It is quite a well-know phenomenon that trading volume has an impact on a stock price: the more you buy the higher is a price because of demand increment. I'm wondering about models that can describe it formally. So I have two questions.
- What are the best models that fit it? For example, I know about Kyle's model (link) that says that $p_T = p_0 + \sum\limits_{n=0}^{N-1}\Delta p_n = p_0 + \lambda\sum\limits_{n=0}^{N-1}\varepsilon_n v_n$, where $p_T$ and $p_0$ are prices at $t=T$ and $t=0$ correspondingly, $\varepsilon_n=1$ if the volume of buys $v_b$ is larger than the volume of sells $v_s$ in the time interval $\Delta t$, $\varepsilon_n=-1$ in the opposite case and $v=\vert v_b - v_s\vert$. Is it suitable for real markets or does there exist something better?
- What statistical methods are usually used when you want to create some model from data or test some model for fitting the data? I think if we are seeking for linear dependence (as Kyle model told) between price and volume then least squares method will be fine for plotting a line between discrete data points.
Any thoughts and suggestions will be very appreciative.