Estimation and inference in the presence of fractional d=1/2 and weakly nonstationary processes

Duffy, James A.; Kasparis, Ioannis

doi:10.1214/20-aos1998

Cited by 9 publications

(3 citation statements)

References 53 publications

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“…In this work, we consider the alternative hypotheses 0 < d < 1/2. Recently, Duffy and Kasparis (2021) investigated the limit theory for fractional processes with d = 1/2. The extension of the proposed tests to d ≥ 1/2 (or d < 0 for null) (see also Tanaka (1999), Wu and Shao (2006)) is also challenging and meaningful.…”

Section: Discussionmentioning

confidence: 99%

Detecting long-range dependence for time-varying linear models

Bai¹,

Wu²

2021

Preprint

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We consider the problem of testing long-range dependence for time-varying coefficient regression models. The covariates and errors are assumed to be locally stationary, which allows complex temporal dynamics and heteroscedasticity. We develop KPSS, R/S, V/S, and K/S-type statistics based on the nonparametric residuals, and propose bootstrap approaches equipped with a difference-based longrun covariance matrix estimator for practical implementation. Under the null hypothesis, the local alternatives as well as the fixed alternatives, we derive the limiting distributions of the test statistics, establish the uniform consistency of the difference-based long-run covariance estimator, and justify the bootstrap algorithms theoretically. In particular, the exact local asymptotic power of our testing procedure enjoys the order O(log −1 n), the same as that of the classical KPSS test for long memory in strictly stationary series without covariates. We demonstrate the effectiveness of our tests by extensive simulation studies. The proposed tests are applied to a COVID-19 dataset in favor of long-range dependence in the cumulative confirmed series of COVID-19 in several countries, and to the Hong Kong circulatory and respiratory dataset, identifying a new type of 'spurious long memory'.

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Section: Discussionmentioning

confidence: 99%

Detecting long-range dependence for time-varying linear models

Bai¹,

Wu²

2021

Preprint

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“…11 In this paper, we extend the framework in Andersen and Varneskov (2021a) to allow for imperfect regressors (in the spirit of Pastor and Stambaugh (2009)) that may exhibit general forms of endogeneity, which is similar to treating an omitted regressor problem, with the latter allowed to be persistent. That is, we expand the LCM approach to handle empirically relevant scenarios, where the regressors may be imperfect, persistent, and endogenous, for which there is currently no 9 As usual, we use the notation I(d) to signify that a variable is integrated of exact order d. 10 In fact, Duffy and Kasparis (2021) show that there is a close link between certain nonstationary fractionally integrated processes with d close to 1/2 and AR processes of the LUR type in a regression context. 11 These issues are not treated in the companion paper (Andersen and Varneskov, 2021b) either, which considers testing for parameter instability and structural breaks in persistent predictive relations (that is, testing on B), adopting the setting of Andersen and Varneskov (2021a).…”

Section: Final Observations: Bridging the Gap To Lcmmentioning

confidence: 99%

Consistent Local Spectrum Inference for Predictive Return Regressions

Andersen¹,

Varneskov

2022

Econom. Theory

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This paper studies the properties of predictive regressions for asset returns in economic systems governed by persistent vector autoregressive dynamics. In particular, we allow for the state variables to be fractionally integrated, potentially of different orders, and for the returns to have a latent persistent conditional mean, whose memory is difficult to estimate consistently by standard techniques in finite samples. Moreover, the predictors may be endogenous and “imperfect.” In this setting, we develop a consistent local spectrum (LCM) estimation procedure, that delivers asymptotic Gaussian inference. Furthermore, we provide a new LCM-based estimator of the conditional mean persistence, that leverages biased regression slopes as well as new LCM-based tests for significance of (a subset of) the predictors, which are valid even without estimating the return persistence. Simulations illustrate the theoretical arguments. Finally, an empirical application to monthly S&P 500 return predictions provides evidence for a fractionally integrated conditional mean component. Our new LCM procedure and tools indicate significant predictive power for future returns stemming from key state variables such as the default spread and treasury interest rates.

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“…Models with this formulation of θ n offer alternatives closer to the stationary and explosive regions and have opened up new robust estimation possibilities and new options for inference. Such models deliver nonstationary alternatives to the random wandering behavior associated with LUR processes and help to deliver connectivity between stationary and nonstationary asymptotics Magdalinos, 2007a, 2007b; hereafter PM) and (Giraitis and Phillips, 2006;Phillips, Magdalinos, and Giraitis, 2010), in addition to long memory processes with the (nonstationary) fractional parameter d = 1 2 (Duffy and Kasparis, 2021). A particular advantage of MI time series is the simple mechanism they provide for constructing endogeneously generated instruments (known as IVX) that validate standard methods of inference in cointegrating and predictive regressions (Phillips and Magdalinos, 2009;Kostakis et al, 2015), thereby overcoming ubiquitous problems of size distortion and non-pivotal inference that are induced by the presence of LUR regressors (Elliott, 1998;Phillips, 2015).…”

Section: Introductionmentioning

confidence: 99%

Estimation and Inference With Near Unit Roots

Phillips

2022

Econom. Theory

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New methods are developed for identifying, estimating, and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit-root (UR), local unit-root (LUR), mildly integrated (MI), and mildly explosive (ME) specifications in the new model formulation. It is shown how a new parameterization involving a localizing rate sequence that characterizes departures from unity can be consistently estimated in all cases. Simple pivotal limit distributions that enable valid inference about the form and degree of nonstationarity apply for MI and ME specifications and new limit theory holds in UR and LUR cases. Normalizing and variance stabilizing properties of the new parameterization are explored. Simulations are reported that reveal some of the advantages of this alternative formulation of nonstationary time series. A housing market application of the methods is conducted that distinguishes the differing forms of house price behavior in Australian state capital cities over the past decade.

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Estimation and inference in the presence of fractional d=1/2 and weakly nonstationary processes

Cited by 9 publications

References 53 publications

Detecting long-range dependence for time-varying linear models

Detecting long-range dependence for time-varying linear models

Consistent Local Spectrum Inference for Predictive Return Regressions

Estimation and Inference With Near Unit Roots

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