Normal Error Distribution Research Articles

THE INFLUENCE OF OBSERVATIONAL ERRORS IN GAIA DR3 ON THE RECONSTRUCTION OF GLOBULAR CLUSTER ORBITS ON A COSMOLOGICAL TIMESCALE

In recent years, the emerging field of astronomy focused on the history of galaxy formation, known as Galactic Archaeology, has been gaining popularity. Globular clusters have been involved in many key processes occurring in the Milky Way, making their study, particularly the reconstruction of their orbits, significantly important. The Gaia DR3 catalog provides parameters for 165 globular clusters, such as proper motions, radial velocity, and heliocentric distance, with certain accuracy. Therefore, it is important to examine the influence of measurement errors in these parameters on the initial data when converting to the Galactocentric coordinate system and, consequently, on the shape of the orbits. We integrated the orbits of globular clusters 10 billion years lookback. For physical justification during the integration, we used the external dynamic potential with the individual number 411321 from the cosmological simulation database IllustrisTNG-100, which best reproduces the potential of the Milky Way. The integration was performed using the parallel N-body code φ-GPU, based on a fourth-order Hermite scheme with hierarchical individual block timesteps. A total of 1,000 randomizations of the initial data were created considering a normal distribution of errors, and the influence of errors on the scatter of initial velocities and on the shape of the orbits was examined. The parameters with the largest relative errors are proper motions and radial velocity, while the smallest errors are in heliocentric distance. It was found that 85% of the globular clusters have relative errors in all parameters of no more than 10%, and 5.4% have errors of no more than 1%. Investigating the influence of measurement errors for clusters with different magnitudes of relative errors, we concluded that for most globular clusters, the influence of measurement errors on the shape of the orbits is not significant. Consequently, it is possible to reconstruct the orbits with high accuracy for these clusters. Since the reconstruction of globular cluster orbits involves cosmological timescales, accounting for measurement errors is an important aspect of the preparatory procedure before the main integration.

Local Walsh-average regression for spatial autoregression single index varying coefficient models

. In real life, a large number of variables are spatially correlated in adjacent regions in various fields, such as finance, sociology, ecology, and geographic information systems. And the factors affecting these variables often have both linear and non linear relationships with them, how to accurately depict the relationship between them with a spatial regression model is a significant work. In order to further accurately describe the relationship between explanatory variables and response variables, we establish a spatial autoregressive single index varying coefficient model. The least squares method is the main method of model estimation but it is not robust enough when the parameter distribution is not normal. We present a new estimation method based on local Walsh average-regression. Under some general assumptions, we establish the asymptotic properties of the parametric and non parametric estimators. We further verify the accuracy and efficiency of the estimators under the condition of non normal error distribution through numerical experiments. In addition, the robustness of the proposed method is verified when the spatial weight matrix is interfered and when the bandwidth is changed within a certain range. Finally, we demonstrate the accuracy of forecasting by our proposed model compared with traditional spatial autoregressive model through real data analysis.

The Gaussian distribution: Derivation method and its applications in selected examples

Gaussian distribution is the most important and common form of distribution in statistical theory, and its density function has more complicated forms. When Gauss dealt with the problem of measurement error, he derived the form of normal distribution from another angle, and proposed the least squares theory based on the normal distribution of error. This helps solve the problem of the probability density distribution of the error, enabling people to make a better statistical measure of the effect of the size of the error. In short, Gaussian distribution is not only a powerful mathematical tool, but also a connection between theory and practical applications. It is also a bridge between theory and practical application. In practice, the Gaussian distribution has a wide range of applications, in the natural sciences, engineering and social sciences and other fields, the Gaussian distribution is used to describe the continuity of random variables, such as measurement error, temperature change, population intelligence level. In this paper, the author briefly deduces the Gaussian distribution derivation process, from the overall and the measurement error of the simple random samples to cut in, to admit that x is already the estimates that should be taken. Hopefully, it will be helpful to scholars who are interested in this area.

Symmetric Q-learning: Reducing Skewness of Bellman Error in Online Reinforcement Learning

In deep reinforcement learning, estimating the value function to evaluate the quality of states and actions is essential. The value function is often trained using the least squares method, which implicitly assumes a Gaussian error distribution. However, a recent study suggested that the error distribution for training the value function is often skewed because of the properties of the Bellman operator, and violates the implicit assumption of normal error distribution in the least squares method. To address this, we proposed a method called Symmetric Q-learning, in which the synthetic noise generated from a zero-mean distribution is added to the target values to generate a Gaussian error distribution. We evaluated the proposed method on continuous control benchmark tasks in MuJoCo. It improved the sample efficiency of a state-of-the-art reinforcement learning method by reducing the skewness of the error distribution.

Error Analysis of Normal Surface Measurements Based on Multiple Laser Displacement Sensors.

The robotic drilling of assembly holes is a crucial process in aerospace manufacturing, in which measuring the normal of the workpiece surface is a key step to guide the robot to the correct pose and guarantee the perpendicularity of the hole axis. Multiple laser displacement sensors can be used to satisfy the portable and in-site measurement requirements, but there is still a lack of accurate analysis and layout design. In this paper, a simplified parametric method is proposed for multi-sensor normal measurement devices with a symmetrical layout, using three parameters: the sensor number, the laser beam slant angle, and the laser spot distribution radius. A normal measurement error distribution simulation method considering the random sensor errors is proposed. The measurement error distribution laws at different sensor numbers, the laser beam slant angle, and the laser spot distribution radius are revealed as a pyramid-like region. The influential factors on normal measurement accuracy, such as sensor accuracy, quantity and installation position, are analyzed by a simulation and verified experimentally on a five-axis precision machine tool. The results show that increasing the laser beam slant angle and laser spot distribution radius significantly reduces the normal measurement errors. With the laser beam slant angle ≥15° and the laser spot distribution radius ≥19 mm, the normal measurement error falls below 0.05°, ensuring normal accuracy in robotic drilling.

G.ridge: An R Package for Generalized Ridge Regression for Sparse and High-Dimensional Linear Models

Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to non-uniform shrinkage; this was shown to perform well in sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package “g.ridge” (first version published on 7 December 2023) that implements both the ridge estimator and generalized ridge estimator. The package is equipped with generalized cross-validation for the automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on the R package “glmnet”. Hence the generalized ridge estimator may be the most recommended estimator for sparse and high-dimensional models. We demonstrate the package using intracerebral hemorrhage data.

Assessment of the global Copernicus, NASADEM, ASTER and AW3D digital elevation models in Central and Southern Africa

ABSTRACT Validation studies of global Digital Elevation Models (DEMs) in the existing literature are limited by the diversity and spread of landscapes, terrain types considered and sparseness of groundtruth. Moreover, there are knowledge gaps on the accuracy variations in rugged and complex landscapes, and previous studies have often not relied on robust internal and external validation measures. Thus, there is still only partial understanding and limited perspective of the reliability and adequacy of global DEMs for several applications. In this study, we utilize a dense spread of LiDAR groundtruth to assess the vertical accuracies of four medium-resolution, readily available, free-access and global coverage 1 arc-second (30 m) DEMs: NASADEM, ASTER GDEM, Copernicus GLO-30, and ALOS World 3D (AW3D). The assessment is carried out at landscapes spread across Cape Town, Southern Africa (urban/industrial, agricultural, mountain, peninsula and grassland/shrubland) and forested national parks in Gabon, Central Africa (low-relief tropical rainforest and high-relief tropical rainforest). The statistical analysis is based on robust accuracy metrics that cater for normal and non-normal elevation error distribution, and error ranking. In Cape Town, Copernicus DEM generally had the least vertical error with an overall Mean Error (ME) of 0.82 m and Root Mean Square Error (RMSE) of 2.34 m while ASTER DEM had the poorest performance. However, ASTER GDEM and NASADEM performed better in the low-relief and high-relief tropical forests of Gabon. Generally, the DEM errors have a moderate to high positive correlation in forests, and a low to moderate positive correlation in mountains and urban areas. Copernicus DEM showed superior vertical accuracy in forests with less than 40% tree cover, while ASTER and NASADEM performed better in denser forests with tree cover greater than 70%. This study is a robust regional assessment of these global DEMs.

A comparative study between the two methods GM6.IDRGP(RMVN) and the GM6 method for analyzing the multiple linear regression model in the presence of outliers using the simulation method.

Multiple linear regression is one of the most widely used statistical analysis methods in many scientific fields. Its parameters are estimated based on the ordinary least squares method. Which gives the best unbiased linear estimate if its assumptions are met. The most important of these assumptions is that it has a normal distribution of error with a mean of zero and a constant variance. If the data does not meet certain assumptions, the sample estimates and results may be misleading. The linear regression model is sensitive to the appearance of outliers and leverage points. Therefore, statistical techniques have been developed capable of dealing with or detecting outliers. This led to the emergence of many alternative methods to the OLS method, such as M-Huber, s, LTS, and MM, which have high efficiency and breakdown points, but are affected by HLPs, which result in the problem of Masking and Swamping. The GM6 method is one of the methods that was developed in order to treat such problems through the use of a weight function, but the weight function depends on the individual diagnosis, which gives inaccurate results. In order to overcome this problem, comprehensive diagnostic methods have been proposed, such as the DRGP and IDRGP.RMVN methods. Therefore, in this study, we proposed to employ the IDRGP.RMVN method in the GM6 method algorithm. And comparing it with some hippocampal regression methods through a simulation study in determining the best methods.

Correcting Regressor-Endogeneity Bias via Instrument-Free Joint Estimation Using Semiparametric Odds Ratio Models

Endogenous regressors can lead to biased estimates for causal effects using methods assuming regressor–error independence. To correct for endogeneity bias, the authors propose a new method that accounts for the regressor–error dependence using flexible semiparametric odds ratio conditional models; the approach requires neither parametric distributional assumptions nor tuning parameters for modeling endogenous regressors’ distributions conditional on the error term and exogenous regressors. Inference is achieved via optimizing the profile likelihood concentrating on the parameters of interest. The proposed approach requires no use of instrumental variables (IVs), observed or latent, that must satisfy the stringent condition of exclusion restriction. Nonnormally distributed endogenous regressors are required for model identification with a normal error distribution. The approach's flexibility in capturing regressor–error dependence increases the capability of IV-free endogeneity correction and provides opportunities to improve the accuracy of causal effect estimation. Unlike existing IV-free methods, the proposed approach can handle discrete endogenous regressors with few levels, such as binary regressors or count regressors with small means, and is thus applicable to a plethora of applications involving such regressors. The authors demonstrate the versatility of the approach for binary, count, and continuous endogenous regressors using comprehensive simulation studies and empirical data.

Review of the Monothematic Series of Publications Concerning Research on Statistical Distributions of Navigation Positioning System Errors

This review presents the main results of the author’s study, obtained as part of the post-doctoral (habilitation) dissertation entitled “Research on Statistical Distributions of Navigation Positioning System Errors”, which constitutes a series of five thematically linked scientific publications. The main scientific aim of this series is to answer the question of what statistical distributions follow the position errors of navigation systems, such as Differential Global Positioning System (DGPS), European Geostationary Navigation Overlay Service (EGNOS), Global Positioning System (GPS), and others. All of the positioning systems under study (Decca Navigator, DGPS, EGNOS, and GPS) are characterised by the Position Random Walk (PRW), which means that latitude and longitude errors do not appear randomly, being a feature of the normal distribution. The research showed that the Gaussian distribution is not an optimal distribution for the modelling of navigation positioning system errors. A higher fit to the 1D and 2D position errors was exhibited by such distributions as beta, gamma, and lognormal. Moreover, it was proven that the Twice the Distance Root Mean Square (2DRMS(2D)) measure, which assumes a priori normal distribution of position errors in relation to latitude and latitude, was smaller by 10–14% than the position error value from which 95% fixes were smaller (it is known as the R95(2D) measure).

ТОЧНІСТЬ КООРДИНАТ ВИЗНАЧЕННЯ МІСЦЯ СУДНА, РОЗРАХОВАНИХ МЕТОДОМ НАЙМЕНШИХ КВАДРАТІВ, ПРИ НАЯВНОСТІ НАДЛИШКОВИХ ЛІНІЙ ПОЛОЖЕННЯ

This article discusses the accuracy of the vessel’s position coordinates, calculated using the least squares method, in the presence of redundant line positions (LP) over time, assuming the LP error is normally distributed. It is stated that for a normal error distribution, the least squares method is the maximum likelihood method, thus the norm of the positional error covariance matrix is minimized, ensuring the highest accuracy of the vessel’s position coordinates. Field observation results are presented, where experimental data were obtained, demonstrating the possibility of altering navigational parameters. Following the adjustment of navigational parameters, a series of tests were conducted, exceeding 100 in total. The analysis of these results indicates that deviations in navigational parameterization, achieved over a limited time interval, conform to the normal law of variability distribution. Adjustments to the parameters over a larger interval are subject to changes in the laws of change, with the degree of power of some of the normal law proportional to the interval of the series value of the navigational parameter. It is demonstrated that the efficiency of observing the vessel’s coordinates, calculated by the least squares method during times of redundant LP, the errors of which can be calculated according to different laws, is less than one. To evaluate the efficiency of coordinate observation derived from overly large LP and gaps using the least squares method, a computer simulation was performed. During this simulation, efficiency values were compared with the highest theoretically achievable efficiency values, as outlined in the article, and the difference between them in the case of high-technological parameters was less than 22.0%. The simulations conducted showed good agreement between the efficiency assessments derived from analytical expressions and those obtained from the simulations, thereby confirming the validity of the analytical method for evaluating the efficiency of observed coordinates, calculated by the least squares method. Keywords: navigational safety, accuracy of coordinates assignment, change of law and subdivision, simulation modelling.

Help the Hong Kong Second-hand Sailboat Broker Make a Big Profit

With the world economy recovering and the increasing activity in the second-hand market, the second-hand sailboat market has shown enormous potential. In order to help a Hong Kong second-hand sailboat broker better understand the market and make accurate predictions, we searched for and supplemented other relevant data on second-hand sailboats based on the given data, and established a multiple linear regression model and other models on this basis.
 In Task 1, we first supplemented the existing data by adding six variables. We then conducted data cleaning and encoding, and performed multicollinearity tests, finding that there was multicollinearity. We used the stepwise regression method for feature selection to reduce multicollinearity, and then established a multiple linear regression model and calculated the mean absolute error for different variants of sailboats. We then used the Shapiro-Wilk test method to judge the normal distribution of errors and found that the data showed a slight deviation from normal distribution. Therefore, this model could be established. The results showed that Length, Make, and Year had the greatest impact on the listing price of each sailboat, and the model had high accuracy in estimating the prices of different variants of sailboats.
 In Task 2, we conducted one-way ANOVA on the regions, calculated the intergroup differences and total dispersion of each feature, and then used classification and summarization to obtain the average prices of each feature. We found that the regions had an impact on the prices, and the regional effects were not consistent for all sailboat variants. In addition, we found differences in the lengths of second-hand sailboats in different countries, which were mostly distributed between 40ft-50ft.
 In Task 3, we first made box plots of the average prices in different geographical regions, then made radar charts of each feature in these three regions, and finally re-established a multiple linear regression model by using whether each sailboat type was sold in Hong Kong as a 0-1 variable. We found that the second-hand sailboat markets in the United States and Hong Kong were similar. The prices of sailboats in Hong Kong were generally higher than those in other regions, and their impact on Monohulled Sailboats and Catamarans was different.
 In Task 4, we calculated the average prices of second-hand sailboats in each country, visualized the data, and established a map model. We found that GDP per capita (USD) and GDP (USD billion) had significant differences in their impact on length.
 In Task 5, based on the searched second-hand sailboat transaction data in Hong Kong, we established a model for the transaction price and frequency of sailboats according to their single or double type, and found that brokers should pay attention to the main features of second-hand sailboats and successful cases in the US second-hand sailboat market, as well as the price range of sailboats.
 To improve our model, we adopted the random forest model that can handle nonlinear relationships, improve the robustness of the model, avoid overfitting, and increase prediction accuracy.

Plant growth forms influence sandhill longleaf pine regeneration

Longleaf pine researchers have quantified many aspects of regeneration, growth and yield, but have focused on productive sites such as pine flatwoods and upland pine. Sandhill longleaf pine woodlands represent >40 % of remnant stands of longleaf pine ecosystems; most have no history of agriculture due to poor site productivity, yet many have been degraded by resin collection, grazing and fire exclusion. Restoration of structure and function of sandhill longleaf pine depends on understanding early stand-development processes, which are governed by fire, propagule availability, and competition from a range of overstory tree species not limited to longleaf pine. We analyzed a 16-year monitoring dataset from Eglin Air Force Base in northwest Florida, USA, focusing on how four tree growth forms influenced longleaf pine juvenile stages of seedling and sapling numbers and ingrowth to the subadult size class. Analyses were done with generalized linear mixed models using Poisson, normal, or negative binomial error distributions according to the response variable.Restoration activities were effective at reducing numbers of sapling evergreen hardwoods, and basal area of overstory sand pine and other non-longleaf conifers was reduced by 35 % over the 16-year study. We observed threshold values for adult longleaf pine effects on seedlings and ingrowth; seedling numbers were maximized at 7.8 m2/ha, and ingrowth was maximum at 5.1 m2/ha. Seedling density was strongly governed by mast year. Sand pine, an invasive native pine, was detrimental to longleaf pine at all juvenile life stages even at low basal area. Deciduous oaks, which have been observed to facilitate longleaf pine seedling establishment, instead facilitated ingrowth to the subadult size class. Evergreen hardwoods, which may dampen fire behavior, only decreased longleaf pine density at the sapling stage. Ongoing silvicultural restoration activities should continue to focus on frequent fire and sand pine removal; deciduous oaks should be retained for their facilitative value; and removal of evergreen hardwoods should not be a high priority as long as prescribed fire can propagate in these lower productivity sites.

Forecasting Exchange Rates Comparison In The Presence Of Instabilities

Exchange rate forecasting is an inherent approach in financial risk management, yet previous forecasting models were criticized for their poor predictive ability, mainly during periods of exceptional macroeconomic weaknesses. This is attributed to their failure to identify the importance and strength of key transmission and amplification channels, especially those linked to financial markets and uncertainty. Though there is no model that can be precise, especially during periods of crises, it is important to find a model that can yield near-accurate results. The present study therefore evaluates the different forecasting models, considering how each handles instabilities. The Rossi Sekhposyan forecast rationality test results reveal that the EGARCH model under general error distribution and APARCH under normal error distribution show the strongest evidence against rationality around the year 2009, identifying the concentration of instabilities during that time. This vindicates the need to control for instabilities in forecasting. This implies that, in the presence of instabilities, the fluctuation tests are more powerful than traditional tests.

Skewness and Staging: Does the Floor Effect Induce Bias in Multilevel AR(1) Models?

Multilevel autoregressive models are popular choices for the analysis of intensive longitudinal data in psychology. Empirical studies have found a positive correlation between autoregressive parameters of affective time series and the between-person measures of psychopathology, a phenomenon known as the staging effect. However, it has been argued that such findings may represent a statistical artifact: Although common models assume normal error distributions, empirical data (for instance, measurements of negative affect among healthy individuals) often exhibit the floor effect, that is response distributions with high skewness, low mean, and low variability. In this paper, we investigated whether—and to what extent—the floor effect leads to erroneous conclusions by means of a simulation study. We describe three dynamic models which have meaningful substantive interpretations and can produce floor-effect data. We simulate multilevel data from these models, varying skewness independent of individuals’ autoregressive parameters, while also varying the number of time points and cases. Analyzing these data with the standard multilevel AR(1) model we found that positive bias only occurs when modeling with random residual variance, whereas modeling with fixed residual variance leads to negative bias. We discuss the implications of our study for data collection and modeling choices

Robust rank-based meta-analyses for two-sample designs with application to platelet counts of malaria infection data.

In this paper, we propose robust meta-analysis procedures for individual studies that report a broad range of robust summary statistics for a two-sample problem. Summary statistics of individual studies could be presented in different forms including full data, medians of the two samples, the Hodges-Lehman and Wilcoxon estimates of the location shift parameters. Data synthesis is made under both fixed-effect and random-effect meta-analysis models. We systematically compare these robust meta-analysis procedures via simulation studies to meta-analysis procedure based on sample means and variances from individual studies under a wide range of error distributions. We show that the coverage probabilities of the robust meta-analysis confidence intervals are quite close to the nominal confidence level. We also show that mean square error (MSE) of the robust meta-analysis estimator is considerably smaller than that of the non-robust meta-analysis estimator under the contaminated normal, heavy tailed and skewed error distributions. The robust meta-analysis procedures are then applied to platelet count reduction for malaria infected patients in Ghana.

Prediction Distribution for Simultaneous Auto-Regressive Model with Multivariate Student-T Error under the Bayesian Approach

Prediction distribution is a basis for predictive inferences applied in many real world situations. The Bayesian approach under uniform prior is employed in this paper to derive the prediction distribution for Simultaneous Auto-regressive model with multivariate Student-t error distribution. Conditional on a set of realized responses, a single and a set of future responses have a univariate and multivariate Student-t distributions respectively, whose degrees of freedom depend on the size of the realized sample and the dimension of the auto-regression parameters' vector but do not depend on the degrees of freedom of the error distribution. Results are identical to those obtained under normal error distribution by a range of statistical approaches such as the normal distribution, autocorrelations and classical methods. This indicates not only the inference robustness with respect to departures from normal error to multivariate Student-t error distributions, but also indicates that the Bayesian approach with uniform prior is competitive with other statistical methods in the derivation of prediction distribution.

Assessment of the Quality of Radio-Frequency Filters Used in the Organization of Communication in Railway Transport in the Production Process

The article discusses the main types of radio-frequency filters in radio-frequency systems. The errors in the characteristics of radio-frequency filters during the production process are analyzed. The characteristics of the tolerance field and the normal distribution of the production error of the output parameters of products are given. It is shown that in order to reduce the percentage of defective products due to the parameters going beyond the permissible limits, the technological process of filter production should be organized in a certain way.

Optimal traffic operation for maximum energy efficiency in signal-free urban networks: A macroscopic analytical approach

The integration of artificial intelligence and wireless communication technologies in communicant autonomous vehicles (CAVs) enables coordinating the movement of CAV platoons at signal-free intersections. The capacity of signal-free intersections can be significantly improved by adjusting traffic variables at a macroscopic scale; however, the resulting improvement in the capacity does not necessarily have a positive impact on the energy consumption of CAVs at the network level. In this research, we develop an analytical model to enhance energy efficiency by optimizing macroscopic traffic variables in signal-free networks. To this end, we adopt a macroscopic modeling approach to estimate the operational capacity by accounting for the stochasticity resulting from the error in synchronizing the arrival and departure of consecutive platoons in crossing directions at intersections. We also develop a macrolevel analytical model to estimate expected energy loss during the acceleration/deceleration maneuver required for resynchronization at intersections as a function of synchronization success probability. We then maximize energy efficiency by minimizing expected energy loss and maximizing expected capacity in a biobjective optimization framework. We solve the energy efficiency problem using an analytical approach to derive a closed-form solution for the optimal traffic speed and the length of the marginal gap between the passage of consecutive platoons in crossing directions through intersections for a (general) normal distribution of the operational error. Having the closed-form solution of the energy efficiency problem, we balance the trade-off between energy loss and operational capacity at a large scale by extending the analytical model to the network level using the Macroscopic Fundamental Diagram (MFD) concept. The results of our two-ring simulation model indicate the accuracy of the proposed analytical model in estimating the macroscopic relationship between the expected energy loss at intersections and the vehicular density in signal-free networks. Our numerical results also show that optimizing the traffic speed and marginal gap length can improve energy efficiency by 31% at the cost of a 16% decrease in maximum capacity.

Forecasting Interest Rate Volatility In Nigeria In The Arch-Garch Family Models

Modeling the volatility of interest rates is essential for many areas in finance. However, it is well known that interest rate series exhibit non-normal characteristics that may not be captured with the standard GARCH model with a normal error distribution. But which GARCH model and error distribution to use is still open to question, especially where the model that best fits the in-sample data may not give the most effective out-of-sample volatility forecasting ability, which we use as the criterion for the selection of the most effective model from among the alternatives. In this work, the GARCH family models were employed in modeling interest rate volatility in Nigeria. A time series of data spanning January 2000 to December 2018 (in-sample data) was used to fit the models and out-of-sample data running from January to December 2019 to determine the best conditional volatility forecast. Twenty-four symmetric and eighteen asymmetric models were estimated and compared using three distribution errors; the normal, student's t, and the generalized error distributions; while four error loss functions, namely, RMSE, MAE, MAPE, and TIC, were adopted to determine the best fit and conditional volatility forecast. The result shows that the symmetric GED-GARCH (1,1) model was considered the overall best fit in both the symmetric and asymmetric models. The best-fitted GED-GARCH (1,1) model exhibited volatility persistence. The in-sample and out-of-sample volatility forecast of the GED-GARCH (1,1) model reveals that unconditional mean and variance will be achieved in the third month of 2019. Some transmission spillover effects running from the exchange and inflation rates to interest rates were also detected.