An Automated Approach Towards Sparse Single-Equation Cointegration Modelling

In this paper we propose the Single-equation Penalized Error Correction Selector (SPECS) as an automated estimation procedure for dynamic single-equation models with a large number of potentially (co)integrated variables. By extending the classical single-equation error correction model, SPECS enables the researcher to model large cointegrated datasets without necessitating any form of pre-testing for the order of integration or cointegrating rank. Under an asymptotic regime in which both the number of parameters and time series observations jointly diverge to infinity, we show that SPECS is able to consistently estimate an appropriate linear combination of the cointegrating vectors that may occur in the underlying DGP. In addition, SPECS is shown to enable the correct recovery of sparsity patterns in the parameter space and to posses the same limiting distribution as the OLS oracle procedure. A simulation study shows strong selective capabilities, as well as superior predictive performance in the context of nowcasting compared to high-dimensional models that ignore cointegration. An empirical application to nowcasting Dutch unemployment rates using Google Trends confirms the strong practical performance of our procedure

Granger Causality Testing in High-Dimensional VARs: a Post-Double-Selection Procedure

We develop an LM test for Granger causality in high-dimensional VAR models based on penalized least squares estimations. To obtain a test retaining the appropriate size after the variable selection done by the lasso, we propose a post-double-selection procedure to partial out effects of nuisance variables and establish its uniform asymptotic validity. We conduct an extensive set of Monte-Carlo simulations that show our tests perform well under different data generating processes, even without sparsity. We apply our testing procedure to find networks of volatility spillovers and we find evidence that causal relationships become clearer in high-dimensional compared to standard low-dimensional VARs

A Residual Bootstrap for Conditional Value-at-Risk

This paper proposes a fixed-design residual bootstrap method for the two-step estimator of Francq and Zako\"ian (2015) associated with the conditional Value-at-Risk. The bootstrap's consistency is proven for a general class of volatility models and intervals are constructed for the conditional Value-at-Risk. A simulation study reveals that the equal-tailed percentile bootstrap interval tends to fall short of its nominal value. In contrast, the reversed-tails bootstrap interval yields accurate coverage. We also compare the theoretically analyzed fixed-design bootstrap with the recursive-design bootstrap. It turns out that the fixed-design bootstrap performs equally well in terms of average coverage, yet leads on average to shorter intervals in smaller samples. An empirical application illustrates the interval estimation

Detrending Bootstrap Unit Root Tests

The role of detrending in bootstrap unit root tests is investigated. When bootstrapping, detrending must not only be done for the construction of the test statistic, but also in the first step of the bootstrap algorithm. It is argued that the two points should be treated separately. Asymptotic validity of sieve bootstrap ADF unit root tests is shown for test statistics based on full sample and recursive OLS and GLS detrending. It is also shown that the detrending method in the first step of the bootstrap may differ from the one used in the construction of the test statistic. A simulation study is conducted to analyze the effects of detrending on finite sample performance of the bootstrap test. It is found that full sample detrending should be preferred in the first step of the bootstrap algorithm and that the decision about the detrending method used to obtain the test statistic should be based on the power properties of the corresponding asymptotic tests.econometrics;

Bootstrap union tests for unit roots in the presence of nonstationary volatility

We provide a joint treatment of three major issues that surround testing for a unit root in practice: uncertainty as to whether or not a linear deterministic trend is present in the data, uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not, and the possible presence of nonstationary volatility in the data. Harvey, Leybourne and Taylor (2010, Journal of Econometrics, forthcoming) propose decision rules based on a four-way union of rejections of QD and OLS detrended tests, both with and without allowing for a linear trend, to deal with the first two problems. However, in the presence of nonstationary volatility these test statistics have limit distributions which depend on the form of the volatility process, making tests based on the standard asymptotic critical values invalid. We construct bootstrap versions of the four-way union of rejections test, which, by employing the wild bootstrap, are shown to be asymptotically valid in the presence of nonstationary volatility. These bootstrap union tests therefore allow for a joint treatment of all three of the aforementioned problems.Unit root; local trend; initial condition; asymptotic power; union of rejections decision rule; nonstationary volatility; wild bootstrap

On the Applicability of the Sieve Bootstrap in Time series Panels

In this paper we investigate the validity of the univariate autoregressive sieve bootstrap appliedto time series panels characterized by general forms of cross-sectional dependence, including butnot restricted to cointegration. Using the final equations approach we show that while it ispossible to write such a panel as a collection of infinite order autoregressive equations, theinnovations of these equations are not vector white noise. This causes the univariateautoregressive sieve bootstrap to be invalid in such panels. We illustrate this result with asmall numerical example using a simple bivariate system for which the sieve bootstrap is invalid,and show that the extent of the invalidity depends on the value of specific parameters. We alsoshow that Monte Carlo simulations in small samples can be misleading about the validity of theunivariate autoregressive sieve bootstrap. The results in this paper serve as a warning about thepractical use of the autoregressive sieve bootstrap in panels where cross-sectional dependence ofgeneral from may be present.econometrics;

Autoregressive Wild Bootstrap Inference for Nonparametric Trends

In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in a simulation study. We use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the Swiss Alps, where the method can easily deal with the many missing observations due to adverse weather conditions