Nonparametric regression for locally stationary time series

Vogt, Michael

doi:10.1214/12-aos1043

Cited by 141 publications

(106 citation statements)

References 24 publications

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“…Then from (iii) in the proof of Theorem 4.2 in Vogt (2012), we can show that B j (τ, x) converges in probability to B j,τ,x .…”

Section: A1 the Npr Modelmentioning

confidence: 87%

“…Typically, y t is (logarithmic) stock returns, but we may also be interested in predicting prices. A locally stationary process is defined as follows (see Vogt (2012)). …”

Section: The Npr Modelmentioning

confidence: 99%

“…Note that locally stationary processes have received a lot of attention. For example, Vogt (2012) studied nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. Dong and Linton (2016) studied nonparametric additive models that have deterministic time trend and both stationary (or locally stationary) and integrated variables as components.…”

Section: Introductionmentioning

confidence: 99%

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Multi-step non- and semi-parametric predictive regressions for short and long horizon stock return prediction

Cheng¹,

Gao²,

Linton³

2018

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In this paper, we propose three new predictive models: the multi-step nonparametric predictive regression model and the multi-step additive predictive regression model, in which the predictive variables are locally stationary time series; and the multi-step time-varying coefficient predictive regression model, in which the predictive variables are stochastically nonstationary. We also establish the estimation theory and asymptotic properties for these models in the short horizon and long horizon case. To evaluate the effectiveness of these models, we investigate their capability of stock return prediction. The empirical resultsshow that all of these models can substantially outperform the traditional linear predictive regression model in terms of both in-sample and out-of-sample performance. In addition, we find that these models can always beat the historical mean model in terms of in-sample fitting, and also for some cases in terms of the out-of-sample forecasting.

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“…Then from (iii) in the proof of Theorem 4.2 in Vogt (2012), we can show that B j (τ, x) converges in probability to B j,τ,x .…”

Section: A1 the Npr Modelmentioning

confidence: 87%

“…Typically, y t is (logarithmic) stock returns, but we may also be interested in predicting prices. A locally stationary process is defined as follows (see Vogt (2012)). …”

Section: The Npr Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multi-step non- and semi-parametric predictive regressions for short and long horizon stock return prediction

Cheng¹,

Gao²,

Linton³

2018

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show abstract

“…errors (even assumed to be Gaussian in some cases) [see Müller (1992) for an early reference and Mallik et al (2011) and Mallik et al (2013) for more recent references]. Recently Vogt and Dette (2015) proposed a generalized CUSUM approach to detect gradual changes in model (2.1) using a different concept of local stationarity [see Vogt (2012)]. …”

Section: Piecewise Locally Stationary Processesmentioning

confidence: 99%

Change Point Analysis of Correlation in Non-stationary Time Series

Dette¹,

Wu²,

Zhou³

2019

STAT SINICA

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A restrictive assumption in change point analysis is "stationarity under the null hypothesis of no change-point", which is crucial for asymptotic theory but not very realistic from a practical point of view. For example, if change point analysis for correlations is performed, it is not necessarily clear that the mean, marginal variance or higher order moments are constant, even if there is no change in the correlation. This paper develops change point analysis for the correlation structures under less restrictive assumptions. In contrast to previous work, our approach does not require that the mean, variance and fourth order joint cumulants are constant under the null hypothesis. Moreover, we also address the problem of detecting relevant change points.

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“…Using a simplified version of the proof for Theorem 4.1 in Vogt (2012) or alternatively applying Theorem 1 of Kristensen (2009), it can be shown that sup u∈[0,1] |g V (u)| = O p ( log T /T h). In addition, straightforward calculations yield that sup u∈[0,1] |g B (u)| ≤ Ch 2 for some sufficiently large constant C. This completes the proof of the uniform convergence result.…”

Section: Proof Of Theoremmentioning

confidence: 99%