A Simple Fractionally Integrated Model with a Time-varying Long Memory Parameter d t

Abstract

Long-memory, Logistic function, STAR, C32, C51, G12,

A smooth transition long-memory model

“…The model given by (5), (6), (7) and (8) Lahiani and Scaillet (2009) consider the case in which z t is a random variable. These models however present some limitations when the number of regimes becomes very high because of computational problems.…”

“…Instead, it may vary if the economic structure itself changes over time, or if markets are permanently hit by different shocks. Authors in the literature have formalized this idea in several ways : multi-scale or multi-fractal processes (Alvarez-Martinez et al (2010), Engelen et al (2011), Pasquini and Serva (1999)), support-vector machine processes (Gravishchaka and Ganguli (2003)) long-memory models with threshold transition dynamics (Boutahar et al (2008), Dufrénot et al (2005aDufrénot et al ( , 2005bDufrénot et al ( , 2008), fractional models with regime shifts (Aloy et al (2010)). …”

A new time-varying model for forecasting long-memory series

“…Others treated the number of breaks as well as their timing as unknown (Ray and Tsay, 2002;Hassler and Meller, 2014). Boutahar et al (2008) and, more recently, Boubaker (2018) generalize the standard long-memory modeling by assuming that the long-memory parameter d is stochastic and time-varying. The authors introduce a STAR process, characterized by a logistic function, on this parameter and propose an estimation method for the model.…”

Time-varying persistence of inflation: evidence from a wavelet-based approach

“…Dufrénot et al (2005 a, b; discover that d(t) follows a Self-Exciting Threshold Autoregressive (SETAR) process. Recently, Boutahar et al (2008) and Aloy et al (2013) determine that d(t) evolves according to a Smooth Transition Regression (STR) process (Teräsvirta 1994(Teräsvirta , 1998.…”

“…This approach has, among other things, the additional benefit of bypassing the rather complex problem of structural breaks. In particular, we assume, following Boutahar et al (2008) and Aloy et al (2013), that the fractional integration parameter varies according to two regimes with smooth transition from one regime to the other. Thus, the model interestingly allows for the presence of both long-range dependence (long-memory) in inflation and asymmetry in the degree of inflation persistence.…”