Academic journal article The European Journal of Comparative Economics

The Out-of-Sample Forecasting Performance of Non-Linear Models of Real Exchange Rate Behaviour: The Case of the South African Rand*

Academic journal article The European Journal of Comparative Economics

The Out-of-Sample Forecasting Performance of Non-Linear Models of Real Exchange Rate Behaviour: The Case of the South African Rand*

Article excerpt

Abstract

This paper analyses the out-of-sample forecasting performance of non-linear vs. linear models for the South African rand against the United States dollar and the British pound, in real terms. We compare the forecasting performance of point, interval and density forecasts for non-linear Band-TAR and ESTAR models to linear autoregressive models. Our data spans from 1970:01 to 2012:07, and we found that there are no significant gains from using either the Band-TAR or ESTAR non-linear models, compared to the linear AR model in terms of out-of-sample forecasting performance, especially at short horizons. We draw similar conclusions to other literature, and find that for the South African rand against the United States dollar and British pound, non-linearities are too weak for Band-TAR and ESTAR models to estimate.

JEL classifications: C22, C52, C53, F31, F47.

Keywords: Real exchange rate; Transaction costs; Band-threshold autoregressive model; Exponential smooth transition autoregressive model; Point forecast; Interval forecast; Density forecast; South Africa.

(ProQuest: ... denotes formulae omitted.)

1. Introduction

Two of South Africa's main trading partners are the United States and the United Kingdom. The size of these two economies alone result in greater volatility of the South African exchange rate in terms of these two currencies. Large fluctuations in real exchange rates have potential trade balance and policy implications. According to Schnatz (2006), it is not necessarily the level of the real exchange rate, but rather the movement towards or away from some long-run equilibrium that makes planning and policy making a challenge. It therefore becomes imperative to be able to accurately forecast real exchange rates, in an attempt to remove some of the uncertainties in decision- and policy making.

Internationally there has been a drive towards estimating real exchange rate behaviour using non-linear models. These are well motivated by theoretical models, developed by Obstfeld and Rogoff(2000), incorporating transaction costs (transportation costs, tariffs and nontariffbarriers, as well as any other costs that agents incur in international trade). Intuitively, transaction costs give rise to a band of inactivity where arbitrage is not profitable, so that real exchange rate fluctuations are not corrected inside of the band. However, arbitrage works to bring the real exchange rate back to the edge of the band if the real exchange rate moves outside of the band.

In line with the theoretical models involving transaction costs, one can characterize real exchange rate movements based on a Band-Threshold Autoregressive (Band-TAR) and exponential smooth-transition autoregressive (ESTAR) models. The Band-TAR model is characterized by unit-root behavior in an inner regime and reversion to the edge of the unit-root band in an outer regime. In contrast to the discrete regime switching that characterizes the Band-TAR model, the ESTAR model allows for smooth transition between regimes. As pointed out by Rapach and Wohar (2006), non-synchronous adjustment by heterogeneous agents and time aggregation are likely to lead to smooth switching of regimes, rather than discrete switches, and this is more likely to be the case for real exchange rates, since they are based on broad price indices.

Against this backdrop, this paper follows the methodology of Rapach and Wohar (2006) and implements Band-TAR and ESTAR models to estimate the non-linear behaviour of real exchange rates within sample as well as out-of-sample for the South African real exchange rate against the US dollar and British pound. The non-linear out-of-sample point, interval and density forecasts are evaluated relative to the corresponding out-of-sample point, interval and density forecasts from the linear AR model. We use the modified M-DM statistic of Harvey et al., and the weighted version of M-DM statistic (MW-DM) developed by van Dijk and Franses (2003) to determine whether the non-linear AR models' point forecasts are superior to the linear AR models' forecasts. …

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