UCLA

Market risk models often deal with risk measurement and modeling in a specific capital

horizon, while model developers have to select an estimation horizon for the parameter

estimation. The use of overlapping data may be a solution for the trade-off between better

signal-to-noise ratio and the lower number of observations in the long-horizon data. We focus

on the beta estimate in one-factor linear regression model. Three data generating process are

considered in simulation: (1) independent identically distributed (iid) model, (2) generalized

autoregressive conditional heteroskedasticity model, (3) decomposition of stock price into a

random walk and stationary components. If the daily data perfectly satisfy a linear model

with iid error, estimate using daily data may be better than estimate using long-horizon

overlapping data. For the general linear regression model, generalized least squares with

longer horizon may produce better results since it takes into account the serial correlation

in overlapping data.