Infinite-order, long-memory heterogeneous autoregressive models

Stationary bootstrapping for structural break tests for a heterogeneous autoregressive model

“…We refer to Remarks 1 and 2 of Hwang and Shin (2014) for a necessary and sufficient condition of (A1) and for the absolutely summability of ϕ i and α j . Proposition 1 characterizes stationarity of Y t , which is given by Hwang and Shin (2014).…”

“…As an extension of Corsi's model (2.1), Hwang and Shin (2014) proposed an infinite-order genuine long-memory HAR(∞) model having an algebraically decreasing ACF, defined by…”

“…Here, we review the discussion of Hwang and Shin (2014) for the HAR(∞) process Y t in (2.3) and adopt their assumptions on the HAR(∞). The HAR(∞) process Y t in (2.3) can be written as an AR(∞) process:…”

“…However, as noted by Corsi (2009), the HAR(3) model has a short memory with a exponentially decreasing autocorrelation function (ACF) because it can be expressed as a stationary AR(22) model. Hwang and Shin (2014) proposed a genuine long-memory HAR model with algebraically decreasing ACF, an infinite-order HAR(∞) model, as an extension of the Corsi (2009)'s HAR(3) model. They characterized stationary conditions for the model, provided some probability theories and statistical methods in terms of consistency and limited the normality of the ordinary least squares estimator (OLSE) and forecasting.…”

“…and Hwang and Shin (2014) recently proposed autoregressive models called heterogeneous autoregressions (HAR) of realized volatility (RV) to address the long-memory properties of financial market volatilities. Corsi (2004Corsi ( , 2009 proposed an additive cascade model having three volatility components defined over three different time periods, called the HAR(3) model.…”