I'm trying to implement the following paper: Avellaneda & Lee (2010), Statistical Arbitrage in the US equities market.
To build the strategy, the idea is to trade a stock and hedge using a basket of ETFs (the signal is based on the residuals of the stocks vs ETFs regression).
In order to estimate the betas on the ETFs, the authors suggest that a regularised regression framework could be used, re-estimating the parameters every 60 days (because these relationships will change over time).
In my attempt to replicate their results, I have chosen LASSO over Ridge/Elastic Net (to build sparse models and reduce to the minimum the ETFs to trade when hedging).
In order to tune the regularisation parameter (alpha) of the LASSO, I have used time-series cross validation (timeseries split in scikit learn, i.e. expanding window).
The problem is that given the 60 days of daily returns used to estimate the regression coefficients, I'm not sure the amount of data would be sufficient to appropriately tune alpha.
Do you think I could tune the alpha parameter on a longer window than the one used to estimate the regression coefficients?
Would be nice to hear any thoughts on this.
Thank in you in advance for your help.