ENH: seasonal unit root tests

[josef-pkt]

just to park a link, question with references

https://stats.stackexchange.com/questions/287548/what-is-the-intuition-for-testing-seasonal-difference-with-ocsb-test-and-its-cor

we might need this for an automatic forecasting project.
Hyndman's auto.arima uses OCSB (after switching from using ???)

some references (downloaded but not read

HEGY and OCSB seem to be the main candidates, and maybe DHF
It looks like ADF has power for seasonal unit root (if I skimmed OCSB correctly), but cannot discriminate between one period unit root and seasonal unit root.)

Demetrescu, Matei, and Uwe Hassler. 2007. “Effect of Neglected Deterministic Seasonality on Unit Root Tests.” Statistical Papers 48 (3): 385–402. https://doi.org/10.1007/s00362-006-0343-6.

Depalo, D. 2009. “A Seasonal Unit-Root Test with Stata.” Stata Journal 9 (3): 422–38.

Dickey, D. A., D. P. Hasza, and W. A. Fuller. 1984. “Testing for Unit Roots in Seasonal Time Series.” Journal of the American Statistical Association 79 (386): 355–67. https://doi.org/10.2307/2288276.

Hassler, Uwe, and Paulo M. M. Rodrigues. 2004. “Seasonal Unit Root Tests Under Structural Breaks*.” Journal of Time Series Analysis 25 (1): 33–53. https://doi.org/10.1111/j.1467-9892.2004.00336.x.

Hylleberg, S., R. F. Engle, C. W. J. Granger, and B. S. Yoo. 1990. “Seasonal Integration and Cointegration.” Journal of Econometrics 44 (1): 215–38. https://doi.org/10.1016/0304-4076(90)90080-D.

Osborn, Denise R., A. P. L. Chui, Jeremy P. Smith, and C. R. Birchenhall. 1988. “Seasonality and the Order of Integration for Consumption.” Oxford Bulletin of Economics and Statistics 50 (4): 361–77. https://doi.org/10.1111/j.1468-0084.1988.mp50004002.x.

there are some articles to get p-values or critical values from response surface modelling (not read either)
Diaz-Emparanza (2014) has add-on/function for Gretl

Barrio Castro, Tomás del, Andrii Bodnar, and Andreu Sansó. 2017. “Numerical Distribution Functions for Seasonal Unit Root Tests with OLS and GLS Detrending.” Computational Statistics 32 (4): 1533–68. https://doi.org/10.1007/s00180-016-0688-9.

Diaz-Emparanza, Ignacio. 2014. “Numerical Distribution Functions for Seasonal Unit Root Tests.” Computational Statistics & Data Analysis, CFEnetwork: The Annals of Computational and Financial Econometrics, 76 (August): 237–47. https://doi.org/10.1016/j.csda.2013.03.006.

(general issue base on superficial skimming seems to be whether to remove a deterministic seasonal component before running seasonal unit test,
i.e. seasonal unit root in addition to instead of as substitute for a deterministic seasonal component.)

[josef-pkt]

bump,
we will need something like this for automatic forecasting to choose seasonal differencing

[josef-pkt]

related: seasonal unit root or unstable seasonal pattern

Canova, Fabio, and Bruce E. Hansen. 1995. “Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability.” Journal of Business & Economic Statistics 13 (3): 237–52. https://doi.org/10.2307/1392184.

aside:
Many typical time series used for forecasting examples have breaks in the seasonal pattern or slowly shifting seasonal pattern. Those will not be capture by a constant deterministic seasonal component. In those cases switching to seasonal unit root or deterministic seasonal component that changes over time will provide more accurate forecasts.

So far, we don't have anything to discriminate between unit roots and nonlinear trends (overall or in seasonal structure), either breaks or polynomial series would capture the latter.

references based on abstracts, I didn't look inside:

Bierens, Herman J. 2000. “Nonparametric Nonlinear Cotrending Analysis, with an Application to Interest and Inflation in the United States.” Journal of Business & Economic Statistics 18 (3): 323–37. https://doi.org/10.2307/1392265.

Enders, Walter, and Junsoo Lee. 2012. “A Unit Root Test Using a Fourier Series to Approximate Smooth Breaks.” Oxford Bulletin of Economics and Statistics 74 (4): 574–99. https://doi.org/10.1111/j.1468-0084.2011.00662.x.

Popp, Stephan. 2007. “Modified Seasonal Unit Root Test with Seasonal Level Shifts at Unknown Time.” Economics Letters 97 (2): 111–17. https://doi.org/10.1016/j.econlet.2007.02.026.