A Monte Carlo Simulation Study on the Performance of Linear and Quadratic Programming Estimators in Fuzzy ARDL Models
DOI:
https://doi.org/10.62933/wbf13z44Keywords:
Fuzzy ARDL, Linear Programming, Quadratic Programming, Monte Carlo Simulation, Estimation PerformanceAbstract
The the study analyzes the relative effectiveness of the Linear Programming (LP) and Quadratic Programming (QP) techniques to estimate the Fuzzy Autoregressive Distributed Lag (FARDL) model, which can be regarded as the generalization of the classical ARDL model and is used to estimate fuzzy dynamic relationships among variables. In this model parameters are represented as fuzzy numbers defined in terms of central value and spread, hence allowing the direct adoption of structural uncertainty as being a part of the model architecture instead of using a conventional stochastic error. A Monte Carlo simulation experiment was implemented to meet the objectives of the study with different sample size and the complexity of the lag structure with the objective of testing the performances of the two estimation methods in different data settings. The comparative evaluation was based on two performance measures: the Root Mean Square Error (RMSE) which is an indicator of the accuracy of the estimation of central parameters and the Fuzzy Degree (FD) which is an indicator that quantifies the amount of uncertainty in the estimates. The results of the simulations show that QP method is always better than the LP method in all the sample sizes and lag settings with lower values in RMSE and FD respectively in most cases. This advantage is very strong especially in small samples and it persists as the sample size increases.
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