Stationarity of seasonal patterns in weekly agricultural prices
Abstract
Weekly series of agricultural prices usually exhibit seasonal variations and the stationarity of these variations should be taken into account to analyse price relationships. However, unit root tests at seasonal frequencies are unlikely to have good power properties. Furthermore, movements in actual price series are often not as expected when unit roots are present. Therefore, stationarity tests at seasonal frequencies also need to be applied. In this paper, a procedure to test for the null hypothesis of stationarity at seasonal frequencies was extended to the weekly case. Once critical values were obtained by simulation exercises, unit root and stationarity tests were applied to weekly retail prices of different agricultural commodities in Spain. The most relevant finding was that many unit roots that seasonal unit root tests failed to reject did not seem to be present from the results of seasonal stationarity tests, whereas seasonal unit root tests led to the rejection of some unit roots that seemed to be present according to the results of seasonal stationarity tests. In conclusion, unit root tests should be complemented with stationarity tests before making decisions about the behaviour of seasonal patterns.
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References
Afonso-Rodríguez JA, Santana-Gallego M, 2014. An analysis of the seasonal persistence for the time series of international monthly tourist arrivals in the Canary Islands. IX Seminario Canario de Economía, Empresa y Turismo, La Laguna (Spain), June 19-20.
Ben-Kaabia M, Gil JM, 2007. Asymmetric price transmission in the Spanish lamb sector. Eur Rev Agric Econ 34 (1): 53-80. https://doi.org/10.1093/erae/jbm009
Boshnjaku L, Ben-Kaabia M, Gil JM, 2003. Transmisión de precios en los mercados regionales de ovino en España. Econ Agr Recur Nat 3 (1): 71-103.
Cáceres-Hernández JJ, 1996. Contraste de raíces unitarias en datos semanales. Estad Esp 38 (141): 139-159.
Cáceres-Hernández JJ, Martín-Rodríguez G, 2017. Evolving splines and seasonal unit roots in weekly agricultural prices. Aust J Agr Econ 61 (2): 304-323. https://doi.org/10.1111/1467-8489.12205
Cruz AI, Ameneiro M, 2007. Transmisión vertical de precios en el mercado nacional de los productos pesqueros frescos. Rev Econ Apl-Spain 44: 85-107.
Del Barrio-Castro T, Sansó A, 2015. On augmented Franses tests for seasonal unit roots. Commun Stat-Theor M 44: 5204-5212. https://doi.org/10.1080/03610926.2013.809121
Díaz-Emparanza I, 2014. Numerical distribution functions for seasonal unit root tests. Comput Stat Data Anal 76: 237-247. https://doi.org/10.1016/j.csda.2013.03.006
Emmanoulides CJ, Fousekis P, 2012. Testing for the LOP under nonlinearity: An application to four major EU pork markets. Agr Econ 43: 715-723. https://doi.org/10.1111/j.1574-0862.2012.00614.x
Emmanoulides CJ, Fousekis P, 2015. Assessing the validity of the LOP in the EU broiler markets. Agribusiness 31 (1): 33-46. https://doi.org/10.1002/agr.21386
Franses PH, 1991. Seasonality, nonstationarity and the forecasting of monthly time series. Int J Forecast 7: 199-208. https://doi.org/10.1016/0169-2070(91)90054-Y
García J, Arteche J, Murillas A, 2010. Fractional integration analysis and its implications on profitability. The case of the mackerel market in the Basque country. Fish Res 106 (3): 420-429. https://doi.org/10.1016/j.fishres.2010.09.015
Ghysels E, Lee HS, Noh J, 1994. Testing for unit roots in seasonal time series. J Econometrics 62: 415-442. https://doi.org/10.1016/0304-4076(94)90030-2
Guillén J, Franquesa R, 2015. Price transmission and volatility along the Spanish fresh fish market chain. New Medit 14 (1): 4-11.
Hylleberg S, 1994. Modelling seasonal variation. In: Nonstationary time series analysis and cointegration; Hargreaves CP (ed.). pp: 153-178. Oxford Univ. Press, Oxford.
Hylleberg S, Engle RF, Granger CWJ, Yoo BS, 1990. Seasonal integration and cointegration. J Econometrics 44: 215-238. https://doi.org/10.1016/0304-4076(90)90080-D
Hyndman RJ, Kostenko AV, 2007. Minimum sample size requirements for seasonal forecasting models. Foresight 6: 12-15.
Khedhiri S, Montasser GE, 2012. An extension of the seasonal KPSS test. J Mod Appl Stat Methods 11 (1): 69-77. https://doi.org/10.22237/jmasm/1335845100
Kwiatkowski D, Phillips PCB, Schmidt P, Shin Y, 1992. How sure are we that economic time series have a unit root? J Econometrics 54: 159-178. https://doi.org/10.1016/0304-4076(92)90104-Y
Lyhagen J, 2006. The seasonal KPSS statistic. Econ Bull 13: 1-9.
Martín-Rodríguez G, Cáceres-Hernández JJ, 2012. Forecasting pseudo-periodic seasonal patterns in agricultural prices. Agr Econ 43: 531-543. https://doi.org/10.1111/j.1574-0862.2012.00601.x
Martín-Rodríguez G, Cáceres-Hernández JJ, 2013. Canary tomato export prices: comparison and relationships between daily seasonal patterns. Span J Agric Res 11: 882-893. https://doi.org/10.5424/sjar/2013114-4063
Meyer J, Von Cramon-Taubadel S, 2004. Asymmetric price transmission: A survey. J Agr Econ 55 (3): 581-611. https://doi.org/10.1111/j.1477-9552.2004.tb00116.x
Montasser GE, 2015. The seasonal KPSS test: examining possible applications with monthly data and additional deterministic terms. Econometrics 3: 339-354. https://doi.org/10.3390/econometrics3020339
Newey WK, West KD, 1987. A simple positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix. Econometrica 55: 703-708. https://doi.org/10.2307/1913610
Palaskas TB, Crowe TJ, 1996. Testing for price transmission with seasonally integrated producer and consumer price series from agriculture. Eur Rev Agric Econ 23 (4): 473-486. https://doi.org/10.1093/erae/23.4.473
Sanjuán AI, Gil JM, 2001. A note on tests for market integration in a multivariate non-stationary framework. J Agr Econ 52 (2): 113-121. https://doi.org/10.1111/j.1477-9552.2001.tb04526.x
Sidhoum AA, Serra T, 2016. Volatility spillovers in the Spanish food marketing chain: The case of tomato. Agribusiness 32 (1): 45-63. https://doi.org/10.1002/agr.21418
Smith RJ, Taylor AMR, del Barrio-Castro T, 2009. Regression-based seasonal unit roots. Econ Theory 25: 527-560. https://doi.org/10.1017/S0266466608090166
Taylor AMR, 2003. Locally optimal tests against unit roots in seasonal time series. J Time Ser Anal 24: 591-612. https://doi.org/10.1111/1467-9892.00324
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