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on Econometric Time Series |
| By: | Güneş Kamber; James Morley; Benjamin Wong |
| Abstract: | The Beveridge-Nelson (BN) trend-cycle decomposition based on autoregressive forecasting models of U.S. quarterly real GDP growth produces estimates of the output gap that are strongly at odds with widely-held beliefs about the amplitude, persistence, and even sign of transitory movements in economic activity. These antithetical attributes are related to the autoregressive coefficient estimates implying a very high signal-to-noise ratio in terms of the variance of trend shocks as a fraction of the overall quarterly forecast error variance. When we impose a lower signal-to-noise ratio, the resulting BN decomposition, which we label the "BN filter", produces a more intuitive estimate of the output gap that is large in amplitude, highly persistent, and typically positive in expansions and negative in recessions. Real-time estimates from the BN filter are also reliable in the sense that they are subject to smaller revisions and predict future output growth and inflation better than for other methods of trend-cycle decomposition that also impose a low signal-to-noise ratio, including deterministic detrending, the Hodrick-Prescott filter, and the bandpass filter. |
| Keywords: | Beveridge-Nelson decomposition, output gap, signal-to-noise ratio |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:bis:biswps:584&r=ets |
| By: | Giovanni Angelini (Università di Bologna); Giuseppe Cavaliere (Università di Bologna); Luca Fanelli (Università di Bologna) |
| Abstract: | This paper explores the potential of bootstrap methods in the empirical evalu- ation of dynamic stochastic general equilibrium (DSGE) models and, more generally, in linear rational expectations models featuring unobservable (latent) components. We consider two dimensions. First, we provide mild regularity conditions that suffice for the bootstrap Quasi- Maximum Likelihood (QML) estimator of the structural parameters to mimic the asymptotic distribution of the QML estimator. Consistency of the bootstrap allows to keep the probability of false rejections of the cross-equation restrictions under control. Second, we show that the realizations of the bootstrap estimator of the structural parameters can be constructively used to build novel, computationally straightforward tests for model misspecification, including the case of weak identification. In particular, we show that under strong identification and boot- strap consistency, a test statistic based on a set of realizations of the bootstrap QML estimator approximates the Gaussian distribution. Instead, when the regularity conditions for inference do not hold as e.g. it happens when (part of) the structural parameters are weakly identified, the above result is no longer valid. Therefore, we can evaluate how close or distant is the esti- mated model from the case of strong identification. Our Monte Carlo experimentations suggest that the bootstrap plays an important role along both dimensions and represents a promising evaluation tool of the cross-equation restrictions and, under certain conditions, of the strength of identification. An empirical illustration based on a small-scale DSGE model estimated on U.S. quarterly observations shows the practical usefulness of our approach. |
| Keywords: | Bootstrap, Cross-equation restrictions, DSGE, QLR test, State space model, Weak identification. |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:bot:quadip:wpaper:133&r=ets |
| By: | Asai, M.; McAleer, M.J. |
| Abstract: | The paper derives a Multivariate Asymmetric Long Memory conditional volatility model with Exogenous Variables (X), or the MALMX model, with dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. The underlying vector random coefficient autoregressive process, which has well established regularity conditions and associated asymptotic properties, is discussed, and a simple explanation is given as to why only the diagonal BEKK model, and not the Hadamard, triangular or full BEKK models, has regularity conditions and asymptotic properties. Various special cases, including the diagonal BEKK model of Baba et al. (1985) and Engle and Kroner (1995), VARMA- GARCH model of Ling and McAleer (2003), and VARMA-AGARCH model of McAleer et al. (2009), are discussed. There does not seem to have been a derivation of a univariate conditional volatility model with exogenous variables (X) that has dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. Therefore, the derivation of a multivariate conditional volatility model with exogenous variables (X) that has regularity conditions and asymptotic theory would seem to be a significant extension of the existing literature. |
| Keywords: | Multivariate conditional volatility, Vector random coefficient autoregressive process, Asymmetry, Long memory, Exogenous variables, Dynamic conditional correlations, Regularity conditions, Asymptotic properties |
| JEL: | C22 C52 C58 G32 |
| Date: | 2016–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureir:93333&r=ets |
| By: | Franses, Ph.H.B.F. |
| Abstract: | A MIDAS regression involves a dependent variable observed at a low frequency and independent variables observed at a higher frequency. This paper relates a true high frequency data generating process, where also the dependent variable is observed (hypothetically) at the high frequency, with a MIDAS regression. It is shown that a correctly specified MIDAS regression usually includes lagged dependent variables, a substantial number of explanatory variables (observable at the low frequency) and a moving average term. Next, the parameters of the explanatory variables unlikely obey certain convenient patterns, and hence imposing such restrictions in practice is not recommended. |
| Keywords: | high frequency, low frequency, MIDAS regression |
| JEL: | C32 |
| Date: | 2016–08–24 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureir:93331&r=ets |
| By: | Asai, M.; McAleer, M.J. |
| Abstract: | The paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive asymptotic theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated asymptotic properties. |
| Keywords: | Multivariate conditional volatility, Vector random coefficient autoregressive process, Asymmetry, Long memory, Dynamic conditional correlations, Regularity conditions, Asymptotic properties |
| JEL: | C13 C32 C58 |
| Date: | 2016–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureir:93334&r=ets |
| By: | Chambers, Marcus J; Kyriacou, Maria |
| Abstract: | This paper considers the specification and performance of jackknife estimators of the autoregressive coefficient in a model with a near-unit root. The limit distributions of sub-sample estimators that are used in the construction of the jackknife estimator are derived and the joint moment generating function (MGF) of two components of these distributions is obtained and its properties are explored. The MGF can be used to derive the weights for an optimal jackknife estimator that removes fully the first-order finite sample bias from the estimator. The resulting jackknife estimator is shown to perform well in finite samples and, with a suitable choice of the number of sub-samples, is shown to reduce the overall finite sample root mean squared error as well as bias. However, the optimal jackknife weights rely on knowledge of the near-unit root parameter, which is typically unknown in practice, and so an alternative, feasible, jackknife estimator is pro- posed which achieves the intended bias reduction but does not rely on knowledge of this parameter. This feasible jackknife estimator is also capable of substantial bias and root mean squared error reductions in finite samples across a range of values of the near-unit root parameter and across different sample sizes. |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:esx:essedp:17623&r=ets |
| By: | Antolin-Diaz, Juan; Rubio-Ramírez, Juan Francisco |
| Abstract: | This paper identifies structural vector autoregressions using narrative sign restrictions. Narrative sign restrictions constrain the structural shocks and the historical decomposition of the data around key historical events, ensuring that they agree with the established account of these episodes. Using models of the oil market and monetary policy, we show that narrative sign restrictions can be highly informative. In particular we highlight that adding a small number of narrative sign restrictions, or sometimes even a single one, dramatically sharpens and even changes the inference of SVARs originally identified via the established practice of placing sign restrictions only on the impulse response functions. We see our approach as combining the appeal of narrative methods with the desire for basing inference on a few uncontroversial restrictions that popularized the use of sign restrictions. |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11517&r=ets |
| By: | António Rua |
| Abstract: | In an increasingly data rich environment, factor models have become the workhorse approach for modelling and forecasting purposes. However, factors are non-observable and have to be estimated. In particular, the space spanned by the unknown factors is typically estimated via principal components. Herein, it is proposed a novel procedure to estimate the factor space resorting to a wavelet based multiscale principal component analysis. Through a Monte Carlo simulation study, it is shown that such an approach allows to improve both factor model estimation and forecasting performance. In the empirical application, one illustrates its usefulness for forecasting GDP growth and inflation in the United States. |
| JEL: | C22 C40 C53 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w201612&r=ets |