PEMODELAN HARGA EMAS DUNIA MENGGUNAKAN METODE NONPARAMETRIK POLINOMIAL LOKAL DILENGKAPI GUI R

Investing in gold is a flexible choice because it can be sold at any time and used as an emergency fund. Investors should have the knowledge to predict data from time to time to achieve investment goals. One of the statistical methods for time series data modeling is ARIMA. The ARIMA model is strict with the assumptions that the data must be stationary, the residuals must be normally distributed, independent, and with constant variance, so an alternative model is proposed, namely nonparametric regression model, which has no modeling assumptions requirement. In this study, the daily world gold price data will be modeled using a local polynomial nonparametric model as an alternative because the assumptions in the ARIMA are not fulfilled. The data is divided into 2 parts, namely in sample data from January 2, 2020 to November 30, 2020 to form a model and out sample data from December 1, 2020 to December 31, 2020 used for evauation of model performance based on MAPE values. The chosen best model is the local polynomial model with Gaussian kernel function of degree 5, bandwidth of 373, and local point of 1744 with an MSE value of 482.6420. The local polynomial model out sample data MAPE value is 0.61%, indicating that the model has excellent forecasting capability. In this study, Graphical User Interface (GUI) using R software with the help of shiny package is also built, making data analyzing easier and generating more interactive display output.

MODELING OF LOCAL POLYNOMIAL KERNEL NONPARAMETRIC REGRESSION FOR COVID DAILY CASES IN SEMARANG CITY, INDONESIA

Coronavirus disease 2019 (COVID-19) is an infectious disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) which was recently discovered. Coronavirus disease is now a pandemic that occurs in many countries in the world, one of which is Indonesia. One of the cities in Indonesia that has found many COVID cases is Semarang city, located in Central Java. Data on cases of COVID patients in Semarang City which are measured daily do not form a certain distribution pattern. We can build a model with a flexible statistical approach without any assumptions that must be used, namely the nonparametric regression. The nonparametric regression in this research using Local Polynomial Kernel approach. Determination of the polynomial order and optimal bandwidth in Local Polynomial Kernel Regression modeling use the GCV (Generalized Cross Validation) method. The data used this research are data on the number of COVID patients daily cases in Semarang, Indonesia. Based on the results of the application of the COVID patient daily cases in Semarang City, the optimal bandwidth value is 0.86 and the polynomial order is 4 with the minimum GCV is 3179.568 so that the model estimation results the MSE is 2922.22 and the determination coefficient is 97%. The estimation results show the highest number of Corona in the Semarang City at the beginning of July 2020. After the corona case increased in July, while the corona case in August decreased.

ESTIMATES OF DERIVATIVES OF (LOG) DENSITIES AND RELATED OBJECTS

We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density function f. The estimator is guaranteed to be non-negative and achieves the same optimal rate of convergence in the interior as on the boundary of the support of f. The estimator is therefore well-suited to applications in which non-negative density estimates are required, such as in semiparametric maximum likelihood estimation. In addition, we show that our estimator compares favorably with other kernel-based methods, both in terms of asymptotic performance and computational ease. Simulation results confirm that our method can perform similarly or better in finite samples compared to these alternative methods when they are used with optimal inputs, that is, an Epanechnikov kernel and optimally chosen bandwidth sequence. We provide code in several languages.

Seasonal forecasts of Indian summer monsoon rainfall using local polynomial based non-parametric regression model

In this paper, details of new statistical models for forecasting southwest monsoon (June-September) rainfall over India (ISMR) and for northwest India summer monsoon rainfall (NWISMR) are discussed. These models are based on the local polynomial based non-parametric regression method. Two predictor sets (SET-I & SET-II consisting of 4 and 5 predictors respectively) were selected for developing two separate models for making predictions in April and late June respectively. Another predictor set (SET-III) was selected for developing model for monsoon rainfall over NW India (NWISMR). Principle Component Analysis (PCA) of predictor data set was done and the first two principal components were selected for model development. Data for the period 1977-2005 have been used for developing the model and the Jackknife method was used to assess the skill of the model. Both the models showed useful skill in predicting ISMR and showed better performance than the model based on pure climatology. The Hit scores for the three category forecasts during the verification period by April and June models are 0.65 and 0.66 respectively. Root Mean Square Error (RMSE) of these models during the verification period is 5.99 and 6.0% respectively from the Long Period Average (LPA) as against 10.0% from the LPA of the model based on climatology alone. RMSE of the Northwest India model during the independent period is 11.5% from LPA as against 18.5% from the LPA of the model based on the climatology alone. Hit score for the three category forecast for NW India during the verification period is 0.55.

Numerical differentiation on scattered data through multivariate polynomial interpolation

We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor’s formula monomial basis. Error bounds for the approximation of partial derivatives of any order compatible with the function regularity are provided, as well as sensitivity estimates to functional perturbations, in terms of the inverse Vandermonde coefficients that are active in the differentiation process. Several numerical tests are presented showing the accuracy of the approximation.

Image Compression and Enlargement Algorithms

In some cases, there are problems associated with the compression and enlargement of images. The use of splines is quite effective in some cases. In this paper, a new image compression algorithm is presented. The features of increasing the size of an image when using local polynomial or non-polynomial splines are considered. The main method for enlarging an image is based on the use of splines of the second and third order of approximation. Polynomial and trigonometric splines are considered. To speed up the process of enlarging the image, we used the parallelization techniques

Improved Output Gap Estimates and Forecasts Using a Local Linear Regression

The output gap, the difference between potential and actual output, has a direct impact on policy decisions, e.g., monetary policy. Estimating this gap and its further analysis remain the subject of controversial debates due to methodological problems. We propose a local polynomial regression combined with a Self-Exciting Threshold AutoRegressive (SETAR) model and its forecasting extension for a systematic output gap estimation. Furthermore, local polynomial regression is proposed for the (multivariate) OECD production function approach and its reliability is demonstrated in forecasting output growth. A comparison of the proposed gap to the Hodrick–Prescott filter as well as to estimations by experts from the FED and OECD shows a higher correlation of our output gap with those from those economic institutions. Furthermore, sometimes gaps with different magnitude and different positions above or below the trend are observed between different methods. This may cause competing policy implications which can be improved with our results.

RELAÇÃO ENTRE DISTRIBUIÇÃO DE RENDIMENTOS DO TRABALHO E INDUSTRIALIZAÇÃO: UMA ANÁLISE PARA OS MUNICÍPIOS BRASILEIROS

O presente estudo investiga, empiricamente, a relação entre industrializaçãoe distribuição dos rendimentos do trabalho nos municípios brasileiros. Com base emdebates históricos sobre distribuição de renda da academia brasileira e em hipótesesassociadas à curva de Kuznets, especialmente, a que se refere à economia dual, o estudo encontra uma relação não linear entre a desigualdade de rendimentos do trabalhoe a industrialização, medida pelas participações industriais no produto e no emprego.A partir de dados municipais referentes a 2000 e 2010, são realizadas regressões paramétricas em painel (efeitos fixos, efeitos aleatórios e tobit) e não paramétricas (kernel--weighted local polynomial regression). As evidências, relativamente robustas, sugeremque a curva derivada da relação entre a desigualdade de renda e a industrialização temum formato próximo a um U invertido. Ou seja, a distribuição dos rendimentos do trabalho piora com a industrialização até certo nível de participação industrial (no produto e no emprego), porém, atingido determinado nível, a distribuição passa a melhorar.

On local hulls of Levi-flat hypersurfaces

We discuss local polynomial convexity of real analytic Levi-flat hypersurfaces in [Formula: see text], [Formula: see text], near singular points.