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.
Highlights
In research on agricultural prices, seasonal effects in a season are usually assumed to be fixed over the sample period
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
Given that the sample distribution of seasonal unit root tests depends on the deterministic components in the data generating process, Monte Carlo simulation experiments have been designed to obtain critical values depending on the inclusion of a slope term in the auxiliary regression
Summary
In research on agricultural prices, seasonal effects in a season are usually assumed to be fixed over the sample period. Such effects are modelled by means of seasonal dummies. As commented by Cáceres-Hernández & Martín-Rodríguez (2017), wrong assumptions about the seasonal component may lead to erroneous conclusions about the dynamic behaviour of the series and the transmission mechanisms between them. Seasonal unit root tests based on the proposals by Hylleberg et al (1990) and Franses (1991) have been proposed by Cáceres-Hernández (1996). As pointed out by Hylleberg (1994), the presence of seasonal unit roots implies the seasonal pattern is more variable than observed in actual series. The KPSS test (Kwiatwokski et al, 1992) has been extended to seasonal frequencies and applied to quarterly and monthly series
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