Notation

Description

BWP

Botswana Pula

$S\left(t\right)$

Beef-cattle price at time t

$\overline{S}$

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 $S_2$

r

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

$T\wedge {\tau }_{ϵ}$

Smaller between T and ${\tau }_{ϵ}$ , where $ϵ$ is an arbitrary small number

${\beta }_t={\varphi }_p\left(B\right)S_{1,t}$

Autoregressive process AR(p) of order p

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(q) of order q

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 $\left(\text{.}\right)$