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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.

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    $\begingroup$ @Micheal, maybe addressing us to the exact page of the book would help $\endgroup$ – Vitomir Jun 8 at 9:58
  • $\begingroup$ @ Vitomir Ch.2 The basics of mean reversion : Augmented Dickey-Fuller Test p.42 $\endgroup$ – Michal Jun 8 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 at 1:39
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The above is just the standard equation for the ADF test.

http://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_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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