변환된 자기회귀이동평균 모형에서의 예측구간추정 = Prediction Interval Estimation in Ttansformed ARMA Models

다국어 초록 (Multilingual Abstract)

One of main aspects of time series analysis is to forecast future values of series based on values up to a given time. The prediction interval for future values is usually obtained under the normality assumption. When the assumption is seriously violated, a transformation of data may permit the valid use of the normal theory. We investigate the prediction problem for future values in the original scale when transformations are applied in ARMA models. In this paper, we introduce the methodology based on Yeo-Johnson transformation to solve the problem of skewed data whose modelling is relatively difficult in the analysis of time series. Simulation studies show that the coverage probabilities of proposed intervals are closer to the nominal level than those of usual intervals.

참고문헌 (Reference)

1 "Value at risk based on the volatility skewness and kurtosis" RiskMetrics Group 1999

2 "The behavior of stock-market prices The Journal of Business" 1965

3 "Probability distribution for ？nancial models" 14 : 427-461, 1996

4 "Journal of the American Statistical Association" 1983

5 "Grouped likelihood for the shifted power transformation Journal of the Royal Statistical Society" 1991

6 "Financial applications of stable distribution" 14 : 393-425, 1996

7 "Convex Transformations of Random Variables" 1964

8 "Conditional heteroskedasticity in asset returns" eco (eco): 1991

9 "Bias and convergence rate of the coverage probability of prediction intervals in Box-Cox transformed linear models" 136 : 3614-3624, 2005

10 "An analysis of transformations Journal of the Royal Statistical Society" 1964

11 "A new family of power transformation to improve normality or symmetry" 87 : 954-959, 2000

12 "A further development of tests for normality" 1930