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

• Journal of Korea Multimedia Society
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• v.11 no.10
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• pp.1325-1337
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• 2008

The difference of environments between training and recognition is the major reason of degradation of speech recognition. To solve this mismatch of environments, various noise processing methods have been studied. Among them, ERN(log-Energy dynamic Range Normalization) and SEN(Silence Energy Normalization) for normalization of log energy features show better performance than others. However, these methods have a problem that they can hardly achieve normalization for the relatively higher values of log energy features and the environmental mismatch caused by this problem becomes bigger especially in low SNR environments. To solve these problems, we propose applying ARMA filter as post-processing for smoothing log energy features by calculating the moving average in auto-regression scheme. From the recognition results conducted on Aurora 2.0 DB, the proposed method shows improved recognition results comparing with conventional methods.

• Proceedings of the KIEE Conference
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• 1986.07a
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• pp.162-166
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• 1986

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.533-541
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• 2006

We consider a autoregressive moving average process of order p and q with Markov switching coefficients and find sufficient conditions for irreducibility of the process. Identifying small sets is also examined.

• Communications for Statistical Applications and Methods
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• v.18 no.1
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• pp.71-77
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• 2011

In this paper, asymptotic results are investigated when a parametric transformation is applied to ARMA models. The conditions are determined to ensure the strong consistency and the asymptotic normality of maximum likelihood estimators and the correct coverage probability of the forecast interval obtained by the transformation and backtransformation approach.

• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.511-527
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• 2015

For time series analysis, power transformation (especially log-transformation) is widely used for variance stabilization or normalization for stationary ARMA(p, q) model. A simple and naive back transformed forecast is obtained by taking the inverse function of expectation. However, this back transformed forecast has a bias. Under the assumption that the log-transformed data is normally distributed. The unbiased back transformed forecast can be obtained by the expectation of log-normal distribution; consequently, the property of this back transformation was studied by Granger and Newbold (1976). We investigate the sensitivity of back transformed forecasts under several different underlying distributions using simulation studies.

• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.293-305
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• 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
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• v.5 no.2
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• pp.373-382
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• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.45-48
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• 1999

Model predictive control algorithm requires a relevant model of the system to be controlled. Unfortunately, the first principle model describing a polymerization reaction system has a large number of parameters to be estimated. Thus there is a need for the identification and control of a polymerization reactor system by using available input-output data. In this work, the polynomial auto-regressive moving average (ARMA) models are employed as the input-output model and combined into the nonlinear model predictive control algorithm based on the successive linearization method. Simulations are conducted to identify the continuous styrene polymerization reactor system. The input variables are the jacket inlet temperature and the feed flow rate whereas the output variables are the monomer conversion and the weight-average molecular weight. The polynomial ARMA models obtained by the system identification are used to control the monomer conversion and the weight-average molecular weight in a continuous styrene polymerization reactor It is demonstrated that the nonlinear model predictive controller based on the polynomial ARMA model tracks the step changes in the setpoint satisfactorily. In conclusion, the polynomial ARMA model is proven effective in controlling the continuous styrene polymerization reactor.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.723-730
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• 2009

Missing values in time series can be treated as unknown parameters and estimated by maximum likelihood or as random variables and predicted by the expectation of the unknown values given the data. The purpose of this study is to impute missing values which are regarded as the maximum likelihood estimator and random variable in incomplete data and to compare with two methods using ARMA model. For illustration, the Mumps data reported from the national capital region monthly over the years 2001 ${\sim}$ 2006 are used, and results from two methods are compared with using SSF(Sum of square for forecasting error).