Evolving splines and seasonal unit roots in weekly agricultural prices

The univariate statistical properties of agricultural price series need to be examined as a first step in the analysis of price transmission mechanisms. However, in the case of weekly price series, increasingly available, the testing procedures usually applied in this step are not suitable to deal with evolving seasonal effects. In this study, a method of testing for seasonal unit roots in weekly series of agricultural prices is described. When the deterministic seasonal component does not remain constant over time, the restricted evolving spline model (RESM) is shown to be a useful parametric formulation to capture the deterministic seasonal pattern. Therefore, the RESM model should be included as a deterministic component in auxiliary regression for unit root tests at seasonal frequencies. This proposal is applied to three weekly series of Canary Islands banana prices. From the standard seasonal unit root tests, the null hypothesis is failed to be rejected at the 5% or 10% significance level at some seasonal frequencies for each one of the series. Once critical values are obtained by simulation exercises when the RESM model is included, the hypotheses of unit root are rejected at each one of the seasonal frequencies for all of the three series.