Econometric Time Series
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Econometric Time Series2014-08-16Yong YinInference in VARs with Conditional Heteroskedasticity of Unknown Form
http://d.repec.org/n?u=RePEc:knz:dpteco:1413&r=ets
We derive a framework for asymptotically valid inference in stable vector autoregressive (VAR) models with conditional heteroskedasticity of unknown form. We prove a joint central limit theorem for the VAR slope parameter and innovation covariance parameter estimators and address bootstrap inference as well. Our results are important for correct inference on VAR statistics that depend both on the VAR slope and the variance parameters as e.g. in structural impulse response functions (IRFs). We also show that wild and pairwise bootstrap schemes fail in the presence of conditional heteroskedasticity if inference on (functions) of the unconditional variance parameters is of interest because they do not correctly replicate the relevant fourth moments' structure of the error terms. In contrast, the residual-based moving block bootstrap results in asymptotically valid inference. We illustrate the practical implications of our theoretical results by providing simulation evidence on the finite sample properties of different inference methods for IRFs. Our results point out that estimation uncertainty may increase dramatically in the presence of conditional heteroskedasticity. Moreover, most inference methods are likely to understate the true estimation uncertainty substantially in finite samples.Ralf Brüggemann, Carsten Jentsch, Carsten Trenkler2014-08-04VAR, Conditional heteroskedasticity, Residual-based moving block bootstrap, Pairwise bootstrap, Wild bootstrapUnit root tests for dependent and heterogeneous micropanels
http://d.repec.org/n?u=RePEc:sgo:wpaper:1404&r=ets
This paper proposes a panel unit root test for micropanels with short time dimension (T) and large cross section (N). There are several distinctive features of this test. First, the test is based on a panel AR(1) model, which allows for cross-sectional dependency, which is introduced by the initial condition's assumption of a factor structure. Second, the test employs the panel AR(1) model with heterogeneous AR(1) coefficients. Third, the test does not use the AR(1) coefficient estimator. The effectiveness of the test rests on the fact that the initial condition has permanent effects on the trajectory of a time series in the presence of a unit root. To measure the effects of the initial condition, this paper employs cross-sectional regression using the first time series observations as a regressor and the last as a dependent variable. If there is a unit root in every individual time series, the coefficient of the regressor is equal to one. The t-ratio for the coefficient is this paper's test statistic and has a standard normal distribution in the limit. The t-ratio is based on the instrumental variables estimator that uses a reshuffled regressor as an instrument. The test proposed in this paper makes it possible to test for a unit root even at T=2 as long as N is large. Simulation results show that the test has reasonable empirical size and power. The test is applied to college graduates' monthly real wage in South Korea. The number of time series observations for this data is only two. The test rejects the null hypothesis of a unit root.In Choi2014Unit root, panel data, factor model, internal instrument, earnings dynamics