# linear model of price changes

I came across the below equation for linear model of price changes in E.Chan book Algorithmic Trading which is the base for a strategy.

Δy(t) = λy(t − 1) + μ + βt + α1Δy(t − 1) + … + αkΔy(t − k) + ∋t   (2.1)


What is the logic behind the model? Is it a commonly used model ? Does it have its name or author? How it is derived? I am trying to find some source where I could learn more about it, please for some hints.

• @Micheal, maybe addressing us to the exact page of the book would help – Vitomir Jun 8 at 9:58
• @ Vitomir Ch.2 The basics of mean reversion : Augmented Dickey-Fuller Test p.42 – Michal Jun 8 at 23:28
• There is plenty of material on stationarity, unit roots, cointegration and ADF test out there. The above is a very standard equation for ADF test en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test – Alex C Jun 9 at 1:39

It looks complicated. You might start by reading about the original, simpler, Dickey Fuller Test, before it became 'Augmented'. Suppose interest rates $$y(t)$$ are mean reverting: when they are high they tend to come down and when low they increase. You could show this by estimating $$\lambda$$ and $$\mu$$ in the equation $$\Delta y(t)=\lambda y(t−1)+\mu$$. You would expect $$\lambda$$ to come out negative. And the neutral point where interest rates neither increase nor decrease would be $$\tilde{y}$$ such that $$\lambda \tilde{y}+\mu=0$$. Above $$\tilde{y}$$ changes tend to be negative and below, positive. That's the basic idea of DF test.
The Augmented DF adds to this a trend term βt in case there is a long term trend in the data (certainly the case for interest rates) and the other autoregressive terms in case there are more complicated dynamics in $$\Delta y(t)$$.