The uroot Package uroot : Unit Root Tests in Seasonal Time Series. - PowerPoint PPT Presentation

The uroot Package uroot : Unit Root Tests in Seasonal Time Series. The uroot and partsm R -Packages: Some Functionalities for Time Series Analysis Javier L´ opez-de-Lacalle Universidad del Pa´ ıs Vasco (Bilbao, Spain) The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.1/8 The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.2/8 The uroot Package The uroot Package uroot : Unit Root Tests in Seasonal Time Series. uroot : Unit Root Tests in Seasonal Time Series. HEGY.test() : Test for the null hypothesis of HEGY.test() : Test for the null hypothesis of non-stationary seasonal cycles. non-stationary seasonal cycles. CH.test() : Test for the null hypothesis of stationary seasonal cycles. The uroot and partsm R-Packages Javier L´ The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.2/8 opez-de-Lacalle – p.2/8

The uroot Package The uroot Package uroot : Unit Root Tests in Seasonal Time Series. uroot : Unit Root Tests in Seasonal Time Series. HEGY.test() : Test for the null hypothesis of HEGY.test() : Test for the null hypothesis of non-stationary seasonal cycles. non-stationary seasonal cycles. CH.test() : Test for the null hypothesis of CH.test() : Test for the null hypothesis of stationary seasonal cycles. stationary seasonal cycles. References: References: S. Hylleberg, R. Engle, C. Granger and B. Yoo (1990), Seasonal integration and cointegration. Journal of Econometrics , 44. The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.2/8 The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.2/8 The uroot Package CH-HEGY Sequence of Tests CH test uroot : Unit Root Tests in Seasonal Time Series. ✟ ❍ ✟✟✟✟✟ ❍ ❍ HEGY.test() : Test for the null hypothesis of ❍ ❍ ❍ non-stationary seasonal cycles. Do not reject H 0 Reject H 0 CH.test() : Test for the null hypothesis of stationary seasonal cycles. HEGY test I ω (1) ✟✟✟✟ ✟ ❍ ❍ ❍ ❍ References: ❍ Do not reject H 0 Reject H 0 S. Hylleberg, R. Engle, C. Granger and B. Yoo (1990), Seasonal integration and cointegration. Journal of Econometrics , 44. F . Canova and B.E. Hansen (1995), Are seasonal patterns constant over I ω (0) Non-informative time? A test for seasonal stability. Journal of Business and Economic Statistics , 13. The uroot and partsm R-Packages Javier L´ The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.2/8 opez-de-Lacalle – p.3/8

A Tree Widget partsm : Periodic Autoregressive Time Series Models The package partsm fits PAR models. Periodic integration and prediction are also considered. A root node is created when a time series is loaded. Transformations of the data (logarithms, first differences, subsamples,...) can be added to the tree as a child node . The nodes in the tree can be drilled-down or drilled-up and removed from the tree. The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.4/8 The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.5/8 partsm : Periodic Autoregressive Time Series Models partsm : Periodic Autoregressive Time Series Models The package partsm fits PAR models. The package partsm fits PAR models. Periodic integration and prediction are also Periodic integration and prediction are also considered. considered. A PAR(p) model is defined as follows: A PAR(p) model is defined as follows: ǫ t ∼ iid (0 , σ 2 ǫ t ∼ iid (0 , σ 2 y t = φ 1 s y t − 1 + ... + φ ps y t − p + ǫ t , ǫ ) , y t = φ 1 s y t − 1 + ... + φ ps y t − p + ǫ t , ǫ ) , for t = 1 , 2 , ..., n and being s = 1 , ..., S the for t = 1 , 2 , ..., n and being s = 1 , ..., S the seasons. seasons. Reference: P .H. Franses (1996) ‘Periodicity and Stochastic Trends in Economic Time Series’, Oxford University Press. The uroot and partsm R-Packages Javier L´ The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.5/8 opez-de-Lacalle – p.5/8

Analysis Procedure 1/2 Analysis Procedure 2/2 Test for Q S ... s =1 α s = 1 Test for periodicity LRurpar.test() Fpar.test() ✟ ❍ ✟✟✟✟✟✟ ❍ ❍ ✟ ❍ ❍ ✟✟✟✟✟ ❍ ❍ ❍ ❍ ❍ ❍ ❍ ❍ Do not reject Reject Do not reject Reject PAR model Test for α s = 1 ∪ − 1 fit.ar.par() Fpari.piar.test() Test for � S s =1 α s = 1 CH-HEGY ✟ ❍ ✟✟✟✟ ❍ ❍ ❍ ❍ LRurpar.test() Do not reject Reject ϕ ( L ) → ARMA PARI model PIAR model ... arima() (1 − L ) or (1 + L ) fit.piar() (1 − α s L ) fit.ar.par() The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.6/8 The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.7/8 Directions for Further Development Directions for Further Development Bootstrap techniques for the HEGY and CH Bootstrap techniques for the HEGY and CH tests. tests. Rolling statistics and leverage investigation over them in the presence of outliers. The uroot and partsm R-Packages Javier L´ The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.8/8 opez-de-Lacalle – p.8/8

Directions for Further Development Directions for Further Development Bootstrap techniques for the HEGY and CH Bootstrap techniques for the HEGY and CH tests. tests. Rolling statistics and leverage investigation Rolling statistics and leverage investigation over them in the presence of outliers. over them in the presence of outliers. Cointegration tests in PAR models for testing Cointegration tests in PAR models for testing for more than one unit root. for more than one unit root. Mixed AR-PAR models. The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.8/8 The uroot and partsm R-Packages Javier L´ opez-de-Lacalle – p.8/8