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

The uroot and partsm

R-Packages:

Some Functionalities for Time Series Analysis

Javier L´

• pez-de-Lacalle

Universidad del Pa´ ıs Vasco (Bilbao, Spain)

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.1/8

The uroot Package

uroot: Unit Root Tests in Seasonal Time Series.

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.2/8

The uroot Package

uroot: Unit Root Tests in Seasonal Time Series. HEGY.test(): Test for the null hypothesis of non-stationary seasonal cycles.

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.2/8

The uroot Package

uroot: Unit Root Tests in Seasonal Time Series. HEGY.test(): Test for the null hypothesis of non-stationary seasonal cycles. CH.test(): Test for the null hypothesis of stationary seasonal cycles.

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.2/8

The uroot Package

uroot: Unit Root Tests in Seasonal Time Series. HEGY.test(): Test for the null hypothesis of non-stationary seasonal cycles. CH.test(): Test for the null hypothesis of stationary seasonal cycles. References:

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.2/8

The uroot Package

uroot: Unit Root Tests in Seasonal Time Series. HEGY.test(): Test for the null hypothesis of non-stationary seasonal cycles. CH.test(): Test for the null hypothesis of stationary seasonal cycles. 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´

• pez-de-Lacalle – p.2/8

The uroot Package

uroot: Unit Root Tests in Seasonal Time Series. HEGY.test(): Test for the null hypothesis of non-stationary seasonal cycles. CH.test(): Test for the null hypothesis of stationary seasonal cycles. References:

• 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 time? A test for seasonal stability. Journal of Business and Economic Statistics, 13.

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.2/8

CH-HEGY Sequence of Tests

CH test

✟✟✟✟✟ ✟ ❍ ❍ ❍ ❍ ❍ ❍

Do not reject H0 HEGY test

✟✟✟✟ ✟ ❍ ❍ ❍ ❍ ❍

Do not reject H0

Non-informative

Reject H0 Iω(0) Reject H0 Iω(1)

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.3/8

A Tree Widget

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´

• pez-de-Lacalle – p.4/8

partsm: Periodic Autoregressive Time Series Models The package partsm fits PAR models. Periodic integration and prediction are also considered.

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.5/8

partsm: Periodic Autoregressive Time Series Models The package partsm fits PAR models. Periodic integration and prediction are also considered. A PAR(p) model is defined as follows: yt = φ1syt−1 +...+φpsyt−p +ǫt, ǫt ∼ iid(0, σ2

ǫ) ,

for t = 1, 2, ..., n and being s = 1, ..., S the seasons.

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.5/8

partsm: Periodic Autoregressive Time Series Models The package partsm fits PAR models. Periodic integration and prediction are also considered. A PAR(p) model is defined as follows: yt = φ1syt−1 +...+φpsyt−p +ǫt, ǫt ∼ iid(0, σ2

ǫ) ,

for t = 1, 2, ..., n and being s = 1, ..., S the 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´

• pez-de-Lacalle – p.5/8

Analysis Procedure 1/2

Test for periodicity Fpar.test()

✟✟✟✟✟ ✟ ❍ ❍ ❍ ❍ ❍ ❍

Do not reject Test for S

s=1 αs = 1

LRurpar.test() ... Reject CH-HEGY ϕ (L) → ARMA arima()

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.6/8

Analysis Procedure 2/2

... Test for QS

s=1 αs = 1

LRurpar.test()

✟✟✟✟✟✟ ✟ ❍ ❍ ❍ ❍ ❍ ❍ ❍

Do not reject Test for αs = 1 ∪ −1

Fpari.piar.test()

✟✟✟✟ ✟ ❍ ❍ ❍ ❍ ❍

Do not reject

PARI model (1 − L) or (1 + L) fit.ar.par()

Reject

PIAR model fit.piar() (1 − αs L)

Reject

PAR model fit.ar.par()

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.7/8

Directions for Further Development

Bootstrap techniques for the HEGY and CH tests.

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.8/8

Directions for Further Development

Bootstrap techniques for the HEGY and CH tests. Rolling statistics and leverage investigation

• ver them in the presence of outliers.

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.8/8

Directions for Further Development

Bootstrap techniques for the HEGY and CH tests. Rolling statistics and leverage investigation

• ver them in the presence of outliers.

Cointegration tests in PAR models for testing for more than one unit root.

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.8/8

Directions for Further Development

Bootstrap techniques for the HEGY and CH tests. Rolling statistics and leverage investigation

• ver them in the presence of outliers.

Cointegration tests in PAR models for testing for more than one unit root. Mixed AR-PAR models.

The uroot and partsm R-Packages Javier L´

• pez-de-Lacalle – p.8/8