Notation | Description |

BWP | Botswana Pula |

$S\left(t\right)$ | Beef-cattle price at time |

$\overline{S}$ | Average beef-cattle price |

${S}_{1}\left(t\right),{S}_{2}\left(t\right)$ | Farmer-BMC price and BMC-EU respectively price at time |

| ( for simplicity we have denoted by ${x}_{1}$ and ${x}_{2}$ respectively) |

${a}_{1},{a}_{2}$ | Respective residuals for ${S}_{1}$ and ${S}_{2}$ |

| The Pearson’s correlation coefficient |

$r\left(t\right)$ | Rate of return |

${r}_{1},{r}_{2}$ | Returns for ${x}_{1}$ and ${x}_{2}$ respectively |

${x}^{\prime}$ | Prime symbol (for derivative) |

| Integral sign |

$\text{d}\left(\text{.}\right)$ | Differential sign |

${\sigma}_{1},{\sigma}_{2}$ | Rate of volatilities for Farmer-BMC price and BMC-EU respectively price |

$\omega \left(B\right)$ | Transfer function |

${\nabla}_{{S}_{1,t}}^{d},{\nabla}_{{S}_{2,t}}^{d}$ | Incremental changes for Farmer-BMC prices and BMC-EU prices respectively |

$\mathbb{E}\left[\text{.}\right]$ | Expectation operator |

$T\wedge {\tau}_{\u03f5}$ | Smaller between |

${\beta}_{t}={\varphi}_{p}\left(B\right){S}_{1,t}$ | Autoregressive process AR( |

| where, $\varphi \left(B\right)=1-{\varphi}_{1}B-\cdots -{\varphi}_{p}{B}^{p}$ |

${\alpha}_{t}={\theta}_{q}\left(B\right){S}_{2,t}$ | Moving average MA( |

| where, $\theta \left(B\right)=1-{\theta}_{1}B-\cdots -{\theta}_{q}{B}^{q}$ |

${\Delta}_{t,i}={t}_{i}-{t}_{i-1}$ | Time interval |

$\mathbb{P}\left(\text{.}\right)$ | Probability of $\left(\text{.}\right)$ |