Martin Sola

Detecting Periodically Collapsing Bubbles: A Markov-Switching Unit Root Test

This paper addresses the problem of testing for the presence of a stochastic bubble in a time series in the case that the bubble is periodically collapsing so that the asset price keeps returning to the level implied by the market fundamentals. As this is essentially a problem of identifying the collapsing periods from the expanding ones, we propose using a generalization of the Dickey-Fuller test procedure which makes use of the class of Markov regime-switching models. The potential of the new methodology is illustrated via simulation, and an empirical example is given.

Intrinsic bubbles and regime-switching

Abstract Froot and Obstfeld (1991) allow for an intrinsic bubble in stock prices, using approximately a century of annual data for the US, in an attempt to model the widely documented deviations from the prices predicted by present values or fundamentals. However they assume that the log of real dividends follows a constant random walk with drift over the whole period. We show that this assumption is invalid, and that a Markov-switching model is a more appropriate representation of dividends. We then generalise the formulation of stock prices (including the intrinsic bubble) to allow for this, and show that regime-switching provides a better explanation for stock prices than the bubble. We show that when allowance is made both for the bubble and for regime-switching in the dividend process, the incremental explanatory contribution of the bubble is low.

Testing the term structure of interest rates using a stationary vector autoregression with regime switching

Abstract The expectations model of the term structure for US data on three- and six-month treasury bills for the period 1962(1)–1987(3) is explored. The analysis allows for the nonstationarity of the data, and for unobserved stochastic switches of regime, by estimating VARs in the yield spread and the change in the three-month rate which allow the time series processes to change between regimes. In contrast to other results for the expectations model, such as those of Hamilton (1988), Mankiw and Miron (1986), and others, we find that the data do not reject the model.

COINTEGRATION AND CHANGES IN REGIME: THE JAPANESE CONSUMPTION FUNCTION

In this paper we examine a model of cointegration where long-run parameters are subject to switching between several different cointegrating regimes. These shifts are allowed to be governed by the outcome of an unobserved Markov chain with unknown transition probabilities. We illustrate this approach using Japanese data on consumption and disposable income, and find that the data favor a Markov-switching long-run relationship over a standard temporally stable formulation.

A test for volatility spillovers

This paper proposes a new procedure for analyzing volatility links between different markets based on a bivariate Markov switching model. An empirical application of this procedure to three emerging markets is examined and discussed.

Switching error-correction models of house prices in the United Kingdom☆

Abstract This paper develops error-correction models of real house prices in the UK in which the adjustment coefficient switches stochastically between a stable regime where disequilibrium correction takes place and an unstable regime where such a correction does not occur. The generating mechanism of the shifts is modelled as a Markov process with transition probabilities which are either time-invariant or depend on the extent to which the system is out of disequilibrium. Estimation of error-correction models for the UK reveals that the observed booms in real house prices are associated with an unstable regime. We also find that the probability that the system remains in an unstable regime decreases as deviations from equilibrium increase.

Stylized facts and regime changes: are prices procyclical?

We investigate empirically the stability of the correlation between output growth and inflation using a technique that allows for changes in regime. We look at recent quarterly data for the G4 and at historical data for the U.S. and U.K. We find evidence of changes both in means and variances in both sources of data. In the quarterly data we find that the covariance between output growth and inflation is typically negative. In the historical data we find, as suggested in previous studies, that inflation was procyclical especially in the inter-war years, but has been countercyclical in the post-war period.

Rational bubbles during Poland's hyperinflation: implications and empirical evidence

Abstract It has been argued that the Polish hyperinflation at the end of the eighties was too excessive to be attributed to market fundamentals only. In this paper a range of indirect non-structural and structural tests for rational, exploding deterministic and stochastic bubbles are carried out. We adopt a new strategy based on the work of Hall and Sola (1993a) which allows for the possibility of switching regimes in the time series properties of the data to allow for both indirect tests and structural tests for the presence of stochastic bubbles.

Finite-sample properties of the maximum likelihood estimator in autoregressive models with Markov switching

This paper examines the finite-sample properties of the maximum likelihood estimator in autoregressive models subject to Markov mean and variance shifts. Our results reveal that conventional asymptotic approximations to the distribution of the maximum likelihood estimator can often be poor for the sample sizes that are typical for annual and quarterly times series.

A simple procedure for detecting periodically collapsing rational bubbles

This paper proposes a new procedure for detecting the presence of periodically collapsing rational bubbles via an analysis of the properties of the relevant observable time series. The procedure is based on random coefficient autoregressive models. An empirical application of the procedure to German hyperinflation data is examined and discussed.