On the transmission of memory in GARCH-in-mean models

摘要: In this article, we show that in times series models with in-mean and level effects, persistence will be transmitted from the conditional variance to mean vice versa. Hence, by studying mean/variance independently, one obtain a biased estimate of true degree persistence. For specific example an AR(1)-APARCH(1,1)-in-mean-level process, derive autocorrelation function, impulse response function optimal predictor. Under reasonable assumptions, process observationally equivalent autoregressive moving average (ARMA)(2,1) largest root being close one. We illustrate empirical relevance our results applications S&P 500 return US inflation data.