Volume 12, Issue 3 - Regime-Switching Models in Economics and Finance

Although linear models have been the central focus of econometrics for most of the twentieth century, great developments in non-linear models took place from the latter part of the century. This paper questions the future development of non-linear models in economics and shows (via White's Theorem) that any non-linear model can be approximated by a time-varying parameter linear model. Compared with non-linear models, multi-step forecasts are more easily prepared using time-varying parameter models, while they are also more readily interpretable and theoretical results on aggregation are straightforward to obtain. Nevertheless, there is some evidence that subtle non-linearities may exist in macroeconomic time series.

In this paper we propose a test of the null hypothesis of time series linearity against a nonlinear alternative, when uncertainty exists as to whether or not the series contains a unit root. We provide a test statistic that has the same limiting null critical values regardless of whether the series under consideration is generated from a linear I(0) or linear I(1) process, and is consistent against nonlinearity of either form, being asymptotically equivalent to the efficient test in each case. Finite sample simulations show that the new procedure has better size control and offers substantial power gains over the recently proposed robust linearity test of Harvey and Leybourne (2007).

Empirically, the sum of GARCH parameter estimates is found to be close to unity, suggesting that the conditional volatility of most stock return data are likely to follow an integrated GARCH (IGARCH) process. However, such an extremely high persistence in unconditional variance may be overstated because of neglected structural breaks or parameter changes. As a result it is important to distinguish between these two processes, one being a globally stationary process and the other being a nonstationary IGARCH process. Though there are a number of studies modelling asymmetry leverage effects and advancing a battery of specification tests, studies that directly propose specification tests against Markov switching (MS) GARCH models are almost nonexistent. This paper develops such tests against MS-GARCH processes, which is shown to be asymptotically equivalent to the LR test. Furthermore, we consider the case in which the conditional variance follows an IGARCH process under the null whilst it is globally stationary under the alternative. Monte Carlo studies show that our proposed tests have a good finite sample performance. In an application to the weekly stock return data for five East Asian emerging markets, we find strong evidence in favor of MS-GARCH models.

The detection of structural change and determination of lag lengths are long-standing issues in time series analysis. This paper demonstrates how these can be successfully married in a Bayesian analysis. By taking account of the inherent uncertainty about the lag length when deciding on the number of structural breaks and vice versa we avoid some common pitfalls and are able to draw more robust conclusions. The approach is illustrated using both real data and a simulation study.

New Keynesian Phillips curves (NKPC) have recently been modified to include additional lags of inflation in the specification in order to capture the considerable persistence in postwar U.S. inflation. Furthermore, many researchers have agreed on the existence of structural changes in the persistence of inflation. Continuing with these literatures, we investigate the nature of structural changes in the hybrid NKPC and reconsider the role of the backward-looking component in the NKPC, taking into account the possibility of structural changes in the steady-state inflation rate. Our empirical results show multiple structural breaks in the NKPC in 1974 and 1982. Accounting for these structural changes, the backward-looking component is no longer significant throughout the whole sample period. In other words, the significant role of the backward-looking component in the earlier literature might be spuriously capturing the structural changes in the steady-state inflation rate. Thus, U.S. inflation dynamics are well explained by a pure NKPC if we take into account the possibility of structural changes in the steady-state inflation rate.

Using 15 years worth of additional data, a study is carried out to explore the extent to which the results in Rothman (1991) still hold. The analysis shows that such a comparison is very much dependent on whether: (i) 1-quarter differences or 4-quarter differences are used to construct the underlying state-indicator sequence; and (ii) the asymptotic distribution of the underlying test statistics is used for inference. The considerably higher staying probabilities obtained with the smoother 4-quarter differences argue in favor of their use in addressing the possible asymmetry of the business cycle, as opposed to higher-frequency fluctuations. Also, Monte Carlo simulations suggest the asymptotic p-values for the Markov chain tests are biased.

This paper proposes an asymmetric Markov regime-switching (MS) GARCH model to estimate value-at-risk (VaR) for both long and short positions. This model improves on existing VaR methods by taking into account both regime change and skewness or leverage effects. The performance of our MS model and single-regime models is compared through an innovative backtesting procedure using daily data for UK and US market stock indices. The findings from exceptions and regulatory-based tests indicate the MS-GARCH specifications clearly outperform other models in estimating the VaR for both long and short FTSE positions and also do quite well for S&P positions. We conclude that ignoring skewness and regime changes has the effect of imposing larger than necessary conservative capital requirements.

Using self-exciting threshold autoregressive models, we explore the validity of the law of one price (LOOP) for sixteen sectors in nine European countries. We find strong evidence of nonlinear mean reversion in deviations from the LOOP and highlight the importance of modelling the real exchange rate in a nonlinear fashion in an attempt to measure speeds of real exchange rate adjustment. Using the US dollar as a reference currency, the half-lives of sectoral real exchange rate shocks, calculated by Monte Carlo integration, imply much faster adjustment than the 'consensus' half-life estimates of three to five years. The results also imply that transaction costs vary significantly across sectors and countries.