2018-02-01

Regression analysis is a statistical process for estimating the linear relationships between two or more variables. It involves several techniques for modeling and analyzing several variables. The earliest form of regression was the Least Squares, commonly known as Ordinary Least Squares (OLS) method which was introduced by the two famous statisticians Legendre and Gauss (Maronna et al., 2006). To this day, empirical researchers use OLS and its generalizations since the Gauss-Markov theorem asserts that OLS provides the Best Linear Unbiased Estimator (BLUE) for the parameters of the standard linear model. The estimator is best, in the sense that it is the most efficient one among the linear estimators when the data are smooth or normally distributed, ie do not contain outlying observations. Rousseeuw and Van Zomeren (1990) distinguished outliers (high leverage points and/or vertical outliers) when

2007-12-20

Time series are frequently affected by external events such as strikes, sales promotions advertising, policy changes, new laws or regulations, and so forth. When these external events are known and are interests of study, they are commonly referred to as interventions. When the events or the timing of the events are unknown and the events have substantial impact on the time series, they are often referred to as outliers [18]. Fox (1972) defines two statistical models additive and innovative outliers in a univariate time series [12]. Box and Tiao (1975) provide a procedure for analyzing a time series in the presence of known external events [18]. Kleiner, Martin and Thomson (1979) examine the effects of outliers on the estimation of spectrum of a time series they find additive outliers to be able to seriously distort the estimated spectra, and discuss some robust alternatives [15]. Smith and West (1983) propose an on-line monitoring procedure to detect the presence of abrupt level change and (additive) outliers with in a state space model formulation [9]. Hillmer (1984) studies the monitoring and adjustment of forecasts in the presence of outliers under ARIMA models [13].