Non-parametric estimation for a pure-jump Lévy process

2017 ◽  
Vol 12 (2) ◽  
pp. 338-349
Author(s):  
Chunhao Cai ◽  
Junyi Guo ◽  
Honglong You
Keyword(s):  
Risk Model ◽  
Low Frequency ◽  
Parametric Estimation ◽  
Large Sample Size ◽  
Simulation Studies ◽  
Finite Sample ◽  
Squared Error ◽  
The Laplace Transform ◽  
Integrated Squared Error ◽  
Non Parametric Estimation

AbstractIn this paper, we propose an estimator of the survival probability for a Lévy risk model observed at low frequency. The estimator is constructed via a regularised version of the inverse of the Laplace transform. The convergence rate of the estimator in a sense of the integrated squared error is studied for large sample size. Simulation studies are also given to show the finite sample performance of our estimator.

scholarly journals A New Volatility Model: GQARCH-Ito Model

2020 ◽  
Author(s):  
Huiling Yuan ◽  
Yong Zhou ◽  
Lu Xu ◽  
Yulei Sun ◽  
Xiangyu Cui
Keyword(s):  
High Frequency ◽  
Historical Data ◽  
Asymptotic Properties ◽  
Low Frequency ◽  
Simulation Studies ◽  
Finite Sample ◽  
Volatility Model ◽  
Forecasting Performance ◽  
Volatility Asymmetry ◽  
Quasi Maximum Likelihood

Volatility asymmetry is a hot topic in high-frequency financial market. In this paper, we propose a new econometric model, which could describe volatility asymmetry based on high-frequency historical data and low-frequency historical data. After providing the quasi-maximum likelihood estimators for the parameters, we establish their asymptotic properties. We also conduct a series of simulation studies to check the finite sample performance and volatility forecasting performance of the proposed methodologies. And an empirical application is demonstrated that the new model has stronger volatility prediction power than GARCH-It\^{o} model in the literature.

scholarly journals Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments

2020 ◽  
Vol 24 ◽  
pp. 842-882
Author(s):  
Jean-Marc Azaïs ◽  
François Bachoc ◽  
Agnès Lagnoux ◽  
Thi Mong Ngoc Nguyen
Keyword(s):  
Gaussian Process ◽  
Scale Parameter ◽  
Parametric Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Asymptotic Results ◽  
Mean And Variance ◽  
The Mean ◽  
The Moment ◽  
Quadratic Variations

We consider the semi-parametric estimation of the scale parameter of the variogram of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based both on quadratic variations and the moment method. We provide asymptotic approximations of the mean and variance of this estimator, together with asymptotic normality results, for a large class of Gaussian processes. We allow for general mean functions, provide minimax upper bounds and study the aggregation of several estimators based on various variation sequences. In extensive simulation studies, we show that the asymptotic results accurately depict the finite-sample situations already for small to moderate sample sizes. We also compare various variation sequences and highlight the efficiency of the aggregation procedure.

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

scholarly journals QUANTILE DOUBLE AUTOREGRESSION

2021 ◽  
pp. 1-47
Author(s):  
Qianqian Zhu ◽  
Guodong Li
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Simulation Studies ◽  
Finite Sample ◽  
Conditional Quantile ◽  
New Model ◽  
Conditional Quantiles ◽  
Financial Time ◽  
Portmanteau Tests ◽  
Strict Stationarity

Many financial time series have varying structures at different quantile levels, and also exhibit the phenomenon of conditional heteroskedasticity at the same time. However, there is presently no time series model that accommodates both of these features. This paper fills the gap by proposing a novel conditional heteroskedastic model called “quantile double autoregression”. The strict stationarity of the new model is derived, and self-weighted conditional quantile estimation is suggested. Two promising properties of the original double autoregressive model are shown to be preserved. Based on the quantile autocorrelation function and self-weighting concept, three portmanteau tests are constructed to check the adequacy of the fitted conditional quantiles. The finite sample performance of the proposed inferential tools is examined by simulation studies, and the need for use of the new model is further demonstrated by analyzing the S&P500 Index.

Non-parametric estimation for aggregated functional data for electric load monitoring

2009 ◽  
Vol 20 (2) ◽  
pp. 111-130 ◽  
Author(s):  
Ronaldo Dias ◽  
Nancy L. Garcia ◽  
Angelo Martarelli
Keyword(s):  
Functional Data ◽  
Parametric Estimation ◽  
Electric Load ◽  
Load Monitoring ◽  
Non Parametric Estimation ◽  
Non Parametric
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