Nonparametric estimation of a periodic sequence in the presence of a smooth trend

Vogt, Michael; Linton, Oliver

doi:10.1093/biomet/ast051

Cited by 22 publications

(18 citation statements)

References 35 publications

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“…This formulation is commonly used in the literature. [12][13][14] The rescaled time is necessary to use for studying asymptotic properties of the estimated mean and variance/covariance functions in the time domain. Otherwise, the distance between two consecutive observation times is 1, which does not go to 0 when n increases, and thus, the asymptotic properties in time cannot be discussed properly.…”

Section: The Model and Its Estimationmentioning

confidence: 99%

Nonparametric estimation of the spatio‐temporal covariance structure

Yang

Qiu

2019

Statistics in Medicine

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Spatio‐temporal modeling is an active research problem with broad applications. In this problem, proper description and estimation of the data covariance structure plays an important role. In the literature, most available methods assume that the data covariance is stationary and follows a specific parametric form. In practice, however, such assumptions are hardly valid or difficult to verify. In this paper, we propose a new and flexible method for estimating the underlying covariance structure. Our proposed method does not require the covariance to be stationary or follow a parametric form. It can accommodate nonparametric space‐time–varying mean structure of the observed data. Under some mild regularity conditions, it is shown that our estimated covariance structure converges to the true covariance structure. The proposed method is also justified numerically by a simulation study and an application to a hand, foot, and mouth disease data.

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Section: The Model and Its Estimationmentioning

confidence: 99%

Nonparametric estimation of the spatio‐temporal covariance structure

Yang

Qiu

2019

Statistics in Medicine

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“…This should be compared with the Diebold and Li (2006) model in which β t has an autoregressive form with stochastic error term. This kind of "local trend model" in (18) is an alternative to dynamic specification, see Starica (2003) and Vogt and Linton (2014). Engle and Rangel (2008), Hafner and Linton (2010) and Koo and Linton (2015) combine the slowly varying nonparametric trend with a short run dynamic model.…”

Section: Forecasting Future Bond Prices and Yieldsmentioning

confidence: 99%

“…It also ensures that the discount function is smooth enough for us to employ a nonparametric kernel estimation method. We maintain here that the factor is stationary but the theory can easily be extended to allow the more general local stationarity property, Vogt and Linton (2014).…”

Section: Asymptotic Distributionmentioning

confidence: 99%

Estimation of a Nonparametric model for Bond Prices from Cross-section and Time series Information

2019

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We develop estimation methodology for an additive nonparametric panel model that is suitable for capturing the pricing of coupon-paying government bonds followed over many time periods. We use our model to estimate the discount function and yield curve of nominally riskless government bonds. The novelty of our approach is the combination of two different techniques: cross-sectional nonparametric methods and kernel estimation for time varying dynamics in the time series context. The resulting estimator is used for predicting individual bond prices given the full schedule of their future payments. In addition, it is able to capture the yield curve shapes and dynamics commonly observed in the fixed income markets. We establish the consistency, the rate of convergence, and the asymptotic normality of the proposed estimator. A Monte Carlo exercise illustrates the good performance of the method under different scenarios. We apply our methodology to the daily CRSP bond market dataset, and compare ours with the popular Diebold and Li (2006) method.

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“…Assumptions A3-A7 are used to derive the properties of σ j (s), in line with Vogt and Linton (2014) and Vogt et al (2012). But we only require that E|u j t | 2+δ < ∞, since we use…”

Section: Large Sample Properties Of Estimatorsmentioning

confidence: 99%

A Coupled Component GARCH Model for Intraday and Overnight Volatility

Linton

2017

SSRN Journal

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We propose a semi-parametric coupled component GARCH model for intraday and overnight volatility that allows the two periods to have different properties. To capture the very heavy tails of overnight returns, we adopt a dynamic conditional score model with t innovations. We propose a several step estimation procedure that captures the nonparametric slowly moving components by kernel estimation and the dynamic parameters by t maximum likelihood. We establish the consistency and asymptotic normality of our estimation procedures. We extend the modelling to the multivariate case. We apply our model to the study of the component stocks of the Dow Jones industrial average over the period 1991-2016. We show that actually overnight volatility has increased in importance during this period. In addition, our model provides better intraday volatility forecast since it takes account of the full dynamic consequences of the overnight shock and previous ones.

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Nonparametric estimation of a periodic sequence in the presence of a smooth trend

Cited by 22 publications

References 35 publications

Nonparametric estimation of the spatio‐temporal covariance structure

Nonparametric estimation of the spatio‐temporal covariance structure

Estimation of a Nonparametric model for Bond Prices from Cross-section and Time series Information

A Coupled Component GARCH Model for Intraday and Overnight Volatility

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