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.

  • 2
    $\begingroup$ @Micheal, maybe addressing us to the exact page of the book would help $\endgroup$ – Vitomir Jun 8 '19 at 9:58
  • $\begingroup$ @ Vitomir Ch.2 The basics of mean reversion : Augmented Dickey-Fuller Test p.42 $\endgroup$ – Michal Jun 8 '19 at 23:28
  • $\begingroup$ 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 $\endgroup$ – Alex C Jun 9 '19 at 1:39

The above is just the standard equation for the ADF test.


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 $\Delta y(t)$.

That's just an overview, the statistical properties of the ADF are complicated.

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