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on Econometric Time Series |
| By: | Zacharias Psaradakis (Birkbeck, University of London); Martin Sola (Universidad Torcuato di Tella, Argentina) |
| Abstract: | This paper proposes a model which allows for discrete stochastic breaks in the time-varying transition probabilities of Markov-switching models with autoregressive dynamics. An extensive simulation study is undertaken to examine the properties of the maximum-likelihood estimator and related statistics, and to investigate the implications of misspecification due to unaccounted changes in the parameters of the Markov transition mechanism. An empirical application that examines the relationship between Argentinian sovereign bond spreads and output growth is also discussed. |
| Keywords: | Markov-switching models; Maximum likelihood; Monte Carlo experiments; Time-varying transition probabilities. |
| JEL: | C32 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:bbk:bbkefp:1702&r=ets |
| By: | Ruben Loaiza-Maya; Michael Stanley Smith |
| Abstract: | We propose a new variational Bayes method for estimating high-dimensional copulas with discrete, or discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is substantially faster than previous likelihood-based approaches. We use it to estimate drawable vine copulas for univariate and multivariate Markov ordinal and mixed time series. These have dimension $rT$, where $T$ is the number of observations and $r$ is the number of series, and are difficult to estimate using previous methods. The vine pair-copulas are carefully selected to allow for heteroskedasticity, which is a common feature of ordinal time series data. When combined with flexible margins, the resulting time series models also allow for other common features of ordinal data, such as zero inflation, multiple modes and under- or over-dispersion. Using data on homicides in New South Wales, and also U.S bankruptcies, we illustrate both the flexibility of the time series copula models, and the efficacy of the variational Bayes estimator for copulas of up to 792 dimensions and 60 parameters. This far exceeds the size and complexity of copula models for discrete data that can be estimated using previous methods. |
| Date: | 2017–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1712.09150&r=ets |
| By: | BREITUNG, Jörg (University of Cologne); HAFNER, Christian M. (Université catholique de Louvain, CORE, Belgium) |
| Abstract: | Popular volatility models focus on the conditional variance given past observations, whereas the (arguably most important) information in the current observation is ignored. This paper proposes a simple model for now-casting volatilities based on a specific ARMA representation of the log-transformed squared returns that allows us to estimate current volatility as a function of current and past returns. The model can be viewed as a stochastic volatility model with perfect correlation between the two error terms. It is shown that the volatility nowcasts are invariant to this correlation and therefore the estimated volatilities coincide. An extension of our now-casting model is proposed that takes into account the so-called leverage effect. The alternative models are applied to estimate daily return volatilities from the S&P 500 stock price index. |
| Keywords: | EGARCH, stochastic volatility, ARMA, realized volatility, leverage |
| JEL: | C22 C58 |
| Date: | 2016–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2016004&r=ets |
| By: | Massimo Franchi; Paolo Paruolo |
| Abstract: | This paper derives a generalization of the Granger-Johansen Representation Theorem valid for $H$-valued autoregressive (AR) processes, where $H$ is an infinite dimensional separable Hilbert space, under the assumption that 1 is an eigenvalue of finite type of the AR operator function and that no other non-zero eigenvalue lies within or on the unit circle. A necessary and sufficient condition for integration of order $d=1,2,\dots$ is given in terms of the decomposition of the space $H$ into the direct sum of $d+1$ closed subspaces $\tau_h$, $h=0,\dots,d$, each one associated with components of the process integrated of order $h$. These results mirror the ones recently obtained in the finite dimensional case, with the only difference that the number of cointegrating relations of order 0 is infinite. |
| Date: | 2017–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1712.07522&r=ets |
| By: | J. Eduardo Vera-Vald\'es |
| Abstract: | Most long memory forecasting studies assume that the memory is generated by the fractional difference operator. We argue that the most cited theoretical arguments for the presence of long memory do not imply the fractional difference operator, and assess the performance of the autoregressive fractionally integrated moving average $(ARFIMA)$ model when forecasting series with long memory generated by nonfractional processes. We find that high-order autoregressive $(AR)$ models produce similar or superior forecast performance than $ARFIMA$ models at short horizons. Nonetheless, as the forecast horizon increases, the $ARFIMA$ models tend to dominate in forecast performance. Hence, $ARFIMA$ models are well suited for forecasts of long memory processes regardless of the long memory generating mechanism, particularly for medium and long forecast horizons. Additionally, we analyse the forecasting performance of the heterogeneous autoregressive ($HAR$) model which imposes restrictions on high-order $AR$ models. We find that the structure imposed by the $HAR$ model produces better long horizon forecasts than $AR$ models of the same order, at the price of inferior short horizon forecasts in some cases. Our results have implications for, among others, Climate Econometrics and Financial Econometrics models dealing with long memory series at different forecast horizons. We show in an example that while a short memory autoregressive moving average $(ARMA)$ model gives the best performance when forecasting the Realized Variance of the S\&P 500 up to a month ahead, the $ARFIMA$ model gives the best performance for longer forecast horizons. |
| Date: | 2017–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1712.08057&r=ets |
| By: | Hepsag, Aycan |
| Abstract: | This paper proposes new three unit root testing procedures which consider jointly for two structural breaks and nonlinear adjustment. The structural breaks are modelled by means of two logistic smooth transition functions and nonlinear adjustment is modelled by means of ESTAR models. The Monte Carlo experiments display that the empirical sizes of tests are quite close to the nominal ones and in terms of power; the three new unit root tests are superior to the alternative tests. An empirical application involving crude oil underlines the usefulness of the new unit root tests. |
| Keywords: | Smooth breaks, nonlinearity, unit root, ESTAR |
| JEL: | C12 C22 |
| Date: | 2017–12–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:83353&r=ets |
| By: | Diebold, Francis X.; Schorfheide, Frank; Shin, Minchul |
| Abstract: | Recent work has analyzed the forecasting performance of standard dynamic stochastic general equilibrium (DSGE) models, but little attention has been given to DSGE models that incorporate nonlinearities in exogenous driving processes. Against that background, we explore whether incorporating stochastic volatility improves DSGE forecasts (point, interval, and density). We examine real-time forecast accuracy for key macroeconomic variables including output growth, inflation, and the policy rate. We find that incorporating stochastic volatility in DSGE models of macroeconomic fundamentals markedly improves their density forecasts, just as incorporating stochastic volatility in models of financial asset returns improves their density forecasts. |
| Keywords: | Dynamic Stochastic General Equilibrium Model,Prediction,Stochastic Volatility |
| JEL: | E17 E27 E37 E47 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cfswop:577&r=ets |