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This paper proposes a contemporaneous-threshold smooth transition GARCH (or C-STGARCH) model for dynamic conditional heteroskedasticity. The C-STGARCH model is a generalization to second conditional moments of the contemporaneous smooth transition threshold autoregressive model of Dueker et al. (2007) in which the regime weights depend on the ex ante probability that a contemporaneous latent regime-specific variable exceeds a threshold value. A key feature of the C-STGARCH model is that its transition function depends on all the parameters of the model as well as on the data. The structural properties of the model are investigated, in addition to the finite-sample properties of the maximum likelihood estimator of its parameters. An application to U.S. stock returns illustrates the practical usefulness of the C-STGARCH model.

The decomposition and filtering of time series is an important issue in economics and econometrics and related fields. Even though there are numerous competing methods on the market, in applications one often meets one of the few favorites, like the Hodrick-Prescott filter or the bandpass filter.In this paper, we suggest to employ penalized splines fitting for detrending. The approach allows to take correlation of the residuals into account and provides a data driven setting of the smoothing parameter, none of which the classical filters allow. We show the simplicity of the penalized spline filter using the open source software R and demonstrate differences and features with numerous data examples.

This paper studies optimal real-time monetary policy when the central bank takes the exogenous volatility of the output gap and inflation as proxy of the undistinguishable uncertainty on the exogenous disturbances and the parameters of its model. The paper shows that when the exogenous volatility surrounding a specific state variable increases, the optimal policy response to that variable should increase too, while the optimal response to the remaining state variables should attenuate or be unaffected. In this way the central bank moves preemptively to reduce the risk of large deviations of the economy from the steady state that would deteriorate the distribution forecasts of the output gap and inflation. When an empirical test is carried out on the U.S. economy the model predictions tend to be consistent with the data.

A growing body of literature concentrates on the linear dependence between stock returns and inflation. Although the recent empirical evidence suggested the presence of complexities, to our knowledge only a few works have investigated the existence of a potential nonlinear stock returns-inflation relationship. In order to study in more depth the dynamic attributes of this puzzle, we suggest a quite different framework where the primary goal is to explore the association between their underlying dynamics. Through the use of the Recurrence Quantification Analysis (Webber and Zbilut (1994)), the test for structural breaks of Bai and Perron (1998) and the test for nonlinear causality of Diks and Panchenko (2006), we find evidence in favour of negative nonlinear linkages between the inherent dynamics of inflation and stock returns. The presence of nonlinearity reinforces uncertainty. As long as inter-dependences are complex and nonlinear, small perturbations in fundamentals can lead to unexpected propagations within the financial system.

In this article, we concentrate on various techniques to quantify long-range dependence: wavelets, Geweke and Porter-Hudak (GPH)'s semi-parametric method, the periodogram method, rescaled range analysis (R/S) and a modification of it aimed at accommodating for short memory, quasi maximum likelihood (QML), de-trended fluctuation analysis (DFA), Modified DFA (MDFA), and Centered Moving Average (CMA) analysis.Based on Monte Carlo experiments, we conclude that if the data generating process (DGP) is an AR(1), MA(1) or ARMA(1, 1) process, with moderate parameter values, the periodogram, GPH, QML, and modified R/S methods, followed by the DFA, MDFA, and CMA ones, perform reasonably well as regards with bias, although some of these techniques exhibit a non-negligible size distortion. Moreover, the QML, the periodogram, DFA, MDFA, and CMA methods overall provide with powerful and low-bias estimators, under alternative ARFIMA (p, d, q)-DGPs. The wavelet-based estimator in turn has high power, but it is noticeably upward (downward) biased when the autoregressive (moving-average) coefficient of the DGP is large.Our Monte Carlo experiments are complemented with an application to Dow Jones AIG Gold Sub-index data, by means of bootstrap re-sampling.

The principal objective of this study is to explore nonparametric testing for linearity in the long-run relationship of the cointegrated vector error-correction model. We develop nonparametric tests, which are predicated on general nonlinear specification, and thus nonlinear models such as the smooth transition and threshold cointegration models are contained in our specification. The test statistics can be computed using the null model of standard error correction. The asymptotic distribution of the test statistics is based on the standard distribution, and thus the proposed tests do not involve semiparametric treatment for the resolution of inferential difficulty. The alternative distribution of the test statistics is explored under the local drift and the smooth functional form. The Monte Carlo simulation shows that the proposed tests evidence adequate finite sample performance in detecting omitted nonlinearity. An economic application to the stock price-dividend relation is also provided.