Modeling the Autocorrelated Errors in Time Series Regression: A Generalized Least Squares Approach

2018 ◽  
Vol 26 (4) ◽  
pp. 1-15 ◽  
Author(s):  
Emmanuel Akpan ◽  
Imoh Moffat
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Generalized Least Squares ◽  
Time Series Regression ◽  
Autocorrelated Errors ◽  
Least Squares Approach

Nuisance vs. Substance: Specifying and Estimating Time-Series-Cross-Section Models

1996 ◽  
Vol 6 ◽  
pp. 1-36 ◽  
Author(s):  
Nathaniel Beck ◽  
Jonathan N. Katz
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Cross Section ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Correlated Errors ◽  
Section Data ◽  
Variable Approach ◽  
Parameter Heterogeneity ◽  
Lagged Dependent Variable

In a previous article we showed that ordinary least squares with panel corrected standard errors is superior to the Parks generalized least squares approach to the estimation of time-series-cross-section models. In this article we compare our proposed method with another leading technique, Kmenta's “cross-sectionally heteroskedastic and timewise autocorrelated” model. This estimator uses generalized least squares to correct for both panel heteroskedasticity and temporally correlated errors. We argue that it is best to model dynamics via a lagged dependent variable rather than via serially correlated errors. The lagged dependent variable approach makes it easier for researchers to examine dynamics and allows for natural generalizations in a manner that the serially correlated errors approach does not. We also show that the generalized least squares correction for panel heteroskedasticity is, in general, no improvement over ordinary least squares and is, in the presence of parameter heterogeneity, inferior to it. In the conclusion we present a unified method for analyzing time-series-cross-section data.

A generalized least-squares approach regularized with graph embedding for dimensionality reduction

2020 ◽  
Vol 98 ◽  
pp. 107023 ◽  
Author(s):  
Xiang-Jun Shen ◽  
Si-Xing Liu ◽  
Bing-Kun Bao ◽  
Chun-Hong Pan ◽  
Zheng-Jun Zha ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Least Squares ◽  
Graph Embedding ◽  
Generalized Least Squares ◽  
Least Squares Approach

scholarly journals What To Do (and Not to Do) with Time-Series Cross-Section Data

1995 ◽  
Vol 89 (3) ◽  
pp. 634-647 ◽  
Author(s):  
Nathaniel Beck ◽  
Jonathan N. Katz
Keyword(s):  
Time Series ◽  
Cross Section ◽  
Generalized Least Squares ◽  
Monte Carlo Analysis ◽  
Standard Errors ◽  
Comparative Political Economy ◽  
Section Data ◽  
Alternative Estimator ◽  
Estimation Of Time ◽  
Least Squares Approach

We examine some issues in the estimation of time-series cross-section models, calling into question the conclusions of many published studies, particularly in the field of comparative political economy. We show that the generalized least squares approach of Parks produces standard errors that lead to extreme overconfidence, often underestimating variability by 50% or more. We also provide an alternative estimator of the standard errors that is correct when the error structures show complications found in this type of model. Monte Carlo analysis shows that these “panel-corrected standard errors” perform well. The utility of our approach is demonstrated via a reanalysis of one “social democratic corporatist” model.

scholarly journals On Least Squares Estimation in a Simple Linear Regression Model with Periodically Correlated Errors: A Cautionary Note

2016 ◽  
Vol 41 (3) ◽  
Author(s):  
Abdullah A. Smadi ◽  
Nour H. Abu-Afouna
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Autoregressive Model ◽  
Relative Efficiency ◽  
Generalized Least Squares ◽  
Correlated Errors ◽  
Simple Linear Regression ◽  
Simple Regression Model ◽  
Autocorrelated Errors

In this research the simple linear regression (SLR) model with autocorrelated errors is considered. Traditionally, correlated errors are assumed to follow the autoregressive model of order one (AR(1)). Beside this model we will also study the SLR model with errors following the periodic autoregressive model of order one (PAR(1)). The later model is useful for modeling periodically autocorrelated errors. In particular, it is expected to beuseful when the data are seasonal. We investigate the properties of the least squares estimators of the parameters of the simple regression model when the errors are autocorrelated and for various models. In particular, the relative efficiency of those estimates are obtained and compared for the white noise, AR(1) and PAR(1) models. Also, the generalized least squares estimates for the SLR with PAR(1) errors are derived. The relative efficiency of the intercept and slope estimates based on both methods is investigated via Monte-Carlo simulation. An application on real data set is also provided.It should be emphasized that once there are sufficient evidences that errors are autocorrelated then the type of this autocorrelation should be uncovered. Then estimates of model’s parameters should be obtained accordingly, using some method like the generalized least squares but not the ordinary least squares.

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