I am trying to create a model that forecasts trading costs (using end of day data, so no intra day data). My trading cost (also called Implemented Shortfall (IS) is defined as such for a single stock,
IS = (vwap - open) / open
for the market as a whole,
IS = abs(IS_single_stock - IS_market_median)
Variables that I am looking at include a companies market cap, the daily spread, vwap, volume & a liquidity measure called liq_m.
Doing a simple linear regression of each variable against IS produced very low r-squares, below 0.1. Combining the variables did very little to to improve the results. The residual plots appear to have some pattern, the one below is similar for most of the variables, this is mcap vs IS residuals.
The normal probability plot also highlights that the residuals are not linear & have a left skew.
In the literal I have read on implemented shortfall all the models are non linear models so this is not unexpected.
I am unsure though of how to proceed next i.e. how to select an appropriate non linear model for testing? The end goal is to have a model that allows me to forecast the cost of trading a certain company.
Below are two more plots. One is the daily plot of mcaps over time - a mean is used to calculate the mcap of the 100 companies used in the sample. Beneath that is the Implemented Shortfall again a mean is used in the plot.