This chapter illustrated that benchmark spreads used in several previous analyses, which investigated the liquidity issue in the development of the financial crisis of 2007-08, are actually integrated of order one. This causes problems for statistical inference, particu- larly when standard errors are estimated with bias. The method of first-differencing the time series has introduced a unit root, therefore there is fundamentally a non-stationary process where innovations cumulate over time. If there is a unit root in the time series, there is also a stochastic trend. The results reveal that there is a long-term causality running in both directions between the GerUS3M, LIBOR-OIS and EUSWEC spreads. The Cholesky decomposition proved that, if a liquidity shock affects the short-term interbank market, the LIBOR-OIS spread is the leader, whereas the EUSWEC and GerUS3M spreads are followers in aligning back into equilibrium. Engle and Granger
(1987) argued that in the long-run, some linear combination of non-stationary variables become stationary. Thus, cointegration provided a framework for estimating parameters of non covariance stationary processes. The evidence found in this chapter suggests that there are long-run cointegrating relationships among the GerUS3M, the LIBOR-OIS, and EUSWEC spreads. Independently, the non-stationary spreads have no predilection to return to a deterministic path, however the spreads together form a stationary rela- tionship and follow an equilibrium path. However, these relationships break down due
Chapter 3 Modelling the Long-run Relationship of Short-term Interest Rate
Spreads 69
to structural breaks. Thus, the implications of structural breaks for stationarity are significant. Nelson and Plosser (1982) argues that non-stationary spreads are affected by permanent effects originating from random shocks (structural breaks), and therefore these follow a random walk. In this particular case, the magnitude of shocks trans- lating into structural breaks is large and infrequent; for example, such was the shock perceived in the short-term interbank market on the 26th of July 2007 as identified by the Gregory-Hansen level shift with trend test (1996). Consequently, in Chapter 4 an autoregressive regime switching model is presented with the aim of exploring and de- tecting multiple structural changes or regime switches in the US LIBOR-OIS spread. To further assess the presence of structural changes, Chapter 5 presents various mul- tivariate regime switching models. The Johansen (1988) test’s coefficients revealed the speed of adjustment back to equilibrium levels, whereas the Gregory-Hansen (1996) test precisely identified when structural breaks occurred. Nonetheless, in the long-run, the cointegrating relationships return to equilibrium. This is a significant finding in the in- terbank liquidity literature and, in terms of theoretical implications, the results support the Dynamic Stochastic General Equilibrium Theory which states that financial markets are disturbed by random shocks, however in the long-run the system is in equilibrium.
Previous analyses looked at spreads in terms of their components and never assessed short-term interbank spreads jointly over a longer period of time. Important relation- ships have been revealed among the three nonstationary variables. The LIBOR-OIS, the currency swap and the German-US bond spread move in a synchronised fashion and this ultimately has implications for policymakers and market players alike.
Furthermore, the above analysis got us closer to advanced understanding of the char- acteristics of the forecast errors variance and also to recognising interrelationships and dependencies among the short-term interbank spreads. However, the forces influencing each of the variables were not identified. These are going to be identified in Chapter
5 where an endogenous variable drives regime changes in the independent variable. In classical cointegration models, the integration order is rigid, either I(1) or I(0), yet real economic and finance events described by time series, which exhibit persistent exoge- nous shocks, could be also investigated with the use of a fractional cointegration method to model long-run equilibriums. In most cases, the presence of fractionally integrated errors can be the reason for rejecting cointegration in conventional methods, such as the Dickey-Fuller or KPSS methods. Therefore, it would be interesting to address these in future research. Short-term interest rate models assume mean-reverting processes and the long-run mean and speed of adjustment is constant throughout the considered sample period. These are the so-called single regime models (Gray, 1996). Thus, the identi- fied structural relationship between the LIBOR-OIS, German-US bond and ESUWEC spread can only be preserved by implementing a non-linear Markov chain model.
Chapter 4
A Univariate Two-regime
Switching Model to Detect Crises
in the Short-term Interbank
Market
4.1
Introduction
Interest rate times series are known to vary persistently in times of uncertainty. It is critical to detect liquidity shocks before they crash the financial system. Moreover, it is imperative that early warning systems (EWS) with forecasting attributes are developed, specifically in the light of the recent financial crisis (and the Eurozone crisis that followed) which affected the majority of developed economies. Such EWSs detect liquidity crashes well before they develop into crises and ultimately spread to neighbouring markets via interbank channels. These two prolonged and financially devastating events are linked, and it is assumed that the Eurozone crisis was the direct result of the credit crunch. If appropriate financial measures and tools were in place to detect crises and forecast subsequent ones, the developed economies would not struggle to recover from the present recession which is still crippling Eurozone countries and the US economy alike.
In this chapter, a new regime switching model is proposed which provides the probability of being in a liquidity crisis state at any given instance. The model is assessed on the daily LIBOR-OIS spread during a period of 10 years. By using thresholds, crisis and tranquil periods are established, which subsequently model the baseline distribution.
72
Chapter 4 A Univariate Two-regime Switching Model to Detect Crises in the Short-term Interbank Market
Bayesian inference1 differs from statistics in the sense that all unknown parameters are treated as random variables, whose prior distribution which describes the data is out- lined from outset. More accurately, the priors provide all available information about the data, such that it summarises the researcher’s knowledge of the uncertain parameters (θ for example) before any data is taken into consideration. Consequently, estimated parameters incorporate uncertainty defined in terms of probability distributions. Prior distributions are grounded on either expert knowledge about the data and/or subjec- tive perceptions (in case of uninformative probability distributions, for example). As new data becomes available, the predicting mechanism updates the system with the information that becomes available. Matching prior distributions with the time series produces not a fixed value, such as an expected mean for example in standard statistical or econometric tests, but a matrix of posterior distributions for all the parameters. This provides an accurate and superior estimation of crisis and non-crisis periods.
This chapter is organised as follows. Section 4.2surveys the literature, while Section 4.3
presents the research questions. The data used in this analysis is discussed in Section 4.4. In Section 4.5 the specification for the two-state regime-switching model is presented. Section 4.6contains the empirical analysis with the results and out-of-sample forecasted estimates. Section 4.8 presents the conclusions, limitations of this study and future research.