Journal of Forecasting

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“…In other words, the set-up of Definition 2 captures the popular modelling strategy of letting {u t } be local-to-unity in the sense of Chan and Wei (1987) and Phillips (1987). It is known (Hochstadt (1973), Chapter 6) that as the sampling interval 1/T converges to zero, the eigenvalues of the covariance matrix of a discretely sampled continuous time process (scaled by T −1 ) converge uniformly to those of the (continuous) covariance kernel of the continuous time process.…”

Section: It Corresponds Tomentioning

confidence: 99%

A theory of robust long-run variance estimation

Müller

2007

Journal of Econometrics

105

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The paper studies the robustness of long-run variance estimators employed for conducting Wald-type tests in standard time series models. It is shown that all long-run variance estimators that are consistent for the variance of Gaussian White Noise lack robustness in the sense that they yield arbitrary results for some underlying process that satisfies a Functional Central Limit Theorem. An analytical measure of robustness of long-run variance estimators is suggested that captures the degree of this fragility.A family of inconsistent long-run variance estimators is derived that optimally trade off this measure of robustness against efficiency. A minor modification of these optimal estimators lead to asymptotically F-distributed test statistics under the null hypothesis, so that robust large sample inference can be conducted very similarly to well-understood small sample Gaussian inference.JEL Classification: C13, C12, C32

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“…The near unit root model in time series has been extensively used in the univariate literature to study the test statistics under local alternatives, starting with Chan and Wei (1987) and Phillips (1987Phillips ( , 1988. Also, the estimation of the autoregressive roots near unity are studied both in time series (Phillips et al 2001) and in the panel data setting Phillips 2000, 2004).…”

Section: Introductionmentioning

confidence: 99%

Near Unit Root in the Spatial Autoregressive Model

Lee¹,

Yu²

2013

Spatial Economic Analysis

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This paper studies the spatial autoregressive (SAR) model for cross sectional data when the true spatial e¤ect parameter is near unity. We decompose the data generating process (DGP) into an unstable component and a stable component and then establish asymptotic properties of QMLE, 2SLSE and linearized QMLE. The spatial e¤ect estimator has a higher rate of convergence and other parameters have the regular p n rate. The higher rate of convergence re ‡ects how fast the spatial root converges to unity. In contrast to near unit root time series, the estimators are all asymptotically normal. Similarly to the regular SAR model, QMLE and linearized QMLE are more e¢ cient than 2SLSE.JEL classi…cation: C13; C23

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Asymptotic Inference for Nearly Nonstationary AR(1) Processes

Cited by 431 publications

References 13 publications

Forecasting volatility

Forecasting volatility

A theory of robust long-run variance estimation

Near Unit Root in the Spatial Autoregressive Model

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