A Multivariate Approach For Outlier Detection In Time Series Data
Author: Sidra Bibi

This study has provided a method for detection of multivariate seasonal level shift in multivariate time series based on joint test statistics which follows a chi-square distribution and also provides a modified joint maximum test statistic of Tsay et al. (2000) method based on one test statistics for multivariate analysis. The J-maximum test statistic is modified by including multivariate seasonal level shift (MSLS). We have detected five types of outliers MSLS, MIO, MAO, MLS and MTC1 and obtained power, size and empirical critical values using simulation and application on monthly time series data of Pakistan, and also checked their impact on the model parameter estimates, covariance matrix and standard error of the residuals. We have observed that multivariate SLS give good performance with large sample size in terms of power and size. Multivariate SLS is not much confusing with other types of outliers in VAR(0)(1)12and VAR(1)(1)12 processes. we have observed that multivariate SLS along with other types of outliers drastically affect all the estimates and J and J-maximum test statistics for MSLS along with other types of outlier depends on dimension, sample size, order and structure of the model. We have used real data example to detect outliers by using monthly time series data of temperature, rainfall and humidity for three stations of Pakistan and concluded that MSLS including other types of outliers in one series cause outlier in another series. We have also observed that estimates and standard error of the residuals have clear changes after adjusting the outliers in the series. At the end we have concluded that MSLS along with other types of outlier badly affect the estimates, analysis, results and decision taken on the basis of these results. There is need to detect and adjust the MSLS along with other types of outliers in the data series to make the results reliable Supervisor:- Dr. Amena Urooj

Meta Data

Keywords : MAO (multivariate additive outlier), MIO (multivariate innovative outlier), MLS (multivariate level shift), MSLS (multivariate seasonal level shift), MTC (multivariate transient change), VAR (vector auto regressive)
Supervisor: Amena Urooj

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