## 1 Introduction

^{1}. To this end, it relies on the tool of quantile coherency (Barunık and Kley 2019) which allows co-movement to be both frequency- and quantile-dependent. Quantile coherency has been employed recently to assess the linkages between cryptocurrencies (Baumohl 2019), between gold, gold mining, oil and energy sector uncertainty indices (Naeem et al. 2020), between emerging markets stocks, gold, and oil (Mensi et al. 2021), and between China’s stock and commodities markets (Wang 2023).

^{2}. This type of information is relevant for research economists (who are interested in market integration and efficiency), for manufacturers utilizing vegetable oils as inputs and for participants in the respective futures markets. The strength and the pattern of the contemporaneous association between the two prices are behind the soybean-palm oil spread (BOPO) that determines whether switching from one vegetable oil to the other is beneficial. At the same time, the BOPO is watched closely by traders in commodity futures markets in order to exploit profit opportunities. The empirical results from the quantile coherency analysis may enable industrialists and futures markets participants to condition their decisions on the state of the markets and the horizons they operate.

## 2 Analytical framework

## 3 The data and the empirical model

^{3}. Typically, soybean oil commands a price premium over palm oil for two reasons: (a) palm oil has the highest yield of oil per hectare relative to other vegetable oils and (b) soybean oil has a better taste and is richer in proteins and in omega-3 fatty acids. For most periods the two prices tended to move in the same direction

^{4}. The BOPO spread, however, exhibited considerable volatility due to the demand and supply dynamics in each market (affected by the weather, government policies such as mandates for blending ratios or intervention in foreign trade, and fluctuation in exchange rates). The narrowing (widening) of the BOPO spread directs price-sensitive users towards soybean (palm) oil.

^{5}. Moreover, to avoid spurious association, the price returns have been filtered using appropriate ARMA-GARCH models as in Tjostheim and Hufthammer (2013) and Barunık and Kley (2019) (for details see Appendix Table 8). To capture the impact of different market states on the intensity and the mode of the price relationship, quantile coherency has been estimated at pairs involving the 0.05, 0.50, and 0.95 quantile levels. The short-term (high-frequency) has been set to one week (5 stock market days), the medium-term (medium-frequency) to one month (22 stock market days), and the long-term (low-frequency) to one year (250 stock market days). All these choices are consistent with the earlier works of Naeem et al. (2020) and Mensi et al. (2021). The single and joint coefficient tests have been conducted using a Wald-type statistic

## 4 The empirical results

^{6}. All estimates are positive and, the large majority of them, statistically significant at the conventional levels. There is strong evidence of co-movement in the bearish-bearish market state (the (0.05, 0.05) pair) and in the normal-normal state (the (0.5, 0.5) pair). The evidence, however, of co-movement in the bullish-bullish state is much weaker; quantile coherency for the pair (0.95, 0.95) is statistically significant only at the 10% level. Given that in well-integrated markets prices should boom and crash together (Reboredo 2012), one may conclude that the degree of integration between palm and soybean oil markets is not high. This is further reinforced by the fact that all quantile coherency estimates for the bearish-bullish and the bullish-bearish states are positive and one of them (for the (95,5) pair at the high-frequency) is statistically significant at the 10% level implying positive co-movement under extreme positive returns of palm oil and extreme negative returns for soybean oil; for a high degree of market integration, a negative sign for quantile coherencies is required at quantile pairs involving strong negative returns in one market and strong positive returns in the other. The visual evidence of Table 1 suggests further that quantile coherency tends to increase with the time-scale

^{7}. Sizable differences in the estimates exist between the high- and the medium- frequencies but very small ones between the medium- and the low- frequencies. This is an indication that adjustments in the BOPO spread due to shocks in one or both markets are likely to be completed within 1 month. Also, under all three frequencies, quantile coherencies at the normal-normal state are substantially higher than those at other market states.

Quantile pair | Frequency | |||
---|---|---|---|---|

1 week | 1 month | 12 months | ||

Soybean oil | Palm oil | |||

5 | 5 | 0.239 (< 0.01) | 0.488 (< 0.01) | 0.506 (< 0.01) |

5 | 50 | 0.211 (< 0.01) | 0.331 (< 0.01) | 0.342 (< 0.01) |

5 | 95 | 0.001 (0.978) | 0.101 (0.128) | 0.111 (0.111) |

50 | 5 | 0.287 (< 0.01) | 0.254 (< 0.01) | 0.257 (< 0.01) |

50 | 50 | 0.440 (< 0.01) | 0.515 (< 0.01) | 0.519 (< 0.01) |

50 | 95 | 0.312 (< 0.01) | 0.362 (< 0.01) | 0.360 (< 0.01) |

95 | 5 | 0.082 (0.093) | 0.111 (0.121) | 0.112 (0.135) |

95 | 50 | 0.209 (< 0.01) | 0.339 (< 0.01) | 0.346 (< 0.01) |

95 | 95 | 0.149 (0.076) | 0.169 (0.088) | 0.175 (0.086) |

(a) Bearish-bearish, normal-normal, and bullish-bullish states symmetry | |

Ho: coherency is equal at the quantile pairs | Test statistics |

(5,5), (50,50), and (95,95) | − 0.191 and 0.282 (< 0.01) 0.09 (0.423) |

(5,5) and (95,95) | |

(b) Exchange symmetry | |

Ho: coherency is equal at the quantile pairs | Test statistic |

(5,50) and (50,5) | − 0.075 (0.296) |

(5,95) and (95,5) | − 0.08 (0.214) |

(50,95) and (95,50) | 0.103 (0.178) |

(a) Bearish-bearish, normal-normal, and bullish-bullish states symmetry | |

Ho: coherency is equal at the quantile pairs | Test statistics |

(5,5), (50,50), and (95,95) | − 0.026 and 0.346 (< 0.01) 0.319 (0.015) |

(5,5) and (95,95) | |

(b) Exchange symmetry | |

Ho: coherency is equal at the quantile pairs | Test statistic |

(5,50) and (50,5) | 0.078 (0.406) |

(5,95) and (95,5) | − 0.01 (0.911) |

(50,95) and (95,50) | 0.022 (0.830) |

(a) Bearish-bearish, normal-normal, and bullish-bullish states symmetry | |

Ho: coherency is equal at the quantile pairs | Test statistics |

(5,5), (50,50), and (95,95) | − 0.012 and 0.343 (< 0.01) 0.331 (0.015) |

(5,5) and (95,95) | |

(b) Exchange symmetry | |

Ho: coherency is equal at the quantile pairs | Test statistic |

(5,50) and (50,5) | 0.086 (0.381) |

(5,95) and (95,5) | − 0.002 (0.985) |

(50,95) and (95,50) | 0.014 (0.896) |

Ho: coherency is equal across the three frequencies at the quantile pairs | Test statistics | Ho: coherency is equal across the three frequencies at the quantile pairs | Test statistics |
---|---|---|---|

(5,5) | − 0.249 and − 0.018 (< 0.01) | (50,95) | − 0.049 and 0.001 (0.467) |

(5,50) | − 0.119 and − 0.011 (0.066) | (95,5) | − 0.029 and − 0.005 (0.852) |

(5,95) | − 0.099 and − 0.01 (0.123) | (95,50) | − 0.13 and -0.007 (0.028) |

(50,5) | 0.034 and − 0.004 (0.480) | (95,95) | − 0.02 − 0.006 (0.774) |

(50,50) | − 0.084 and − 0.004 (0.229) |

Ho: coherency is equal in large and small frequency at the quantile pairs | Test statistic | Ho: coherency is equal in large and small frequency at the quantile pairs | Test statistic |
---|---|---|---|

(5,5) | − 0.267 (< 0.01) | (50,95) | − 0.049 (0.406) |

(5,50) | − 0.131 (0.02) | (95,5) | − 0.03 (0.613) |

(5,95) | − 0.109 (0.041) | (95,50) | − 0.138 (0.013) |

(50,5) | 0.03 (0.614) | (95,95) | − 0.026 (0.674) |

(50,50) | − 0.088 (0.111) |

## 5 Conclusions

^{8}. At the same time, the EU (a major importer of palm oil) has recently revised, due to environmental considerations, its biofuels policy to phase out palm oil-based biodiesel by 2030

^{9}. These policy changes are going to have opposite effects on palm oil prices while soybean oil demand in the US is expected to remain robust. Therefore, the relationship between soybean and palm oil prices is likely to be an important topic for empirical analysis in the next few years.