An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series

Abstract

This paper addresses the notion that many fractional I(d) processes may fall into the "empty box" category, as discussed in Granger (1999). We begin by showing that so-called spurious long memory may arise not only in the presence of (stochastic) structural breaks and regime switches, but also when the true data generating processes (DGPs) are linear with no structural breaks, and/or regime switching properties. However, we also present ex ante forecasting evidence based on an updated version of the absolute returns series examined by Ding, Granger and Engle (1993) that suggests that ARFIMA models estimated using a variety of standard estimation procedures yield "approximations" to the true unknown underlying DGP that provide significantly better out-of-sample predictions than AR, MA, and random walk models, with no models being "better" than ARFIMA models, based on analysis of point mean square forecast errors (MSFEs) as well as using Diebold and Mariano (DM: 1995) predictive accuracy tests. We also provide ex ante prediction evidence that 130 of the 215 macroeconomic variables used in Stock and Watson (SW: 2002) have lower (or equal) point MSFEs for ARFIMA-best models than for a large class of non-ARFIMA models. This result is obtained even though our ex-ante forecasting experiments using these variables involve prediction periods of only 200-250 months, and even though there is clear and substantial evidence of severe bias in various in-sample estimates of the differencing parameter. Furthermore, when a new prediction based estimator of d that we introduce is used to construct ARFIMA models for a subset of the SW dataset, many point MSFE error improvements associated with the use of ARFIMA models also become significant. These findings, taken together with the results of an empirical analysis of stock returns for 5 different countries and an extensive Monte Carlo analysis of a variety of different estimation and testing methods lead us to conclude that ARFIMA models might not fall into the "empty box" category after all, although much further research is needed before conclusive evidence in either direction can be given.JEL classification: C15, C22, C53.

Forecasting the Intraday Market Price of Money

“…LOP weights in Figure 5 show that there is some uncertainty at the beginning of the sample, but after September 2007 Abbassi and Linzert (2011), where the mean of the series shifts upward and volatility is high but less than for the previous period. We find as in Bhardwaj and Swanson (2006) that ARFIMA models produce accurate forecasts when there are several stochastic and unknown structural breaks. Which ARFIMA model to use is however unclear ex-ante; LOP can cope with such uncertainty and mixing predictive density can also approximate different regimes over time caused by different types of shocks.…”

“…We require 0 < d < 1, forecasting exercises when the data sample is small. Moreover, spurious long memory behaviors arise in many contexts, such as when there are (stochastic) structural breaks in linear and nonlinear models, regime switching models, and when forming models using variables that are nonlinear transformations of underlying "short memory" variables, see for example Byers et al (1997), Diebold and Inoue (2001), Engle and Smith (1999) and Bhardwaj and Swanson (2006).…”

Changing-regime volatility: a fractionally integrated SETAR model

“…These data were used by Bhardwaj and Swanson (2005), who applied ARFIMA models to the series and found that the latter frequently outperform linear models in terms of prediction. In their paper, the authors suggested, as an interesting extension to their work, to see whether nonlinear models with regime-switching or thresholds would perform better than the ARFIMA models.…”

Predicting BRICS stock returns using ARFIMA models

“…3 Bhardwaj and Swanson (2006) challenged this evidence by showing that ARFIMA models estimated using a variety of standard estimation procedures yield ''approximations'' to the true unknown underlying DGP. These in turn can sometimes provide significantly better out-of-sample predictions than simple linear non-ARFIMA models such MA, ARMA GARCH among others, when evaluated on the basis of point MSFE's as well as on the predictive accuracy tests and t-tests.…”

“…Understanding of the dynamic behavior of stock returns in these markets is crucial for portfolio managers, policy makers, and researchers. Therefore, the current paper attempts to add to the limited volume of literature on the usefulness of long-memory models in predicting stock 3 By "empty box", Granger means ARFIMA models have stochastic properties that essentially do not mimic the properties of the data (Bhardwaj and Swanson, 2006). …”