Fourier Series Estimator Research Articles

PREDICTION OF UNIT VALUE INDEX OF EXPORTS OF SITC 897 JEWELRY AND PRECIOUS GOODS GROUP IN INDONESIA

Export is an international trade activity that plays an important role in the economic progress in Indonesia. One of Indonesia's leading commodities that dominate the export market is jewelry. In export activities, the export unit value index is an important component that serves to describe the development of export commodity prices. This unit value index always changes every time and fluctuates. This research conducts a comparative analysis of the performance of parametric method, non-parametric method, and machine learning, specifically, ARIMA, Fourier series estimator, and Support Vector Regression (SVR). This study aims to evaluate the effectiveness of various methods in improving prediction accuracy for the unit value index of the SITC code 897 in Indonesia. The research data used is secondary data including monthly export unit value index data with SITC code 897 in Indonesia obtained from the Central Bureau of Statistics. The data divided into 90% training data and 10% testing data. The methods used in this analysis are ARIMA, Fourier series estimator, and SVR. The best model obtained from each method is ARIMA (1,1,1) with MAPE of 10.92%, Fourier series estimator with MAPE of 8.47%, and an SVR RBF kernel function with MAPE of 3.73%. The results of this study obtained the best method for predicting the unit value index of SITC code 897 is SVR with an RMSE value of 8.288 and very good prediction accuracy.

Nonparametric regression estimator of multivariable Fourier Series for categorical data

In recent years, Fourier Series estimators in nonparametric regression for quantitative data have received significant attention. However, in reality, there is often a relationship between response and predictor, where the response is categorical data. Some methods developed today to address the case of qualitative response data use only certain approaches. No Fourier Series estimator can handle categorical response data. This paper introduces a new method that uses response variable in the form of categorical data. This study aimed to develop a multivariable Fourier Series nonparametric regression estimator for categorical data. The research methods used are literature and theoretical studies. To apply this method, we used two application data. The results obtained indicate that the nonparametric regression of the Fourier Series provides significantly better estimation results and accuracy for both data applications, due to the small deviance value and larger AUC and Press'Q values. The highlights of this research are summarized below.•The Fourier Series method for categorical data assumes a relationship between the logit function and predictor variables that has a repeating pattern.•The estimator was obtained through Maximum Likelihood Estimation and Newton–Raphson method.•The Fourier Series nonparametric regression method provides better estimation than binary logistic regression.

COMPARISION OF RICE PRICE PREDICTION RESULTS IN EAST JAVA USING FOURIER SERIES ESTIMATOR AND GAUSSIAN KERNEL ESTIMATOR SIMULTANEOUSLY

Extreme weather changes and the El Nino phenomenon in 2023 will cause drought, resulting in a decrease in rice production and an increase in rice prices. It has significantly impacted East Java Province as it is the most extensive rice supplier in Indonesia. This study aims to predict the price of rice with six different qualities using the Fourier series estimator and Gaussian kernel function simultaneously. The results show that the Gaussian kernel method, with a bandwidth value of 1, produces a better model with a MAPE value of 0.228259% than the sine function Fourier series method in predicting rice prices based on six different qualities. The prediction results using the Gaussian kernel function method are categorized as highly accurate because they are less than 10%. This research accelerates the realization of SDG 2 related to "Zero Hunger" through government policies to control the high price of rice in Indonesia. Recommendations that can be given through the research results include cooperation with the government, which can help access information and resources needed to manage price risks.

PREDICTION OF CRUDE OIL PRICES IN INDONESIA USING FOURIER SERIES ESTIMATOR AND ARIMA METHOD

Crude oil is one of the non-renewable natural resources that is crucial for countries around the world in driving economic development. However, the availability of crude oil is decreasing over time. The high demand for crude oil results in scarcity which causes price fluctuations. Low oil prices can reduce state revenues, disrupt development programs, and even trigger budget deficits. On the other hand, an increase in crude oil prices can make a positive contribution to state revenues. Crude oil exports become more profitable, which can increase state revenue through royalties and taxes levied on the oil and gas sector. This additional revenue can be used to support infrastructure development, social programs, and investment in key sectors of the economy. High oil prices can also harm the economy. With the many impacts that can be caused by crude oil prices, the government must be able to anticipate and prepare for it. The data used in this study are data on crude oil prices in Indonesia for monthly periods from January 2018 to October 2023 sourced from the official website of the Ministry of Energy and Mineral Resources (ESDM) of the Republic of Indonesia. The researcher tried to compare two analysis methods, namely the Fourier series and the ARIMA estimator. The results of this study show that the best method in predicting crude oil prices in Indonesia is the Fourier series estimator with Cos-Sin function which produces RMSE and MAPE values of 7.93 and 8.4%. The prediction results can be used as a reference for the government to anticipate and make programs or policies that are more focused and targeted toward the impacts that can be caused by changes in crude oil prices.

Nonparametric Regression Modeling with Multivariable Fourier Series Estimator on Average Length of Schooling in Central Java in 2023

Nonparametric Regression Modeling with Multivariable Fourier Series Estimator on Average Length of Schooling in Central Java in 2023

Price Prediction of Staples with Simultaneous Fourier Series Estimator as a Contribution to Solve the National Food Problem

This study provides an overview related to the prediction of prices for staples that are widely consumed by the Indonesian people and often experience price fluctuations at certain times, namely cooking oil, chili, and chicken eggs. Based on the Market Monitoring System and Staples of the Ministry of Trade, the national average price of cooking oil as of January 3, 2022, reached USD 1.17per liter. The average price of chicken eggs reached USD 1,98 per kilogram, an increase of 20.16% at the same time. In addition, based on the National Strategic Food Price Information Center, the average price of chili in traditional markets throughout the province rose by USD 0.19 or about 3.16% and reached USD 6.29 per kilogram. The prediction of staple food prices in this study was formed using a nonparametric regression model of the Fourier series estimator. This regression model has high flexibility in forming the model and estimating the fluctuation data pattern, which is not known in the form of time-series data. The data in this study is sourced from the National Strategic Food Price Information Center website with the response variables used being the daily prices of cooking oil, chicken eggs, and chili from September 1, 2021, to December 31, 2021, as training data. In addition, the same commodity data from January 1, 2022, to January 10, 2022, is used as testing data. The best model from the estimation results with the Fourier series is a model with an oscillation parameter of 25 which contains a sine cosine basis with a coefficient of determination of 83.05%and an MSE value of 1.628. The selected model also has a very good performance predicting the prices of the three staples with a MAPE value of 1.082%.

MODELING OPEN UNEMPLOYMENT RATE IN KALIMANTAN ISLAND USING NONPARAMETRIC REGRESSION WITH FOURIER SERIES ESTIMATOR

Nonparametric regression is a regression approach that is used to determine the relationship between the response variable and the predictor variable if the shape of the regression curve is unknown. One of the popular estimators used in nonparametric regression is the Fourier series estimator. Fourier series nonparametric regression is generally used when the pattern of the investigated data is unknown and there is a tendency for the pattern to repeat. The purpose of this study is to estimate nonparametric regression using the Fourier series approach and to find out the factors that influence the open unemployment rate on the island of Borneo in 2021. The criteria for the goodness of the model used Generalized Cross Validation (GCV) and the coefficient of determination ( ). Based on the results, it was found that the best nonparametric regression model for the Fourier series was the model with 5 oscillations which indicated a minimum GCV of 10.47 and an of 74.22%. Furthermore, based on the results of parameter significance testing either simultaneously or partially, it shows that all predictor variables have a significant effect on the open unemployment rate. The predictor variables include the labor force participation rate, the average length of schooling, the percentage of poor people, economic growth rate, and total population.

Prediction of extreme weather using nonparametric regression approach with Fourier series estimators

In Jepara, Central Java, Indonesia, significant correlations between high rainfall and wind speed impact multiple sectors including health, agriculture, and infrastructure. This study aims to predict the effects of extreme weather by employing nonparametric regression based on Fourier series estimators. Data from December 2023 to March 2024, sourced from NASA, were analyzed using sinus, cosinus, and combined Fourier functions to model the dynamic and seasonal fluctuations of weather variables. This approach allows for a flexible modeling of these previously undefined functional relationships. The analysis revealed that the combined function model was superior, achieving an optimal Generalized Cross-Validation (GCV) score of 0,236498 with a Fourier coefficient K=3, indicating a well-fitted model. Moreover, this model exhibited a low Mean Absolute Percentage Error (MAPE) of 1,887, demonstrating high predictive accuracy. These findings not only affirm the efficacy of Fourier series in nonparametric regression for weather forecasting but also underscore its potential in informing public policy and bolstering disaster preparedness in Jepara and similar regions vulnerable to extreme weather conditions

Prediksi Harga Ekspor Non Migas di Indonesia Berdasarkan Metode Estimator Deret Fourier dan Support Vector Regression

Economic growth is one of the indicators in the Sustainable Development Goals (SDGs) on increasing economic activity. One of the activities that supports the running of the economy is trade between countries, such as exports. In Indonesia, non-oil and gas exports have played an important role in total exports in recent years, including coal exports being the main export. Therefore, price predictions for Indonesia's non-oil and gas exports are very important as material for evaluating policies to encourage economic growth. This is the main focus of this research. In this study, non-oil and gas export price forecasts are made taking into account current issues such as the COVID-19 pandemic and the Russia-Ukraine war. The accuracy of the model obtained from the Fourier series estimator and Support Vector Regression (SVR) is investigated by comparing the Mean Absolute Percentage Error (MAPE) value to predict Indonesia's non-oil and gas export prices. The results of the study show that the COVID-19 pandemic and the Russia-Ukraine war have had a significant impact on non-oil and gas export prices. The SVR model with the Radial Basis Function (RBF) kernel shows better accuracy than the Fourier series estimator model of the cos sin function, with MAPE values of 9.29 and 15.26% for each test data, respectively. Therefore, this study is expected to be the basis for formulating policies related to regulating non-oil and gas export processes to support economic growth in Indonesia.

Fourier Series Nonparametric Regression Modeling in the Case of Rainfall in West Java Province

The Fourier series is a trigonometric polynomial that has flexibility, so it adapts effectively to the local nature of the data. This Fourier series estimator is generally used when the data used is investigated for unknown patterns and there is a tendency for seasonal patterns. This study aims to determine the results of the best Fourier series nonparametric regression model and the level of accuracy of the Fourier series nonparametric regression model on rainfall data by month in West Java Province in 2015-2019. This research is about a nonparametric regression model of Fourier series which is estimated using Ordinary Least Square method. Nonparametric regression using the Fourier series approach was applied to Rainfall data in West Java Province in 2015-2019. The independent variables used were the average air humidity, air pressure, wind speed, and air temperature. The model used to model the amount of rainfall in West Java Province is a nonparametric Fourier series. The nonparametric regression model is the best Fourier series with K =13 values obtained Generalized Cross Validation, Mean Square Error, and R2 respectively at 549.92; 462.09; and 97.30%. The results showed that the variables of air humidity and air pressure had a significant effect on rainfall.

Bias reduction by transformed flat-top Fourier series estimator of density on compact support

The problem of nonparametric estimation of a univariate density with rth continuous derivative on compact support is addressed (). If the density function has compact support and is non-zero at either boundary, regular kernel estimator will be completely biased at such boundary. Although several correction methods were proposed to improve the bias at the boundary to in the last decades, this paper initiates a way to further improve bias to higher order () for interior area of density function support, while remaining the order of bias at boundary. We will first review flat-top kernel estimator and flat-top series estimator, then propose the Transformed Flat-top Series estimator. The theoretical analysis is supplemented with simulation results as well as real data applications.

Comparison of simultaneously nonparametric regression based on spline and Fourier series estimator related social aid distribution in Indonesia

Several estimators in the nonparametric regression approach that are often used are the Spline estimator and the Fourier series. Both estimators have high flexibility and can adapt to the local nature of the data effectively. This study applies these two methods to compare the best performance of the formed model. The data used in this study are multi-response data in the form of types of government assistance and multi-predictor data in the form of factors that are thought to affect the distribution of aid receipts in the community. This research is important to optimize the distribution of welfare assistance in Indonesia, especially during the Coronavirus Disease-19 (Covid-19) pandemic. By using the Generalized Cross-Validation (GCV) criteria for the parsimony model, the estimator chosen to predict the distribution of welfare assistance in Indonesia is the Fourier series estimator with cosine and sine bases. The goodness of the nonparametric regression model with the Fourier series estimator can be seen from the minimum GCV value generated with one oscillation parameter, which is 1.483961, with a Mean Square Error (MSE) of 2.1257374, and R 2 of 0.923143. The prediction results are expected to be the government's recommendation for the restoration of community welfare through equitable distribution of aid to support the achievement of the Sustainable Development Goals (SDGs).

Simultaneous identification, modeling and registration refinement of poles using laser scanning point clouds

The method presented herein performs the tasks of identification, modeling, and registration refinement of poles using Light Detection And Ranging (LiDAR) point clouds. This method starts with a preliminary segmentation followed by eliminating outliers by integrating Fourier series and robust estimators. Poles’ cross sectional shapes are then identified by a customized template matching. Afterwards, points belonging to poles are extracted and the as-built model and registration-refined version of poles are generated. The algorithm was tested on five datasets including point clouds of three industrial sites, an urban environment, and a pole-like monument with very different volumes, resolutions, and configurations. The developed method works robustly despite the challenges that are often present in LiDAR data comprising outliers, non-uniform point sampling, gaps, and registration error. The obtained results indicate that 116 out of 117 poles in all five datasets were identified with no false positives at the object level. At point level, it reached greater than 98% average precision and 98% average accuracy in all datasets. Poles were modeled with a sub-millimeter precision in all datasets except for the third dataset in which poles were modeled with millimeter precision.

An Analysis about Fourier Series Estimator in Nonparametric Regression for Longitudinal Data

Fourier series is a function that is often used Mathematically and Statistically especially for modeling. Here, Fourier series can be constructed as an estimator in nonparametric regression. Nonparametric regression is not only using cross section data, but also longitudinal data. Some of nonparametric regression estimators have been developed for longitudinal data case, such as kernel, and spline. In this study, we concentrate to develop an inference analysis that related to Fourier series estimator in nonparametric regression for longitudinal data. Nonparametric regression based on Fourier series is capable to model data relationship with fluctuation or oscillation pattern that represents with sine and cosine functions. For point estimation analysis, Penalized Weighted Least Square (PWLS) is used to determine an estimator for parameter vector in nonparametric regression. Different with previous studies, PWLS is used to get smooth estimator. The result is an estimator for nonparametric regression curve for longitudinal data based on Fourier series approach. In addition, this study also investigated the asymptotic properties of the nonparametric regression curve estimators using the Fourier series approach for longitudinal data, especially linearity and consistency. Some study cases based on previous research and a new study case is given to make sure that Fourier series estimator in nonparametric regression has good performance in longitudinal data modeling. This study is important in order to develop further inferences Statistics, such as interval estimation and test hypothesis that related nonparametric regression with Fourier series estimator for longitudinal data.

Contribution Analysis of “Suroboyo Bus” in Waste Management Based on Two Form of Complete Fourier Series Estimator

Plastic waste is a problem that almost exists in all countries. This problem arises because of the lack of facilities that can handle the plastic waste. Suroboyo Bus is an innovation for this problem because Suroboyo Bus uses plastic bottles as payment. The purpose of this research is to predict the percentage contribution of Suroboyo Bus in handling plastic waste. The Fourier series estimator performs well for data modeling with seasonal trend patterns. This paper examines two approaches to the Fourier series. The difference between the approaches is the inclusion of the phi (π) function in the model. The result shows the goodness of fit criterion model with π function are for and 0,08% for MAPE whereas the fit criterion model without π function is 100% for and 0,07% for MAPE. In conclusion, the Fourier series model without the π function is better because the Fourier series model without the π function is more satisfy the goodness of fit criteria than the Fourier series model with the π.

The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression

Nonparametric regression becomes a potential solution if the parametric regression assumption is too restrictive while the regression curve is assumed to be known. In multivariable nonparametric regression, the pattern of each predictor variable’s relationship with the response variable is not always the same; thus, a combined estimator is recommended. In addition, regression modeling sometimes involves more than one response, i.e., multiresponse situations. Therefore, we propose a new estimation method of performing multiresponse nonparametric regression with a combined estimator. The objective is to estimate the regression curve using combined truncated spline and Fourier series estimators for multiresponse nonparametric regression. The regression curve estimation of the proposed model is obtained via two-stage estimation: (1) penalized weighted least square and (2) weighted least square. Simulation data with sample size variation and different error variance were applied, where the best model satisfied the result through a large sample with small variance. Additionally, the application of the regression curve estimation to a real dataset of human development index indicators in East Java Province, Indonesia, showed that the proposed model had better performance than uncombined estimators. Moreover, an adequate coefficient of determination of the best model indicated that the proposed model successfully explained the data variation.

Semiparametric regression based on fourier series for longitudinal data with Weighted Lest Square (WLS) optimization

Regression modelling is one Statistical methods that be used to investigate the relationship between predictor variable and response variable. In regression modelling can be estimated with three approaches, such as parametric, nonparametric and semiparametric regression. In this case, we concentrated to elaborate semiparametric regression. Semiparametric regression consists of parametric and nonparametric component. This research examined semiparametric regression model with Fourier series estimator for longitudinal data. By minimizing Weighted Least Square (WLS), the Fourier series estimator depends on the oscillation parameter. The result is the estimator for parameter and curve regression, that be used to model with real data. The optimal model is selected based on minimum Generalized Cross Validation (GCV) which affects the small value of Mean Square Error (MSE) and high determination coefficient so that the model can be used further as estimation and prediction.

Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression

So far, most of the researchers developed one type of estimator in nonparametric regression. But in reality, in daily life, data with mixed patterns were often encountered, especially data patterns which partly changed at certain subintervals, and some others followed a recurring pattern in a certain trend. The estimator method used for the data pattern was a mixed estimator method of smoothing spline and Fourier series. This regression model was approached by the component smoothing spline and Fourier series. From this process, the mixed estimator was completed using two estimation stages. The first stage was the estimation with penalized least squares (PLS), and the second stage was the estimation with least squares (LS). Those estimators were then implemented using simulated data. The simulated data were gained by generating two different functions, namely, polynomial and trigonometric functions with the size of the sample being 100. The whole process was then repeated 50 times. The experiment of the two functions was modeled using a mixture of the smoothing spline and Fourier series estimators with various smoothing and oscillation parameters. The generalized cross validation (GCV) minimum was selected as the best model. The simulation results showed that the mixed estimators gave a minimum (GCV) value of 11.98. From the minimum GCV results, it was obtained that the mean square error (MSE) was 0.71 and R2 was 99.48%. So, the results obtained indicated that the model was good for a mixture estimator of smoothing spline and Fourier series.

Three form fourier series estimator semiparametric regression for longitudinal data

Analysis of regressionis one technique that is often used in statistical analysis. There are three regression analysis approaches, such as parametric regression, nonparametric regression and semiparametric regression. Semiparametric regression consists of parametric components and nonparametric components. Parametric component that used such as linear estimator and nonparametric component by using a Fourier series estimator. Semiparametric regression approach that use Fourier series, have an advantages which is can resolve oscillation data pattern. This study compares the three Fourier series estimators such as sine, cosine, and combination between cosine and sine or complete estimator for longitudinal data. Longitudinal data can explain more complete information than cross section data or time series data. The purpose of this study is to introduce another Fourier series for the application of electricity consumption in Madura island. The results of this study indicated the optimal model in predicting electricity consumption in Madura island. The best estimator is the Fourier series estimator with the smallest Generalized Cross Validation (GCV) and Mean Square Error (MSE), and the biggest determination coefficient values by considering the parsimony of the model.

Semiparametric regression curve estimation for longitudinal data using mixed spline truncated and fourier series estimator

Semiparametric regression is a regression approach that is used when the form of regression curve is assumed to be partly known and partly unknown. In the semiparametric regression model, the same type of estimation method is generally used for some or all of the predictor variables. There are many examples of data cases that have different patterns on each predictor variable, so if the data is forced to use only one form of estimator to estimate the regression curve, it will produce estimation that will not be appropriate to the data pattern. Therefore, a mixed estimator needs to be developed. However, mixed estimator in previous studies was only able to handle cross-sectional data. So this study uses longitudinal data that has advantages, one of which is estimation of each individual characteristic and time (period) characteristic are obtained separately in longitudinal data. Therefore, this study develops a mixed Spline Truncated and Fourier Series estimator in semiparametric regression for longitudinal data using the Weighted Least Square method. Estimation of the semiparametric regression model for longitudinal data using mixed estimator of Spline Truncated and Fourier Series is where D (K,m) = XA (K,m) + TB (K,m) + ZC (K,m). The selection of the best model is based on knot points and optimum oscillation parameters that should be selected optimally using minimum Generalized Cross Validation (GCV) value.