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on Econometric Time Series |
| By: | Jean-David Fermanian; Hassan Malongo |
| Abstract: | We provide conditions for the existence and the unicity of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie's (1988) criteria, after having rewritten DCC-GARCH models as nonlinear Markov chains. Moreover, we study the existence of their finite moments. |
| Date: | 2014–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1405.6905&r=ets |
| By: | Sergey A. Kamenshchikov |
| Abstract: | The goal of this investigation was to overcome limitations of a persistency analysis, introduced by Benoit Mandelbrot for fractal Brownian processes: nondifferentiability, Brownian nature of process and a linear memory measure. We have extended a sense of a Hurst factor by consideration of a phase diffusion power law. It was shown that pre-catastrophic stabilization as an indicator of bifurcation leads to a new minimum of momentary phase diffusion, while bifurcation causes an increase of the momentary transport. Basic conclusions of a diffusive analysis have been compared to the Lyapunov stability model. An extended Reynolds parameter has been introduces as an indicator of phase transition. A combination of diffusive and Reynolds analysis has been applied for a description of a time series of Dow Jones Industrial weekly prices for a world financial crisis of 2007-2009. Diffusive and Reynolds parameters shown an extreme values in October 2008 when a mortgage crisis was fixed. A combined R/D description allowed distinguishing of short-memory and long memory shifts of a market evolution. It was stated that a systematic large scale failure of a financial system has begun in October 2008 and started fading in February 2009. |
| Date: | 2014–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1405.6990&r=ets |
| By: | Sun, Yixiao |
| Abstract: | New asymptotic approximations are established for the Wald and t statistics in the presence of unknown but strong autocorrelation. The asymptotic theory extends the usual fixed-smoothing asymptotics under weak dependence to allow for near unit root and weak unit root processes. As the locality parameter that characterizes the neighborhood of the autoregressive root increases from zero to infinity, the new fixed-smoothing asymptotic distribution changes smoothly from the unit-root fixed-smoothing asymptotics to the usual fixed-smoothing asymptotics under weak dependence. Simulations show that the new approximation is more accurate than the usual fixed-smoothing approximation. |
| Keywords: | Social and Behavioral Sciences, Autocorrelation Robust Test, Fixed-smoothing Asymptotics, Local-to-Unity, Strong Autocorrelation, Weak Unit Root |
| Date: | 2014–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsdec:qt8479f4s2&r=ets |
| By: | Ghysels, Eric; Miller, J. Isaac |
| Abstract: | We examine the effects of mixed sampling frequencies and temporal aggregation on standard tests for cointegration. We find that the effects of aggregation on the size of the tests may be severe. Matching sampling schemes of all series generally reduces size, and the nominal size is obtained when all series are skip sampled in the same way. When matching all schemes is not feasible, but when some high-frequency data are available, we show how to use mixed-frequency models to improve the size distortion of the tests. We test stock prices and dividends for cointegration as an empirical demonstration. |
| Keywords: | cointegration; mixed sampling frequencies; residual-based cointegration test; temporal aggregation; trace test |
| JEL: | C12 C32 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9654&r=ets |
| By: | Ghysels, Eric; Hill, Jonathan B.; Motegi, Kaiji |
| Abstract: | It is well known that temporal aggregation has adverse effects on Granger causality tests. Time series are often sampled at different frequencies. This is typically ignored, and data are merely aggregated to the common lowest frequency. We develop a set of Granger causality tests that explicitly take advantage of data sampled at different frequencies. We show that taking advantage of mixed frequency data allows us to better recover causal relationships when compared to the conventional common low frequency approach. We also show that the mixed frequency causality tests have higher local asymptotic power as well as more power in finite samples compared to conventional tests. |
| Keywords: | Granger causality; mixed data sampling (MIDAS); temporal aggression; vector autoregression (VAR) |
| JEL: | C12 C32 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9655&r=ets |
| By: | Jarocinski, Marek; Mackowiak, Bartosz Adam |
| Abstract: | A researcher is interested in a set of variables that he wants to model with a vector autoregression and he has a dataset with more variables. Which variables from the dataset to include in the VAR, in addition to the variables of interest? This question arises in many applications of VARs, in prediction and impulse response analysis. We develop a Bayesian methodology to answer this question. We rely on the idea of Granger-causal-priority, related to the well-known concept of Granger-noncausality. The methodology is simple to use, because we provide closed-form expressions for the relevant posterior probabilities. Applying the methodology to the case when the variables of interest are output, the price level, and the short-term interest rate, we find remarkably similar results for the United States and the euro area. |
| Keywords: | Bayesian model choice; Granger-causal-priority; Granger-noncausality; Structural vector autoregression; Vector autoregression |
| JEL: | C32 C52 E32 |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9686&r=ets |
| By: | Foroni, Claudia; Guérin, Pierre; Marcellino, Massimiliano |
| Abstract: | This paper introduces regime switching parameters in the Mixed-Frequency VAR model. We first discuss estimation and inference for Markov-switching Mixed-Frequency VAR (MSMF-VAR) models. Next, we assess the finite sample performance of the technique in Monte-Carlo experiments. Finally, the MSMF-VAR model is applied to predict GDP growth and business cycle turning points in the euro area. Its performance is compared with that of a number of competing models, including linear and regime switching mixed data sampling (MIDAS) models. The results suggest that MSMF-VAR models are particularly useful to estimate the status of economic activity. |
| Keywords: | Fore-; Markov-switching; MIDAS; Mixed-frequency VAR; Nowcasting |
| JEL: | C53 E32 E37 |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9815&r=ets |
| By: | Inoue, Atsushi; Kilian, Lutz |
| Abstract: | Many users of structural VAR models are primarily interested in learning about the shape of structural impulse response functions. This requires joint inference about sets of structural impulse responses, allowing for dependencies across time as well as across response functions. Such joint inference is complicated by the fact that the joint distribution of structural impulse response becomes degenerate when the number of structural impulse responses of interest exceeds the number of model parameters, as is often the case in applied work. This degeneracy may be overcome by transforming the estimator appropriately. We show that the joint Wald test is invariant to this transformation and converges to a nonstandard distribution, which can be approximated by the bootstrap, allowing the construction of asymptotically valid joint confidence sets for any subset of structural impulse responses, regardless of whether the joint distribution of the structural impulse responses is degenerate or not. We demonstrate by simulation the coverage accuracy of these sets in finite samples under realistic conditions. We make the case for representing these joint confidence sets in the form of "shotgun plots" rather than joint confidence bands for impulse response functions. Several empirical examples demonstrate that this approach not only conveys the same information as confidence bands about the statistical significance of response functions, but provides economically relevant additional information about the shape of response functions that is lost when reducing the joint confidence set to two-dimensional bands. |
| Keywords: | Bootstrap; Confidence regions; Degenerate limiting distribution; Impulse response shapes; Joint inference; Shotgun plots |
| JEL: | C32 C52 C53 |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9892&r=ets |
| By: | Banbura, Marta; Giannone, Domenico; Lenza, Michele |
| Abstract: | This paper describes an algorithm to compute the distribution of conditional forecasts, i.e. projections of a set of variables of interest on future paths of some other variables, in dynamic systems. The algorithm is based on Kalman filtering methods and is computationally viable for large vector autoregressions (VAR) and dynamic factor models (DFM). For a quarterly data set of 26 euro area macroeconomic and financial indicators, we show that both approaches deliver similar forecasts and scenario assessments. In addition, conditional forecasts shed light on the stability of the dynamic relationships in the euro area during the recent episodes of financial turmoil and indicate that only a small number of sources drive the bulk of the fluctuations in the euro area economy. |
| Keywords: | Bayesian Shrinkage; Conditional Forecast; Dynamic Factor Model; Large Cross-Sections; Vector Autoregression |
| JEL: | C11 C13 C33 C53 |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9931&r=ets |
| By: | Guillermo Carlomagnol; Antoni Espasa |
| Abstract: | The objective of this paper is to model and forecast all the components of a macro orbusiness variable. Our contribution concerns cases with a large number (hundreds) ofcomponents where multivariate approaches are not feasible. We extend in several directions the pairwise approach originally proposed by Espasa and Mayo-Burgos(2013) and study its statistical properties. The pairwise approach consists on performing common features tests between the N(N-1)/2 pairs of series that exist in a group of N of them. Once this is done, groups of series that share common features can be formed. Next, all the components are forecast using single equation models that include the restrictions derived by the common features. In this paper we focus on discovering groups of components that share single common trends. The asymptotic properties of the procedure are studied analytically. Monte Carlo evidence on the small samples performance is provided and a small samples correction procedure designed. A comparison with a DFM alternative is also carried out, and results indicate that the pairwise approach dominates in many empirically relevant situations. A relevant advantage of the pairwise approach is that it does not need common features to be pervasive. A strategy for dealing with outliers and breaks in the context of the pairwise procedure is designed and its properties studied by Monte Carlo. Results indicate that the treatment of these observations may considerably improve the procedure's performance when series are 'contaminated'. |
| Keywords: | Common trends, Cointegration, Factor Models, Disaggregation, Forecast model selection, Forecast Combination, Outliers treatment |
| Date: | 2014–05 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws141309&r=ets |
| By: | Yiannis Karavias; Elias Tzavalis |
| Abstract: | We extend Breitung's (2000) large-T panel data unit root test to the case of fixed time dimension while still allowing for heteroscedastic and serially correlated error terms. The analytic local power function of the new test is derived assuming that only the cross section dimension of the panel grows large. It is found that if the errors are serially uncorrelated the test also has trivial power, but, if not, this is no longer the case. Monte Carlo experiments show that the suggested test is more powerful than its large-T, original version when the number of cross section units is moderate or large, regardless of the number of time series observations. |
| Keywords: | Panel unit root; local power function; serial correlation; incidental trends JEL classi?cation: C22, C23 |
| URL: | http://d.repec.org/n?u=RePEc:not:notgts:14/02&r=ets |
| By: | Cláudia Duarte |
| Abstract: | Focusing on the MI(xed) DA(ta) S(ampling) regressions for handling different sampling frequencies and asynchronous releases of information, alternative techniques for the autoregressive augmentation of these regressions are presented and discussed. For forecasting quarterly euro area GDP growth using a small set of selected indicators, the results obtained suggest that no specific kind of MIDAS regressions clearly dominates in terms of forecast accuracy. Nevertheless, alternatives to common-factor MIDAS regressions with autoregressive terms perform well and in some cases are the best performing regressions. |
| JEL: | C53 E37 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w201401&r=ets |