Asymptotic theory of least squares estimator of a nonlinear time series regression model

1996 ◽  
Vol 25 (1) ◽  
pp. 133-141 ◽  
Author(s):  
Debasis Kundu ◽  
Amit Mitra
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Least Squares ◽  
Asymptotic Theory ◽  
Nonlinear Time Series ◽  
Least Squares Estimator ◽  
Time Series Regression

Rates of convergence for time series regression

1978 ◽  
Vol 10 (04) ◽  
pp. 740-743
Author(s):  
E. J. Hannan
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Least Squares ◽  
Continuous Spectrum ◽  
Rates Of Convergence ◽  
Absolutely Continuous Spectrum ◽  
Time Series Regression ◽  
Absolutely Continuous ◽  
Least Squares Estimate ◽  
Image Position

Consider, initially, a time series regression model of the simplest kind, namely Assume that x(t) is second-order stationary with zero mean and absolutely continuous spectrum with density f(ω) so that The y(t) are taken to be part of a sequence generated entirely independently of x(t) and will be treated as constants. Let β N be the least squares estimate of β and Call the numerator and denominator of b(N), respectively, c(N), d(N). We shall use K for a positive finite constant, not always the same one. We have the following result, which is Menchoff's inequality [3].

scholarly journals Asymptotic normality of the least squares estimate in trigonometric regression with strongly dependent noise

2019 ◽  
pp. 24-41
Author(s):  
T. O. Drabyk ◽  
O. V. Ivanov
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Least Squares ◽  
Regression Function ◽  
Least Squares Estimator ◽  
Stationary Time Series ◽  
Model Parameters ◽  
Local Transformation ◽  
Stationary Time ◽  
Trigonometric Regression

The least squares estimator asymptotic properties of the parameters of trigonometric regression model with strongly dependent noise are studied. The goal of the work lies in obtaining the requirements to regression function and time series that simulates the random noise under which the least squares estimator of regression model parameters are asymptotically normal. Trigonometric regression model with discrete observation time and open convex parametric set is research object. Asymptotic normality of trigonometric regression model parameters the least squares estimator is research subject. For obtaining the thesis results complicated concepts of time series theory and time series statistics have been used, namely: local transformation of Gaussian stationary time series, stationary time series with singular spectral density, spectral measure of regression function, admissibility of singular spectral density of stationary time series in relation to this measure, expansions by Chebyshev-Hermite polynomials of the transformed Gaussian time series values and it’s covariances, central limit theorem for weighted vector sums of the values of such a local transformation and Brouwer fixed point theorem.

Rates of convergence for time series regression

1978 ◽  
Vol 10 (4) ◽  
pp. 740-743 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Least Squares ◽  
Continuous Spectrum ◽  
Rates Of Convergence ◽  
Absolutely Continuous Spectrum ◽  
Time Series Regression ◽  
Absolutely Continuous ◽  
Least Squares Estimate ◽  
Image Position

Consider, initially, a time series regression model of the simplest kind, namely Assume that x(t) is second-order stationary with zero mean and absolutely continuous spectrum with density f(ω) so that The y(t) are taken to be part of a sequence generated entirely independently of x(t) and will be treated as constants. Let βN be the least squares estimate of β and Call the numerator and denominator of b(N), respectively, c(N), d(N). We shall use K for a positive finite constant, not always the same one. We have the following result, which is Menchoff's inequality [3].

Edgeworth Expansion for the OLS Estimator in a Time Series Regression Model

1985 ◽  
Vol 1 (2) ◽  
pp. 223-239 ◽  
Author(s):  
Koichi Maekawa
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Least Squares ◽  
Edgeworth Expansion ◽  
Ordinary Least Squares ◽  
Exogenous Variable ◽  
Time Series Regression ◽  
Technical Device ◽  
Numerical Studies

In this paper we consider the situation in which ordinary least squares (OLS) is used to estimate an ARMA (1,1) model with one exogenous variable. Applying Edgeworth expansion techniques, we examine the misspecification errors and the approximate distributions of the OLS estimator. Extensive numerical studies were performed and selected results are shown graphically. In addition, a technical device is developed to calculate the Edgeworth coefficients.

scholarly journals Real-Time Prediction of the COVID-19 Epidemic in Thailand using Simple Model-Free Method and Time Series Regression Model

2021 ◽  
Vol 18 (14) ◽  
Author(s):  
Rati WONGSATHAN
Keyword(s):  
Genetic Algorithm ◽  
Time Series ◽  
Regression Model ◽  
Regression Models ◽  
Gaussian Function ◽  
Logistic Function ◽  
Hyperbolic Tangent ◽  
Time Series Regression ◽  
Model Free ◽  
Tangent Function

The novel coronavirus 2019 (COVID-19) pandemic was declared a global health crisis. The real-time accurate and predictive model of the number of infected cases could help inform the government of providing medical assistance and public health decision-making. This work is to model the ongoing COVID-19 spread in Thailand during the 1st and 2nd phases of the pandemic using the simple but powerful method based on the model-free and time series regression models. By employing the curve fitting, the model-free method using the logistic function, hyperbolic tangent function, and Gaussian function was applied to predict the number of newly infected patients and accumulate the total number of cases, including peak and viral cessation (ending) date. Alternatively, with a significant time-lag of historical data input, the regression model predicts those parameters from 1-day-ahead to 1-month-ahead. To obtain optimal prediction models, the parameters of the model-free method are fine-tuned through the genetic algorithm, whereas the generalized least squares update the parameters of the regression model. Assuming the future trend continues to follow the past pattern, the expected total number of patients is approximately 2,689 - 3,000 cases. The estimated viral cessation dates are May 2, 2020 (using Gaussian function), May 4, 2020 (using a hyperbolic function), and June 5, 2020 (using a logistic function), whereas the peak time occurred on April 5, 2020. Moreover, the model-free method performs well for long-term prediction, whereas the regression model is suitable for short-term prediction. Furthermore, the performances of the regression models yield a highly accurate forecast with lower RMSE and higher R2 up to 1-week-ahead. HIGHLIGHTS COVID-19 model for Thailand during the first and second phases of the epidemic The model-free method using the logistic function, hyperbolic tangent function, and Gaussian function  applied to predict the basic measures of the outbreak Regression model predicts those measures from one-day-ahead to one-month-ahead The parameters of the model-free method are fine-tuned through the genetic algorithm  GRAPHICAL ABSTRACT

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