Addressing the IGARCH puzzle

We address the IGARCH puzzle, by which we understand the fact that a GARCH(1,1) model fitted to virtually any financial dataset exhibit the property thatˆα + ˆ β is close to one. We do this by proving that if data is generated by a stochastic volatility model but fitted to a GARCH(1,1) model one would get thatˆα + ˆ β tends to one in probability as the sampling frequency is increased. We also demonstrate that the conditional variance based on the GARCH(1,1) model converges in probability to the true unobserved volatility process even when the model is misspecified. An included study of simulations and empirical high frequency data is found to be in very good accordance with the mathematical results. The paper establishes that the IGARCH effect is apparently merely a consequence of the mathematical structure of a GARCH model and not a property of the true data generating mechanism.