Forecasting Realized Volatility with HAR-RV

Among the models proposed to forecast Realized Volatility, the HAR-RV from Corsi stands out in terms of performance and simplicity.
“HAR-RV” stands for Heterogenous Autoregressive model of Realized Volatility and is based on the so called “Heterogenous Market Hypothesis”. This states that financial markets are an interaction of people acting at different fequencies (eg firms operating on High-Frequency, dealers trading intraday and institutional investors looking at much lower frequencies). Each class of market agents will cause volatility at difference frequencies, which will affect each other class to a certain degree. From these considerations it comes the idea to model each volatility frequency independently but jointly.  This brings us to the following, very simple in structure, model:

RV_d+1 = b_0 + b_1 * RV_d + b_2*RV_w + b_3*RV_m

where RV_d+1 is the next day RV, RV_d is the previous day RV, RV_w is the previous week average daily RV, and RV_m is the previous month average daily RV. RV in this case is the square root of the sum of squared intraday returns at a given frequency.
b_0,b_1,b_2 and b_3 are the regression parameters to be found.

As you can see, the model is basically a simple regression, however it compares in terms of performance with way more complicate model, such as ARFIMA. In fact, HAR-RV is able to model the main stylzed facts about RV, such as autocorrelations and long memory effects (although the model itself is not a long memory model, it takes advantage of the finding that simple sum of AR(1) processes can appear as a long memory process).

Here is a plot of forecasted Realized Volatility:

and here are the residuals over the actual RV:

Andrea