scholarly journals Shapes of stationary autocovariances

2006 ◽  
Vol 43 (04) ◽  
pp. 1186-1193
Author(s):  
Robert Lund ◽  
Ying Zhao ◽  
Peter C. Kiessler
Keyword(s):  
Time Series ◽  
Hazard Rate ◽  
Convergence Rates ◽  
Stationary Time Series ◽  
Time Series Models ◽  
Mean Squared Errors ◽  
Geometric Convergence ◽  
One Step ◽  
New Better Than Used ◽  
Better Than

This note introduces shape orderings for stationary time series autocorrelation and partial autocorrelation functions and explores some of their convergence rate ramifications. The shapes explored include decreasing hazard rate and new better than used, orderings that are familiar from stochastic processes settings. Time series models where these shapes arise are presented. The shapes are used to obtain explicit geometric convergence rates for mean squared errors of one-step-ahead forecasts.

scholarly journals Shapes of stationary autocovariances

2006 ◽  
Vol 43 (4) ◽  
pp. 1186-1193
Author(s):  
Robert Lund ◽  
Ying Zhao ◽  
Peter C. Kiessler
Keyword(s):  
Time Series ◽  
Hazard Rate ◽  
Convergence Rates ◽  
Stationary Time Series ◽  
Time Series Models ◽  
Mean Squared Errors ◽  
Geometric Convergence ◽  
One Step ◽  
New Better Than Used ◽  
Better Than

This note introduces shape orderings for stationary time series autocorrelation and partial autocorrelation functions and explores some of their convergence rate ramifications. The shapes explored include decreasing hazard rate and new better than used, orderings that are familiar from stochastic processes settings. Time series models where these shapes arise are presented. The shapes are used to obtain explicit geometric convergence rates for mean squared errors of one-step-ahead forecasts.

Geometric renewal convergence rates from hazard rates

2001 ◽  
Vol 38 (01) ◽  
pp. 180-194 ◽  
Author(s):  
Kenneth S. Berenhaut ◽  
Robert Lund
Keyword(s):  
Convergence Rate ◽  
Hazard Rate ◽  
Convergence Rates ◽  
Hazard Rates ◽  
Finite Support ◽  
Good Convergence ◽  
Renewal Sequence ◽  
Geometric Convergence ◽  
New Better Than Used ◽  
Better Than

This paper studies the geometric convergence rate of a discrete renewal sequence to its limit. A general convergence rate is first derived from the hazard rates of the renewal lifetimes. This result is used to extract a good convergence rate when the lifetimes are ordered in the sense of new better than used or increasing hazard rate. A bound for the best possible geometric convergence rate is derived for lifetimes having a finite support. Examples demonstrating the utility and sharpness of the results are presented. Several of the examples study convergence rates for Markov chains.

Geometric renewal convergence rates from hazard rates

2001 ◽  
Vol 38 (1) ◽  
pp. 180-194 ◽  
Author(s):  
Kenneth S. Berenhaut ◽  
Robert Lund
Keyword(s):  
Convergence Rate ◽  
Hazard Rate ◽  
Convergence Rates ◽  
Hazard Rates ◽  
Finite Support ◽  
Good Convergence ◽  
Renewal Sequence ◽  
Geometric Convergence ◽  
New Better Than Used ◽  
Better Than

This paper studies the geometric convergence rate of a discrete renewal sequence to its limit. A general convergence rate is first derived from the hazard rates of the renewal lifetimes. This result is used to extract a good convergence rate when the lifetimes are ordered in the sense of new better than used or increasing hazard rate. A bound for the best possible geometric convergence rate is derived for lifetimes having a finite support. Examples demonstrating the utility and sharpness of the results are presented. Several of the examples study convergence rates for Markov chains.

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 Asymptotic Optimality of Estimating Function Estimator for CHARN Model

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Tomoyuki Amano
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Financial Time Series ◽  
Asymptotic Optimality ◽  
Time Series Models ◽  
Estimating Function ◽  
Asymptotically Optimal ◽  
Financial Time ◽  
Conditional Least Squares ◽  
Better Than

CHARN model is a famous and important model in the finance, which includes many financial time series models and can be assumed as the return processes of assets. One of the most fundamental estimators for financial time series models is the conditional least squares (CL) estimator. However, recently, it was shown that the optimal estimating function estimator (G estimator) is better than CL estimator for some time series models in the sense of efficiency. In this paper, we examine efficiencies of CL and G estimators for CHARN model and derive the condition that G estimator is asymptotically optimal.

Econometrics and econometric modeling in Excel and R

2020 ◽  
Author(s):  
Lyudmila Babeshko ◽  
Irina Orlova
Keyword(s):  
Time Series ◽  
Stationary Time Series ◽  
Economic Research ◽  
Federal State ◽  
Practical Implementation ◽  
Time Series Models ◽  
Econometric Modeling ◽  
Software Environment ◽  
Multidimensional Time Series ◽  
State Educational

The textbook includes topics of modern econometrics, often used in economic research. Some aspects of multiple regression models related to the problem of multicollinearity and models with a discrete dependent variable are considered, including methods for their estimation, analysis, and application. A significant place is given to the analysis of models of one-dimensional and multidimensional time series. Modern ideas about the deterministic and stochastic nature of the trend are considered. Methods of statistical identification of the trend type are studied. Attention is paid to the evaluation, analysis, and practical implementation of Box — Jenkins stationary time series models, as well as multidimensional time series models: vector autoregressive models and vector error correction models. It includes basic econometric models for panel data that have been widely used in recent decades, as well as formal tests for selecting models based on their hierarchical structure. Each section provides examples of evaluating, analyzing, and testing models in the R software environment. Meets the requirements of the Federal state educational standards of higher education of the latest generation. It is addressed to master's students studying in the Field of Economics, the curriculum of which includes the disciplines Econometrics (advanced course)", "Econometric modeling", "Econometric research", and graduate students."

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