can anyone help me to explain how the following model works?

enter image description here

In this formula $P(t)$ is a price at time $t$ and $F(t)$ is the residual noise term.

The $\omega(i;T_i)$ and $P_{o}(i;T_i)$ are uniquely determined from the past $T_{i}$ data points by condition that minimizes the root-mean square of $F(t)$.

Why $(\omega_{1}(i;T_i)-1)$?

Thanks in advance.

  • $\begingroup$ I dont see how to help you without more detailed info. What paper/textbook is this from? What is omega meant to mean? $\endgroup$ – Jan Sila Sep 18 '16 at 15:07
  • $\begingroup$ The link of the article researchgate.net/publication/…. $\endgroup$ – user3610659 Sep 18 '16 at 15:13

The paper explains it quite well I think: There are three cases:

(1) $\omega>1$ the price is either exponentially increasing or decreasing and $P_{0}$ gives the base line of the exponential divergence. We define such behavior as a bubble or a crash. In this case the positive feedback from the past price change becomes larger as the time passes.

(2) $\omega=0$ the price follows a random walk.

(3) $\omega<0$ the price is convergent to $P_{0}$.

So the value of the parameter just either magnifies the expression $\{P(t-1)-P_{0}\}$, renders it zero, or makes the price increments revert to $P_{0}$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.