Prediction in the one‐way error component model with serial correlation

Abstract

This paper derives the best linear unbiased predictor for a one-way error component model with serial correlation. A transformation derived by Baltagi and Li (1991) is used to show how the forecast can be easily computed from the GLS estimates and residuals. This result is useful for panel data applications which utilize the error component specification and exhibit serial correlation in the remainder disturbance term. Analytical expressions for this predictor are given when the remainder disturbances follow (1) an AR(1) process, (2) an AR(2) process, (3) a special AR(4) process for quarterly data, and (4) an MA(1) process.

Forecasting with panel data

“…= Σ T t=1 û it /T is the average of the ith individual's GLS residuals. Baltagi and Li (1992) showed that when both error components and serial correlation are present, i.e. .…”

Forecasting with spatial panel data

“…1 Best linear unbiased prediction (BLUP) in panel data using an error component model have been considered by Taub (1979), Baltagi and Li (1992), and Baillie and Baltagi (1999) to mention a few. Applications include Baltagi and Griffin (1997), Hsiao and Tahmiscioglu (1997), Schmalensee, Stoker and Judson (1998), Baltagi, Griffin and Xiong (2000), Hoogstrate, Palm and Pfann (2000), Baltagi, Bresson andPirotte (2002, 2004), Frees and Miller (2004), Rapach and Wohar (2004), and Brucker and Siliverstovs (2006), see Baltagi (2008) for a recent survey.…”

Socio-economics characteristics and spatial persistence of homicides in Colombia, 2000-2010

“…Therefore, when using a panel to capture the spatial autocorrelation between regions located close together and maintaining heterogeneous individuality, it is possible to obtain an unbiased estimate of the dependent variable (Anselin, Le Gallo, & Jayet, 2008), (Baltagi, 2008), (Baltagi & Li, 1992), (Baltagi & Li, 2006), maintaining a disturbance component that not only shows an spatial autoregressive (SAR) parameter associated with the weights matrix, but also an error term with independent distribution (Anselin, 1988), (Anselin & Bera, 1998). It should also be noted that the weights matrix W* is symmetrical and presents binary outcomes that relate to neighboring and non neighboring elements, as well as diagonal elements are zero in order to have robustness (Moscone & Tosetti, 2011).…”

“…With the proposed dynamic spatial panel in the model, the prediction for the homicide rate is made for a one period of time following (Baltagi & Li, 1992) and (Baltagi & Li, 2006) with the purpose of explaining if the spatial autocorrelation arises by pressures in the density of the population. The diverse municipal conditions in terms of the local young and displaced population who migrate to near by regions due to the presence of armed groups is taken into consideration.…”