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.

Confidence Sets for the Coefficients Vector of a Linear Regression Model with Nonspherical Disturbances

1997 ◽  
Vol 13 (3) ◽  
pp. 406-429 ◽  
Author(s):  
Anoop Chaturvedi ◽  
Hikaru Hasegawa ◽  
Ajit Chaturvedi ◽  
Govind Shukla
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Least Squares Estimator ◽  
Regression Coefficients ◽  
Confidence Sets ◽  
Generalized Least Squares Estimator ◽  
Coverage Probabilities

In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.

scholarly journals Extreme return, extreme volatility and investor sentiment

Filomat ◽  
2016 ◽  
Vol 30 (15) ◽  
pp. 3949-3961 ◽  
Author(s):  
Xu Gong ◽  
Fenghua Wen ◽  
Zhifang He ◽  
Jia Yang ◽  
Xiaoguang Yang ◽  
...  
Keyword(s):  
Linear Regression ◽  
Quantile Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Investor Sentiment ◽  
Generalized Least Squares ◽  
Regression Methods ◽  
Leading Role ◽  
The Impact

The extreme return and extreme volatility have great influences on the investor sentiment in stock market. However, few researchers have taken the phenomenon into consideration. In this paper, we first distinguish the extreme situations from non-extreme situations. Then we use the ordinary generalized least squares and quantile regression methods to estimate a linear regression model by applying the standardized AAII, the return and volatility of SP 500. The results indicate that, except for extremely negative return, other return sequences can cause great changes in investor sentiment, and non-extreme return plays a leading role in affecting the overall American investor sentiment. Extremely positive (negative) return can rapidly improve (further reduce) the level of investor sentiment when investors encounter extremely pessimistic situations. The impact gradually decreases with improvement of the sentiment until the situation turns optimistic. In addition, we find that extreme and non-extreme volatility cannot a_ect the overall investor sentiment.

Wouldn't It Be Nice …? The Automatic Unbiasedness of OLS (and GLS)

2008 ◽  
Vol 16 (3) ◽  
pp. 345-349 ◽  
Author(s):  
Robert C. Luskin
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Recent Issue ◽  
The Face ◽  
Best Linear Unbiased

In a recent issue of this journal, Larocca (2005) makes two notable claims about the best linear unbiasedness of ordinary least squares (OLS) estimation of the linear regression model. The first, drawn from McElroy (1967), is that OLS remains best linear unbiased in the face of a particular kind of autocorrelation (constant for all pairs of observations). The second, much larger and more heterodox, is that the disturbance need not be assumed uncorrelated with the regressors for OLS to be best linear unbiased. The assumption is unnecessary, Larocca says, because “orthogonality [of disturbance and regressors] is a property of all OLS estimates” (p. 192). Of course OLS's being best linear unbiased still requires that the disturbance be homoskedastic and (McElroy's loophole aside) nonautocorrelated, but Larocca also adds that the same automatic orthogonality obtains for generalized least squares (GLS), which is also therefore best linear unbiased, when the disturbance is heteroskedastic or autocorrelated.

scholarly journals Variation Comparison of OLS and GLS Estimators using Monte Carlo Simulation of Linear Regression Model with Autoregressive Scheme

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Sajid Ali Khan ◽  
Sayyad Khurshid ◽  
Tooba Akhtar ◽  
Kashmala Khurshid
Keyword(s):  
Monte Carlo ◽  
Linear Regression ◽  
Regression Model ◽  
Sample Size ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Small Samples ◽  
Sample Sizes

In this research we discusses to Ordinary Least Squares and Generalized Least Squares techniques and estimate with First Order Autoregressive scheme from different correlation levels by using simple linear regression model. A comparison has been made between these two methods on the basis of variances results. For the purpose of comparison, we use simulation of Monte Carlo study and the experiment is repeated 5000 times. We use sample sizes 50, 100, 200, 300 and 500, and observe the influence of different sample sizes on the estimators. By comparing variances of OLS and GLS at different values of sample sizes and correlation levels with , we found that variance of ( ) at sample size 500, OLS and GLS gives similar results but at sample size 50 variance of GLS ( ) has minimum values as compared to OLS. So it is clear that variance of GLS ( ) is best. Similarly variance of ( ) from OLS and GLS at sample size 500 and correlation -0.05 with , GLS give minimum value as compared to all other sample sizes and correlations. By comparing overall results of Ordinary Least Squares (OLS) and Generalized Least Squares (GLS), we conclude that in large samples both are gives similar results but small samples GLS is best fitted as compared to OLS.

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