## 16 Citations

On the Estimation of Locally Stationary Long-Memory Processes

- MathematicsStatistica Sinica
- 2019

A central limit theorem for the Whittle likelihood estimation method is derived under mild distributional conditions, extending its application to a wide range of non-Gaussian time series.

Time varying long memory parameter estimation for locally stationary long memory processes

- MathematicsCommunications in Statistics - Theory and Methods
- 2018

Abstract The semiparametric estimators of time varying long memory parameter are investigated for locally stationary long memory processes. The GPH estimator and the local Whittle estimator are…

0472 1 ON THE ESTIMATION OF LOCALLY STATIONARY LONG-MEMORY PROCESSES

- Mathematics
- 2018

This paper establishes the statistical properties of a spectrum-based Whittle parameter estimation procedure for long-range dependent locally stationary processes. Both theoretical and empirical…

Estimation of slowly time-varying trend function in long memory regression models

- Mathematics
- 2018

ABSTRACT We study the asymptotic properties of the least-squares estimator for the trend function of a particular class of locally stationary models, which are defined by considering a smooth…

Simultaneous quantile inference for non-stationary long-memory time series

- MathematicsBernoulli
- 2018

We consider the simultaneous or functional inference of time-varying quantile curves for a class of non-stationary long-memory time series. New uniform Bahadur representations and Gaussian…

Measuring stationarity in long-memory processes

- Mathematics
- 2013

In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an $L_2$-distance between the spectral density of the locally stationary…

Minimum distance estimation of locally stationary moving average processes

- Mathematics, Computer ScienceComput. Stat. Data Anal.
- 2019

Asymptotics of partial sums of linear processes with changing memory parameter*

- Mathematics
- 2013

We study the limit distribution of partial sums of nonstationary truncated linear process {Xt, t = 1,…, n} with long memory and changing memory parameter dt,n ∈ (0,∞). Two classes of linear processes…

Statistical analysis of locally stationary processes

- Computer Science
- 2013

This work reviews estimation and predictions techniques, illustrating the application of these methods to real-life data examples, and shows that the locally stationary methods provide a useful theoretical and practical framework for the statistical analysis of nonstationary time series data.

Estimation and Forecasting of Locally Stationary Processes

- Mathematics, Environmental Science
- 2013

The proposed Kalman filter approach provides a numerically efficient methodology for estimating and predicting locally stationary models and allows for the handling of missing values and it provides both exact and approximate maximum likelihood estimates.

## References

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- Mathematics
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. When estimating the unknown mean of a stationary time series, the best linear unbiased estimator is often a significantly better estimator than the ordinary least squares estimates Xn. The relative…

Statistics for long-memory processes

- Mathematics
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Theorems of Stationary Processes with Long Memory Limit Theorems and Estimations of Long Memory-Heuristic Approaches, Forecasting Regression Goodness of Fit Tests, and Robust Estimation of Long memory estimates are presented.

Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series

- Mathematics
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Behavior of sample means and nonparametric time-series estimation

- MathematicsWSC '86
- 1986

This paper consists of five sections discussing notation; spectral density classification of memory type of a time series; equivalent degrees of freedom of asymptotic confidence intervals for the mean; sample Fourier transforms and sample spectral density; sample Brownian Bridge functionals and standardized time series.

THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS

- Mathematics
- 1983

Abstract. The definitions of fractional Gaussian noise and integrated (or fractionally differenced) series are generalized, and it is shown that the two concepts are equivalent. A new estimator of…

Long-Memory Time Series: Theory and Methods

- Mathematics
- 2007

Preface. Acronyms. 1. Stationary Processes. 2. State Space Systems. 3. Long-Memory Processes. 4. Estimation Methods. 5. Asymptotic Theory. 6. Heteroskedastic Models. 7. Transformations. 8. Bayesian…

Locally stationary random processes

- MathematicsIRE Trans. Inf. Theory
- 1957

In the case of locally stationary random processes, a relation is found between the covariance and the spectral density which constitutes a natural generalization of the Wiener-Khintchine relations.

On a time deformation reducing nonstationary stochastic processes to local stationarity

- MathematicsJournal of Applied Probability
- 2004

A stochastic process is locally stationary if its covariance function can be expressed as the product of a positive function multiplied by a stationary covariance. In this paper, we characterize…

Quantile spectral analysis and long-memory time series

- Computer ScienceJournal of Applied Probability
- 1986

An approach to time series model identification is described which involves the simultaneous use of frequency, time and quantile domain algorithms; the approach is called quantile spectral analysis.…