Abstract
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.
Highlights
Regression analysis is a very important statistical method that investigates the relationship between a response variable Y and a set of other variables named as independent variables or predictors X1, . . . , Xp
The terms {εt} satisfying such conditions are named in the time series context as the white noise (WN) process (Wei, 2006)
The simple linear regression (SLR) model generalizes to what is known as the multiple linear regression model
Summary
Regression analysis is a very important statistical method that investigates the relationship between a response variable Y and a set of other variables named as independent variables or predictors X1, . . . , Xp. Is named as generalized linear regression (GLR) model, a direct remedial measure is to work with a model that calls for correlated error terms In this article we study the properties of OLS estimates for the parameters of SLR when the errors are periodically correlated. McLeod proposed to apply this test on the residuals resulted from fitting seasonal ARIMA models for some seasonal time series. If significant, this test will indicate that the errors are periodically correlated
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