Maize Price Seasonal Analysis: The Augmented Dickey Fuller (ADF) Series

The Market pairs depicted in all three figures all seem to follow similar stochastic trends with price series that do not drift too far apart for each market pair indicating price co-movement. Indeed, the bivariate correlation coefficient included in Table 7 in the appendix shows that the price series are highly correlated and that the correlation is invariant to distance. In addition, observed price Spikes are common to all markets and can be observed around the years 2001, 2005, 2008 and 2014. Droughts in 2001 and 2005 explain the price spikes for the first two years but the 2008 price spikes occurred despite record maize production levels in that year.
4.1.2. Maize Price Seasonal Analysis
Figure 5 below shows the price variation by month.
The Augmented Dickey Fuller (ADF) test is used to determine the order of integration. The results for the ADF test are presented in Table 1 below. The null hypothesis for the ADF test was that the series has a unit root and is therefore nonstationary. However, the model does not provide enough evidence to reject the Null hypothesis for all the markets analyzed. All the variables are nonstationary in the levels but are stationary in their first differences. Therefore all the variables are integrated of order
Since we are testing pairwise co-integration, the two hypotheses are that there is no co-integrating relationship among the two markets and that there is one co-integrating relationship. The values of the trace statistic in the null hypothesis that r=0 are all greater than the 95% critical value, therefore we reject the null hypothesis. In contrast, the values of the trace statistic are all less than the critical values at the 95% level so we cannot reject the null hypothesis of the existence of a co-integrating relationship. Pairwise trace statistics for all possible market pairs are reported in table 8 in the appendix. The pairwise results indicate a strong support for cointegration with 91% of the market pairs showing a long-run equilibrium relationship.
Since we have established the existence of co-integrating relationships, the VECM can be used to estimate the parameters of interest. Table 3 below presents the results for the Johansen Vector Error Correction Model (VECM). The error correction model is useful for understanding how current variables change in response to the disequilibrium, in the previous period. Important parameters in the Johansen test are: the co-integrating vector parameter, β; the speed of adjustment coefficients, α; and the short-run