On strong consistency and asymptotic normality of one-step Gauss-Newton estimators in ARMA time series models

Statistics ◽  
2020 ◽  
Vol 54 (5) ◽  
pp. 1030-1057
Author(s):  
Pierre Duchesne ◽  
Pierre Lafaye de Micheaux ◽  
Joseph François Tagne Tatsinkou
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Strong Consistency ◽  
Time Series Models ◽  
One Step ◽  
Consistency And Asymptotic Normality

THE GLOBAL WEIGHTED LAD ESTIMATORS FOR FINITE/INFINITE VARIANCE ARMA(p,q) MODELS

2012 ◽  
Vol 28 (5) ◽  
pp. 1065-1086 ◽  
Author(s):  
Ke Zhu ◽  
Shiqing Ling
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Simulation Study ◽  
Strong Consistency ◽  
Asymptotic Theory ◽  
Infinite Variance ◽  
Time Series Models ◽  
Absolute Deviation ◽  
Consistency And Asymptotic Normality ◽  
First Time

This paper investigates the global self-weighted least absolute deviation (SLAD) estimator for finite and infinite variance ARMA(p, q) models. The strong consistency and asymptotic normality of the global SLAD estimator are obtained. A simulation study is carried out to assess the performance of the global SLAD estimators. In this paper the asymptotic theory of the global LAD estimator for finite and infinite variance ARMA(p, q) models is established in the literature for the first time. The technique developed in this paper is not standard and can be used for other time series models.

scholarly journals A COMPARATIVE ANALYSIS OF ALTERNATIVE UNIVARIATE TIME SERIES MODELS IN FORECASTING TURKISH INFLATION

2012 ◽  
Vol 13 (2) ◽  
pp. 275-293 ◽  
Author(s):  
A. Nazif Çatık ◽  
Mehmet Karaçuka
Keyword(s):  
Time Series ◽  
Time Series Models ◽  
Unobserved Components ◽  
Inflation Forecasting ◽  
Long Run ◽  
Univariate Time Series ◽  
Forecasting Performance ◽  
Unobserved Components Model ◽  
One Step ◽  
Conventional Models

This paper analyses inflation forecasting power of artificial neural networks with alternative univariate time series models for Turkey. The forecasting accuracy of the models is compared in terms of both static and dynamic forecasts for the period between 1982:1 and 2009:12. We find that at earlier forecast horizons conventional models, especially ARFIMA and ARIMA, provide better one-step ahead forecasting performance. However, unobserved components model turns out to be the best performer in terms of dynamic forecasts. The superiority of the unobserved components model suggests that inflation in Turkey has time varying pattern and conventional models are not able to track underlying trend of inflation in the long run.

scholarly journals Forecasting admissions in psychiatric hospitals before and during Covid-19

2021 ◽  
Author(s):  
Jan Wolff ◽  
Ansgar Klimke ◽  
Michael Marschollek ◽  
Tim Kacprowski
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Hospital Admissions ◽  
Model Performance ◽  
Psychiatric Hospitals ◽  
Time Series Models ◽  
Learning Models ◽  
One Step ◽  
Machine Learning Models ◽  
Better Than

Introduction The COVID-19 pandemic has strong effects on most health care systems and individual services providers. Forecasting of admissions can help for the efficient organisation of hospital care. We aimed to forecast the number of admissions to psychiatric hospitals before and during the COVID-19 pandemic and we compared the performance of machine learning models and time series models. This would eventually allow to support timely resource allocation for optimal treatment of patients. Methods We used admission data from 9 psychiatric hospitals in Germany between 2017 and 2020. We compared machine learning models with time series models in weekly, monthly and yearly forecasting before and during the COVID-19 pandemic. Our models were trained and validated with data from the first two years and tested in prospectively sliding time-windows in the last two years. Results A total of 90,686 admissions were analysed. The models explained up to 90% of variance in hospital admissions in 2019 and 75% in 2020 with the effects of the COVID-19 pandemic. The best models substantially outperformed a one-step seasonal naive forecast (seasonal mean absolute scaled error (sMASE) 2019: 0.59, 2020: 0.76). The best model in 2019 was a machine learning model (elastic net, mean absolute error (MAE): 7.25). The best model in 2020 was a time series model (exponential smoothing state space model with Box-Cox transformation, ARMA errors and trend and seasonal components, MAE: 10.44), which adjusted more quickly to the shock effects of the COVID-19 pandemic. Models forecasting admissions one week in advance did not perform better than monthly and yearly models in 2019 but they did in 2020. The most important features for the machine learning models were calendrical variables. Conclusion Model performance did not vary much between different modelling approaches before the COVID-19 pandemic and established forecasts were substantially better than one-step seasonal naive forecasts. However, weekly time series models adjusted quicker to the COVID-19 related shock effects. In practice, different forecast horizons could be used simultaneously to allow both early planning and quick adjustments to external effects.

scholarly journals TRUNCATED SUM OF SQUARES ESTIMATION OF FRACTIONAL TIME SERIES MODELS WITH DETERMINISTIC TRENDS

2019 ◽  
Vol 36 (4) ◽  
pp. 751-772 ◽  
Author(s):  
Javier Hualde ◽  
Morten Ørregaard Nielsen
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Relative Strength ◽  
Sum Of Squares ◽  
Monte Carlo Experiment ◽  
Time Series Models ◽  
Finite Sample ◽  
Generalized Polynomial ◽  
Finite Sample Properties ◽  
Deterministic Components

We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behavior of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers but also lying in arbitrarily large (but finite) intervals. Thus, our model captures different forms of nonstationarity and noninvertibility. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to nonuniform convergence of the objective function over a large admissible parameter space, but, in addition, our framework is substantially more involved due to the competition between stochastic and deterministic components. We establish consistency and asymptotic normality under quite general circumstances, finding that results differ crucially depending on the relative strength of the deterministic and stochastic components. Finite-sample properties are illustrated by means of a Monte Carlo experiment.

scholarly journals Nonparametric estimation of boundary measures and related functionals: asymptotic results

2009 ◽  
Vol 41 (2) ◽  
pp. 311-322 ◽  
Author(s):  
Inés Armendáriz ◽  
Antonio Cuevas ◽  
Ricardo Fraiman
Keyword(s):  
Asymptotic Normality ◽  
Surface Area ◽  
Nonparametric Estimation ◽  
Strong Consistency ◽  
Nonparametric Method ◽  
Asymptotic Results ◽  
Minkowski Content ◽  
Compact Body ◽  
Consistency And Asymptotic Normality ◽  
The One

We study a nonparametric method for estimating the boundary measure of a compact body G ⊂ ℝd (the boundary length when d = 2 and the surface area for d = 3) in the case when this measure agrees with the corresponding Minkowski content. The estimator we consider is closely related to the one proposed in Cuevas, Fraiman and Rodríguez-Casal (2007). Our method relies on two sets of random points, drawn inside and outside the set G, with different sampling intensities. Strong consistency and asymptotic normality are obtained under some shape hypotheses on the set G. Some applications and practical aspects are briefly discussed.

scholarly journals Non-linear time series regression

1971 ◽  
Vol 8 (04) ◽  
pp. 767-780 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Time Series ◽  
Strong Consistency ◽  
Linear Time ◽  
Stationary Time Series ◽  
Compact Set ◽  
Time Series Regression ◽  
Non Linear ◽  
Consistency And Asymptotic Normality ◽  
Image Position ◽  
Least Squares Estimates

In Jennrich (1969) the modelis considered, wherex(n) is a sequence of i.i.d. (0,σ2) random variables andz(n;θ) is a continuous but possibly non-linear function ofθ∈Θ, Θ being a compact set inRp. We shall use a second subscript when referring to a particular coordinate ofθ0so thatθ0jis thejth coordinate. Jennrich establishes, under suitable conditions onz(n;θ) andx(n), the strong consistency and asymptotic normality of the least squares estimates ofθ.Our main purpose here is to extend these results to the case wherex(n) is generated by a stationary time series.

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