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Many Information Theoretic Measures have been proposed for a quantitative assessment of causality relationships. While Gouriéroux, Monfort, and Renault (1987) had introduced the so-called “Kullback Causality Measures,” extending Geweke’s (1982) work in the context of Gaussian VAR processes, Schreiber (2000) has set a special focus on Granger causality and dubbed the same measure “transfer entropy.” Both papers measure causality in the context of Markov processes. One contribution of this paper is to set the focus on the interplay between measurement of (non)-markovianity and measurement of Granger causality. Both of them can be framed in terms of prediction: how much is the forecast accuracy deteriorated when forgetting some relevant conditioning information? In this paper we argue that this common feature between (non)-markovianity and Granger causality has led people to overestimate the amount of causality because what they consider as a causality measure may also convey a measure of the amount of (non)-markovianity. We set a special focus on the design of measures that properly disentangle these two components. Furthermore, this disentangling leads us to revisit the equivalence between the Sims and Granger concepts of noncausality and the log-likelihood ratio tests for each of them. We argue that Granger causality implies testing for non-nested hypotheses.

In this paper, the gamma test is used to determine the order of lag-k tail dependence existing in financial time series. Using standardized return series, statistical evidences based on the test results show that jumps in returns are not transient. New time series models which combine a specific class of max-stable processes, Markov processes, and GARCH processes are proposed and used to model tail dependencies within asset returns. Estimators for parameters in the models are developed and proved to be consistent and asymptotically joint normal. These new models are tested on simulation examples and some real data, the S&P 500.

The authors propose novel tests for the detection of Markov switching deviations from forecast rationality. Existing forecast rationality tests either focus on constant deviations from forecast rationality over the full sample or are constructed to detect smooth deviations based on non-parametric techniques. In contrast, the proposed tests are parametric and have an advantage in detecting abrupt departures from unbiasedness and efficiency, which the authors demonstrate with Monte Carlo simulations. Using the proposed tests, the authors investigate whether Blue Chip Financial Forecasts (BCFF) for the Federal Funds Rate (FFR) are unbiased. The tests find evidence of a state-dependent bias: forecasters tend to systematically overpredict interest rates during periods of monetary easing, while the forecasts are unbiased otherwise. The authors show that a similar state-dependent bias is also present in market-based forecasts of interest rates, but not in the forecasts of real GDP growth and GDP deflator-based inflation. The results emphasize the special role played by monetary policy in shaping interest rate expectations above and beyond macroeconomic fundamentals.

This paper proposes an efficient test designed to have power against alternatives where the error correction term follows a Markov switching dynamics. The adjustment to long run equilibrium is different in different regimes characterised by the hidden state Markov chain process. Using a general nonlinear MS-ECM framework, we propose an optimal test for the null of no cointegration against an alternative of a globally stationary MS cointegration. The Monte Carlo studies demonstrate that our proposed tests display superior powers compared to the linear tests. In an application to price-dividend relationships, our test is able to find cointegration while linear based tests fail to do so.

The purpose of this study is to contrast the forecasting performance of two non-linear models, a regime-switching vector autoregressive model (RS-VAR) and a recurrent neural network (RNN), to that of a linear benchmark VAR model. Our specific forecasting experiment is U.K. inflation and we utilize monthly data from 1969 to 2003. The RS-VAR and the RNN perform approximately on par over both monthly and annual forecast horizons. Both non-linear models perform significantly better than the VAR model.