Email this article Bayesian Analysis of a Stationary AR (1) model and outlier
Abstract
The time varying observation recorded in chronological order is called time series. The extreme values are from the same time series model or appear because of some unobservable causes having serious implications in the estimation and inference. This change deviate the error more and the recorded observation is called outlier. The present paper deals the Bayesian analysis to the extreme value(s) is/are from the same time series model or appears because of some unobservable causes. We derived the posterior odds ratio in different setups of unit root hypothesis. We have also explored the possibility of studying the impact of outlier on stationarity of time series. Using the simulation study, it has been observed that if outlier is ignored a non-stationary series concluded difference stationary.
References
Acuna E. and Rodriguez C., (2004), A Meta Analysis Study of Outlier Detection Methods in Classification, Technical paper, Department of Mathematics, University of Puerto Rico at Mayaguez,
Balke N.S. and Fomby T.S.(1994): Large shocks, small shocks, and economic fluctuations: Outliers in macroeconomic time series. Journal of Applied Econometrics 9, 181–200.
Barnett V. and Lewis T. (1994): Outliers in Statistical Data , John Wiley.
Bay S.D. and Schwabacher M. (2003): Mining distance-based outliers in near linear time with randomization and a simple pruning rule, In Preceding of the ninth ACM-SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, DC, USA.
Billor N. and Kiral G. (2008): A Comparison of Multiple Outlier Detection Methods for Regression Data, Communications in Statistics - Simulation and Computation, 37 (3) 521 – 545
Breunig M.M., Kriegel H.P., Ng R.T. and Sander J. (2000): Lof: Identifying density-based local outliers, In Preceding ACMSIGMOD Conference, 93–104.
Chen C. and Liu L. (1993): Joint estimation of model parameters and outlier effect in time series, Journal of American statistical Association 88, 284-97.
Deutsch S.J., Richards J.E. and Swain J.J.(1990): Effects of a single outlier on ARMA identification, Communications in Statistics - Theory and Methods, 19 (6) , 2207 – 2227
DuMouchel W. and Schonlau M. (1998): A fast computer intrusion detection algorithm based on hypothesis testing of command transition probabilities, In Proceedings of the 4th International Conference on Knowledge Discovery and Data-mining (KDD98), 189–193.
Fawcett T. and Provost F (1997): Adaptive fraud detection, Data-mining and Knowledge Discovery, 1(3), 291–316.
Franses P. and Haldrup N. (1994): The effects of additive outliers on tests for unit roots and cointegration, Journal of Business and Economic Statistics 12, 471-478
Haldrup N., A. Montañés and A. Sansó (2005): Measurement errors and outliers in seasonal unit root testing, Journal of Econometrics 127 (1), 103-128.
Haldrup N., Montanes A. and Sanso A. (2011): Detection of outlier in seasonal time series, Journal of Time Series Econometrics, 3, article 2.
Hamid L. (2008): Outlier Detection in ARMA Models, Journal of Time Series Analysis, 29 (6), 1057-1065.
Hawkins S. Williams H. X., and Baxter R. A. (2002): Outlier detection using replicator neural networks, In Proceedings of the Fifth International Conference and Data Warehousing and Knowledge Discovery (DaWaK02), Aix en Provence, France.
Jin W., Tung A., and Han J. (2001): Mining top-n local outliers in large databases, In Proceedings of the 7th International Conference on Knowledge Discovery and Data-mining (KDD), San Francisco, CA.
Johnson T., Kwok I., Ng R. (1998): Fast Computation of 2-Dimensional Depth Contours. In Proceedings of the Fourth International Conference on Knowledge Discovery and Data Mining (KDD), AAAI Press, 224–228.
Knorr E. and Ng R. (1997): A unified approach for mining outliers, In Proceedings Knowledge Discovery and Data-mining (KDD), 219–222.
Knorr E., Ng R. and Tucakov V. (2000): Distance-based outliers: Algorithms and applications. VLDB Journal: Very Large Data Bases, 8(3–4), 237–253
.
Lu C., Chen, D., Kou Y., (2003): Algorithms for spatial Outlier detection, In Proceedings of the 3rd IEEE International Conference on Data-mining (ICDM'03), Melbourne, FL.
McCulloch R.E. and Tsay R.S. (1994): Bayesian analysis of autoregressive time series via the Gibbs Sampler, Journal Time Series Analysis 15, 235-50.
Moore, D. S. and McCabe, G. P (1999): Introduction to the Practice of Statistics, 3rd edition New York: W. H. Freeman.
Panichkitkosolkul W and Niwitpong S A (2010). Multistep-ahead predictors for Gaussian AR(1) process with additive outlier following unit root tests, International Journal of Innovative Management, Information & Production, 1, 49-55.
Penny K.I. and Jolliffe I.T. (2001): A comparison of multivariate Outlier detection methods for clinical laboratory safety data, The Statistician, 50(3), 295-308.
Pyle D. (1999): Data Preparation for Data Mining, Morgan Kaufmann Publishers, Los Altos, California.
Ruts I. and Rousseeuw P. (1996): Computing Depth Contours of Bivariate Point Clouds, In Computational Statistics and Data Analysis, 23,153–168.
Shin D.W., Sarkar S. and Lee J.H.(1996): Unit root tests for time series with outliers, Statistics and Probability Letters, 30, 189-197.
Tsay R.S. (1988): Outlier, level shift, and variance changes in time series, Journal of Forecasting 7, 1-20.
Williams G. J., and Huang Z. (1997): Mining the knowledge mine: The hot spots methodology for mining large real world databases, In Abdul Sattar, editor, Advanced Topics in Artificial Intelligence, volume 1342 of Lecture Notes in Artificial Intelligence, 340–348, Springer.
Williams G. J., Baxter, R. A., He H. X., Hawkins S. and Gu L. (2002): A Comparative Study of RNN for Outlier detection Data Mining, IEEE International Conference on Data-mining (ICDM'02), Maebashi City, Japan, CSIRO Technical Report CMIS-02/102.
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