• Journal of the Korean Data and Information Science Society
• /
• v.27 no.2
• /
• pp.559-564
• /
• 2016

The Durbin-Watson (DW) test in regression model and the Ljung-Box (LB) test in ARMA (autoregressive moving average) model are typical examples of correlated error tests. The DW test is used for detecting autocorrelation of errors using the residuals from a regression analysis. The LB test is used for specifying the correct ARMA model using the first some sample autocorrelations based on the residuals of a tted ARMA model. In this article, simulations with four data generating processes have been carried out to evaluate their performances as correlated error tests. Our simulations show that the DW test is severely dependent on the assumed AR(1) model but isn't sensitive enough to reject the misspecified model and that the LB test reports lackluster performance in general.

• Communications for Statistical Applications and Methods
• /
• v.16 no.1
• /
• pp.127-135
• /
• 2009

It is necessary to forecast the amount of the maximum electricity demand for stabilizing the flow of electricity. The time series data was collected from the Korea Energy Research between January 2000 and December 2006. The data showed that they had a strong linear trend and seasonal change. Winters seasonal model, ARMA model were used to examine it. Root mean squared prediction error and mean absolute percentage prediction error were a criteria to select the best model. In addition, a nonstationary generalized extreme value distribution with explanatory variables was fitted to forecast the maximum electricity.

• Communications for Statistical Applications and Methods
• /
• v.10 no.3
• /
• pp.981-996
• /
• 2003

Bayesian inference is considered for switching mean models with the ARMA errors. We use noninformative improper priors or uniform priors. The fractional Bayes factor of O'Hagan (1995) is used as the Bayesian tool for detecting the existence of a single change or multiple changes and the usual Bayes factor is used for identifying the orders of the ARMA error. Once the model is fully identified, the Gibbs sampler with the Metropolis-Hastings subchains is constructed to estimate parameters. Finally, we perform a simulation study to support theoretical results.

• Communications for Statistical Applications and Methods
• /
• v.29 no.4
• /
• pp.471-486
• /
• 2022

Autoregressive moving average (ARMA) models involve nonlinearity in the model coefficients because of unobserved lagged errors, which complicates the likelihood function and makes the posterior density analytically intractable. In order to overcome this problem of posterior analysis, some approximation methods have been proposed in literature. In this paper we first review the main analytic approximations proposed to approximate the posterior density of ARMA models to be analytically tractable, which include Newbold, Zellner-Reynolds, and Broemeling-Shaarawy approximations. We then use the Kullback-Leibler divergence to study the relation between these three analytic approximations and to measure the distance between their derived approximate posteriors for ARMA models. In addition, we evaluate the impact of the approximate posteriors distance in Bayesian estimates of mean and precision of the model coefficients by generating a large number of Monte Carlo simulations from the approximate posteriors. Simulation study results show that the approximate posteriors of Newbold and Zellner-Reynolds are very close to each other, and their estimates have higher precision compared to those of Broemeling-Shaarawy approximation. Same results are obtained from the application to real-world time series datasets.

• The Korean Journal of Applied Statistics
• /
• v.24 no.2
• /
• pp.293-305
• /
• 2011

The volatility is one of most important parameters in the areas of pricing of financial derivatives an measuring risks arising from a sudden change of economic circumstance. We propose a Bayesian approach to estimate the volatility varying with time under a linear model with ARMA(p, q)-GARCH(r, s) errors. This Bayesian estimate of the volatility is compared with the ML estimate. We also present the probability of existence of the unit root in the GARCH model.

• Journal of applied mathematics & informatics
• /
• v.5 no.2
• /
• pp.373-382
• /
• 1998

Most of the works in Time Series Analysis are based on the Auto Regressive Integrated Moving Average (ARIMA) models presented by Box and Jeckins(1976). If the data exhibits no ap-parent deviation from stationarity and if it has rapidly decreasing autocorrelation function then a suitable ARIMA(p,q) model is fit to the given data. Selection of the orders of p and q is one of the crucial steps in Time Series Analysis. Most of the methods to determine p and q are based on the autocorrelation function and partial autocor-relation function as suggested by Box and Jenkins (1976). many new techniques have emerged in the literature and it is found that most of them are over very little use in determining the orders of p and q when both of them are non-zero. The Durbin-Levinson algorithm and Innovation algorithm (Brockwell and Davis 1987) are used as recur-sive methods for computing best linear predictors in an ARMA(p,q)model. These algorithms are modified to yield an effective method for ARMA model identification so that the values of order p and q can be determined from them. The new method is developed and its validity and usefulness is illustrated by many theoretical examples. This method can also be applied to an real world data.

• Journal of Advanced Marine Engineering and Technology
• /
• v.41 no.1
• /
• pp.56-61
• /
• 2017

This paper presents a data prediction method and its application to haptic-based teleoperation systems. In general, time delays inevitably occur during data transmission in a network environment, which degrades the overall performance of haptic-based teleoperation systems. To address this situation, this paper proposes an autoregressive moving average (ARMA) model-based data prediction algorithm for estimating model parameters and predicting future data recursively in real time. The proposed method was applied to haptic data captured every 5 ms while bilateral haptic interaction was carried out by two users with an object in a virtual space. The results showed that the prediction performance of the proposed method had an error of less than 1 ms when predicting position-level data 100 ms ahead.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.35 no.10
• /
• pp.438-444
• /
• 1986

The signal can be modeled as a linear combination of its past values and present and past values of a hypothetical input to system whose output is given signal. Using this model spectral estimation problem can be reduced to estimate the ARMA parameters. This paper presents recursive modified instrumental variable algorithm which can estimate AR and MA parameters. For more accurate estimation, overdetermined modified IV algorithm is also derived. Computer simulations are presented to illustrate the above methods.

• 제어로봇시스템학회:학술대회논문집
• /
• 1987.10b
• /
• pp.442-445
• /
• 1987

In this paper, a new ARMA spectrum estimation algorithm based on Circular Lattice filter is presented. Since APMA model is used in signal modeling, high-resolution spectrum can be obtained. And the computational burden is reduced by using Circular Lattice filter. By modifying the input estimation part of other proposed methods, we can get high-resolution spectrum with less computation and less memory compared with other Lattice methods. Some computer simulations are performed.

• Communications for Statistical Applications and Methods
• /
• v.2 no.2
• /
• pp.85-93
• /
• 1995

Hannan and Rissanen proposed an innovation regression method of ARMA modeling, which is composed of three stages. Its second-stage is to choose orders of the ARMA model using the BIC, which needs a lot of calculation to estimate several regression models. We are going to present a simple and efficient algorithm for the second stage using a special property of triangular Toeplitz matrices.