Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending

Castro, Tomás del Barrio; Bodnar, Andrii; Sansó, Andreu

doi:10.1007/s00180-016-0688-9

Cited by 3 publications

(5 citation statements)

References 19 publications

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“…In addition to the usual OLS detrending, one can also use GLS detrending, as was recently proposed by Rodrigues and Taylor (2007). Finally, we reported 1%, 5%, and 10% critical values by means of the response surfaces implemented in del Barrio Castro, Bodnar, and Sansó (2015). We illustrated the command with an empirical application using monthly UK airport arrivals to Mallorca.…”

Section: Discussionmentioning

confidence: 92%

“…Also, the user can choose between OLS detrending and GLS detrending to deal with the specified deterministic part of the process. For all the possible specifications of the deterministic part (see section 2 for details) and for both OLS and GLS detrending, the command provides critical values, obtained from response surfaces according to the proposal in MacKinnon (1996) (see del Barrio Castro, Bodnar, and Sansó [2015] for details), at the 1%, 5%, and 10% levels of significance. With our hegy command, a wider range of possibilities for determining the order of augmentation in the HEGY regression is available.…”

Section: Introductionmentioning

confidence: 99%

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The Lag-length Selection and Detrending Methods for HEGY Seasonal Unit-root Tests Using Stata

Castro

Bodnar²,

Sansó

2016

The Stata Journal: Promoting communications on statistics and S

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The article extends the previous Hylleberg, Engle, Granger, and Yoo seasonal unit-root test commands (Baum and Sperling, 2001, https://ideas.repec.org/c/boc/bocode/s416502.html; Depalo, 2009, Stata Journal 9: 422-438), which allow for the use of both quarterly and monthly data. It is also possible to choose between ordinary least-squares and generalized leastsquares detrending (Rodrigues and Taylor, 2007, Journal of Econometrics 141: 548-573) procedures to deal with the deterministic part of the process. The command allows for the use of the sequential method proposed by Hall (1994, Journal of Business and Economic Statistics 12: 461-470) and Ng and Perron (1995, Journal of the American Statistical Association 90: 268-281), the adaptation of the modified Akaike information criteria to the case of seasonal unit-root tests (del Barrio Castro, Osborn, and Taylor, 2016, Econometric Reviews 35: 122-168) as well as the inclusion of Akaike information and Bayesian information criteria to determine the order of augmentation of the serial correlation in the augmented Hylleberg, Engle, Granger, and Yoo regression. Finally, the use of the command is illustrated with an empirical application to the case of monthly passenger airport arrivals to Palma de Mallorca. Taylor, and del Barrio Castro (2009), we can define six scenarios for the deterministic part μ St+s : no deterministic terms, zero-frequency intercept (one intercept), zero-frequency intercept and a trend, seasonal intercepts, seasonal intercepts and a zero-frequency trend, and seasonal intercepts and trends. Hence, in terms of μ St+s = δ z St+s,ζ , we have the following: Case 0: No deterministic terms: μ St+s = 0 Case 1: Only a constant: z St+s,1 = [1] with δ = (δ 0 ) Case 2: Constant and a zero-frequency trend: z St+s,2 = [1, St + s] with δ = δ 0 , δ 0 Case 3: Seasonal intercepts: z St+s,3 = [1, cos(2π(St + s)/S), sin(2π(St + s)/S), . . . , cos(2πS * (St + s)/S), sin(2πS * (St + s)/S), (−1) St+2 with δ = (δ 0 ,

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Section: Discussionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

The Lag-length Selection and Detrending Methods for HEGY Seasonal Unit-root Tests Using Stata

Castro

Bodnar²,

Sansó

2016

The Stata Journal: Promoting communications on statistics and S

Self Cite

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“…Results are obtained using both OLS and GLS detrending and the MAIC criteria is used to determine the order of augmentation; see del Barrio Castro, Osborn and Taylor (2016) for details. Asymptotic critical values are employed, with these obtained from the quantile functions in del Barrio Castro, Bodnar and Sansó (2017). As usual, one-sided t-type tests are employed for the null hypotheses π 0 = 0 and π 2 = 0 (associated with the zero and Nyquist frequencies, respectively), together with a joint F -type test for π α 1 = π β 1 = 0 (associated with the frequency π/2).…”

Section: Empirical Applicationmentioning

confidence: 99%

“…Results are obtained using both OLS and GLS detrending and the MAIC criteria is used to determine the order of augmentation; see del Barrio Castro et al (2016) for details. Asymptotic critical values are employed, with these obtained from the quantile functions in del Barrio Castro et al (2017). As usual, one-sided t-type tests are employed for the null hypotheses 𝜋 0 = 0 is judged to be a seasonally integrated process, with unit roots at the zero and both seasonal frequencies, 𝜋∕2 and 𝜋, while ln ( emp t ) apparently has only a zero frequency unit root.…”

Section: Empirical Applicationmentioning

confidence: 99%

“…Asymptotic critical values are employed, with these obtained from the quantile functions in del Barrio Castro et al . (2017). As usual, one‐sided t ‐type tests are employed for the null hypotheses

π_{0} = 0

and

π_{2} = 0

(associated with the zero and Nyquist frequencies, respectively), together with a joint F ‐type test for

π_{1}^{α} = π_{1}^{β} = 0

(associated with the frequency

π false/ 2

).…”

Section: Empirical Applicationmentioning

confidence: 99%

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On cointegration for processes integrated at different frequencies

Castro

Cubada

Osborn

2021

Journal Time Series Analysis

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This paper explores the possibility of cointegration existing between processes integrated at different frequencies. Using the demodulator operator, we show that such cointegration can exist and explore its form using both complex-and real-valued representations. A straightforward approach to test for the presence of cointegration between processes integrated at different frequencies is proposed, with a Monte Carol study and an application showing that the testing approach works well.

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Impact of diesel price reforms on asymmetricity of oil price pass-through to inflation: Indian perspective

Pradeep

2022

The Journal of Economic Asymmetries

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Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending

Cited by 3 publications

References 19 publications

The Lag-length Selection and Detrending Methods for HEGY Seasonal Unit-root Tests Using Stata

The Lag-length Selection and Detrending Methods for HEGY Seasonal Unit-root Tests Using Stata

On cointegration for processes integrated at different frequencies

Impact of diesel price reforms on asymmetricity of oil price pass-through to inflation: Indian perspective

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