MIDAS and GARCH; A comparison of predictive ability using real world data

Abstract

I compare GARCH and MIDAS one-day-ahead forecasts of volatility using high frequency data from the CRSP U.S. Mega Cap Index. The MIDAS models are estimated using high frequency data sampled at 5, 15 and 30 minute intervals and estimated using both exponential Almon and beta lag distributions with two shape parameters. The GARCH(1,1) model with a skewed t-distribution is the benchmark model to which the MIDAS models are compared. The study finds that MIDAS models have superior predictive ability in volatility spikes due to its ability to incorporate high frequency data and that the GARCH model is more prone to underestimate volatility but is able to produce smaller forecast errors during calm periods. The MIDAS models using data sampled at a frequency of 5 minutes perform poorly suggesting that high frequency noise plays an important role when sampling at this frequency. Sampling frequency appears to be more important than lag length when deciding on which MIDAS model to use.