Implementation of Conjugate Gradient Method for Estimating Inflation Rate in Malaysia

Optimization methods are valuable for making decisions and identifying the most suitable alternative based on a given objective function. One of the mathematical optimization methods is Conjugate Gradient (CG) method which is commonly used to solve large-scale unconstrained optimization systems with less storage space. Recently, various optimization methods have been studied and used in economics estimating. However, just a few studies have predicted inflation rate using modified CG method. Random initial points are tested on New Three-Terms (NTT) which are modified Rivaie-Mustafa-Ismail-Leong (RMIL+) and Umar Mustapha Waziri (UMW) CG method with ten optimization test functions suggested by Andrei using MATLAB. NOI and CPU time obtained are compared by performance ratio of Dolan and Moré. NTT CG method stands out as the best performance. Data set of year 2010 until 2022 from Department of Statistics Malaysia (DOSM) is transformed into optimization problems to be solved. Estimated results of Least Square Conjugate Gradient (LSCG) are based on NTT CG and LS both for linear and quadratic models. Relative errors for LSCG, Least Square (LS) and Trendline Method are calculated. Linear LS is shown as the most suitable to estimator in inflation rate in Malaysia as it yields the least relative error compatible with the linear LSCG and Trendline Method that produce similar relative error in estimating inflation rate in Malaysia.