Forecasting Time Series with Long Memory and Level Shifts, A Bayesian Approach

Recent studies have showed that it is troublesome, in practice, to distinguish between long memory and nonlinear processes. Therefore, it is of obvious interest to try to capture both features of long memory and non-linearity into a single time series model to be able to assess their relative importance. In this paper we put forward such a model, where we combine the features of long memory and Markov nonlinearity. A Markov Chain Monte Carlo algorithm is proposed to estimate the model and evaluate its forecasting performance using Bayesian predictive densities. The resulting forecasts are a significant improvement over those obtained by the linear long memory and Markov switching models.Markov-Switching models, Bootstrap, Gibbs Sampling

Bootstrap LR tests of stationarity, common trends and cointegration

The paper considers likelihood ratio (LR) tests of stationarity, common trends and cointegration for multivariate time series. As the distribution of these tests is not known, a bootstrap version is proposed via a state space representation. The bootstrap samples are obtained from the Kalman filter innovations under the null hypothesis. Monte Carlo simulations for the Gaussian univariate random walk plus noise model show that the bootstrap LR test achieves higher power for medium-sized deviations from the null hypothesis than a locally optimal and one-sided LM test, that has a known asymptotic distribution. The power gains of the bootstrap LR test are significantly larger for testing the hypothesis of common trends and cointegration in multivariate time series, as the alternative asymptotic procedure -obtained as an extension of the LM test of stationarity- does not possess properties of optimality. Finally, it is showed that the (pseudo) LR tests maintain good size and power properties also for non-Gaussian series. As an empirical illustration, we find evidence of two common stochastic trends in the volatility of the US dollar exchange rate against european and asian/pacific currencies.Kalman filter, state-space models, unit roots

Granger-causality in Markov Switching Models

In this paper we propose a new parametrisation of transition probabilities that allows us to characterize and test Granger-causality in Markov switching models by means of an appropriate specification of the transition matrix. Test for independence are also provided. We illustrate our methodology with an empirical application. In particular, we investigate the causality and interdependence between financial and economic cycles using a bivariate Markov switching model. When applied to U.S. data, we find that financial variables are useful for forecasting the direction of aggregate economic activity, and vice versa.Granger Causality, Markov Chains, Switching Models

Unemployment and Hysteresis: A Nonlinear Unobserved Components A Nonlinear Unobserved Components A Nonlinear Unobserved Components A Nonlinear Unobserved Components A Nonlinear Unobserved Components Approach

A new test for hysteresis based on a nonlinear unobserved components model is proposed. Observed unemployment rates are decomposed into a natural rate component and a cyclical component. Threshold type nonlinearities are introduced by allowing past cyclical unemployment to have a different impact on the natural rate depending onthe regime of the economy. The impact of lagged cyclical shocks on thecurrent natural component is the measure of hysteresis. To derive anappropriate p-value for a test for hysteresis two alternative bootstrapalgorithms are proposed: the first is valid under homoskedastic errorsand the second allows for heteroskedasticity of unknown form. A MonteCarlo simulation study shows the good performance of both bootstrapalgorithms. The bootstrap testing procedure is applied to data fromItaly, France and the United States. We find evidence of hysteresis forall countries under study.Hysteresis, Unobserved Components Model, Threshold Autoregressive Models, Nuisance parameters, Bootstrap

UNEMPLOYMENT AND HYSTERESIS: A NONLINEAR UNOBSERVED COMPONENTS APPROACH

The aim of this paper is to find a possible hysteresis effect on unemployment rate series from Italy, France and the United States. We propose a definition of hysteresis taken from Physics which allows for nonlinearities. To test for the presence of hysteresis we use a nonlinear unobserved components model for unemployment series. The estimation methodology used can be assimilated into a threshold autoregressive representation in the framework of a Kalman filter. To derive an appropriate p-value for a test for hysteresis we propose two alternative bootstrap procedures: the first is valid under homoskedastic errors and the second allows for general heteroskedasticity. We investigate the performance of both bootstrap procedures using Monte Carlo simulation.Hysteresis; Unobserved Components Model; Threshold Autoregressive Models; Nuisance parameters; Bootstrap

Unemployment and hysteresis: a nonlinear unobserved components approach

The aim of this paper is to find a possible hysteresis effect on unemployment rate series from Italy, France and the United States. We propose a definition of hysteresis taken from Physics which allows for nonlinearities. To test for the presence of hysteresis we use a nonlinear unobserved components model for unemployment series. The estimation methodology used can be assimilated into a threshold autoregressive representation in the framework of a Kalman filter. To derive an appropriate p-value for a test for hysteresis we propose two alternative bootstrap procedures: the first is valid under homoskedastic errors and the second allows for general heteroskedasticity. We investigate the performance of both bootstrap procedures using Monte Carlo simulation

Unemployment and Hysteresis: A Nonlinear Unobserved Components Approach

A new test for hysteresis based on a nonlinear unobserved components model is proposed. Observed unemployment rates are decomposed into a natural rate component and a cyclical component. Threshold type nonlinearites are introduced by allowing past cyclical unemployment to have a different impact on the natural rate depending on the regime of the economy. The impact of lagged cyclical shocks on the current natural component is the measure of hysteresis. To derive an appropriate p-value for a test for hysteresis two alternative bootstrap algorithms are proposed: the first is valid under homoskedastic errors and the second allows for heteroskedasticity of unknown form. A Monte Carlo simulation study shows the good performance of both bootstrap algorithms. The bootstrap testing procedure is applied to data from Italy, France and the United States. We find evidence of hysteresis for all countries under study.

Testing for linearity in Markov switching models: a bootstrap approach

Markov switching autoregressive model, Bootstrap, Nuisance parameter, Monte Carlo simulation,