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Weighted Least Squares Estimator for ARPD(1) Model: Methodology and Properties |
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PP: 493-505 |
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doi:10.18576/jsap/140401
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Author(s) |
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Ahmed A. El-Sheikh,
Hamada A. A. Salama,
Mohamed K. A. Issa,
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Abstract |
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| Autoregressive models are fundamental tools in time series and panel data analysis, enabling the modeling of a variable based on its past values to predict future outcomes. These models become particularly useful in panel data contexts, where observations are collected across multiple entities over time. The Autoregressive Panel Data (ARPD) model is a prominent variant, offering insights into both time-dependent and cross-sectional variations. Specifically, the ARPD model of order one, denoted as ARPD(1), is a first- order model where the current value of the dependent variable is influenced by its immediate past value. The importance of the ARPD(1) model lies in its ability to capture the dynamic behavior of the data while accounting for individual-specific effects. This paper focuses on estimating parameters in a fixed-effect conditional ARPD(1) model using the Weighted Least Squares (WLS) method with different weights. The study delves into the properties of this estimator, demonstrating its linearity, unbiasedness, and variance. Furthermore, the performance of the WLS estimator is compared with alternative methods under the ARPD(1) framework. A Monte Carlo simulation is conducted to evaluate the effectiveness of the WLS method versus the Ordinary Least Squares (OLS) method, using Mean Squared Error (MSE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) as benchmarks. The results from the simulation highlight the superiority of the WLS estimator over OLS, making it the preferred choice for parameter estimation in ARPD(1) models. Moreover, empirical estimation using real ARPD(1) data is performed, further reinforcing the advantages of the WLS approach over traditional methods, particularly in terms of providing more accurate and reliable estimates. |
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