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"Giraitis, Liudas"
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ROBUST TESTS FOR WHITE NOISE AND CROSS-CORRELATION
Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung–Box tests can be significantly distorted. This paper adapts standard correlogram and portmanteau tests to accommodate hidden dependence and nonstationarities involving heteroskedasticity, thereby uncoupling these tests from limiting assumptions that reduce their applicability in empirical work. To enhance the Ljung–Box test for non-i.i.d. data, a new cumulative test is introduced. Asymptotic size of these tests is unaffected by hidden dependence and heteroskedasticity in the series. Related extensions are provided for testing cross-correlation at various lags in bivariate time series. Tests for the i.i.d. property of a time series are also developed. An extensive Monte Carlo study confirms good performance in both size and power for the new tests. Applications to real data reveal that standard tests frequently produce spurious evidence of serial correlation.
Journal Article
ESTIMATION OF TIME-VARYING COVARIANCE MATRICES FOR LARGE DATASETS
Time variation is a fundamental problem in statistical and econometric analysis of macroeconomic and financial data. Recently, there has been considerable focus on developing econometric modelling that enables stochastic structural change in model parameters and on model estimation by Bayesian or nonparametric kernel methods. In the context of the estimation of covariance matrices of large dimensional panels, such data requires taking into account time variation, possible dependence and heavy-tailed distributions. In this paper, we introduce a nonparametric version of regularization techniques for sparse large covariance matrices, developed by Bickel and Levina (2008) and others. We focus on the robustness of such a procedure to time variation, dependence and heavy-tailedness of distributions. The paper includes a set of results on Bernstein type inequalities for dependent unbounded variables which are expected to be applicable in econometric analysis beyond estimation of large covariance matrices. We discuss the utility of the robust thresholding method, comparing it with other estimators in simulations and an empirical application on the design of minimum variance portfolios.
Journal Article
Estimating the Dynamics and Persistence of Financial Networks, with an Application to the Sterling Money Market
We propose a novel methodology for dynamic econometric modelling of large financial networks subject to persistence, structural changes and sparsity. We estimate bivariate dynamic Tobit-type models for each pair of banks, allowing for deterministic or stochastic time-varying parameters, and then aggregate across all bank pairs. To tackle the high dimensionality of the model, we construct a few lagged variables that efficiently summarize the position of a bank pair in the network. We propose a simple and computationally easy kernel-based local maximum likelihood estimator of the time-varying parameters of the model and establish its asymptotic properties. We then apply the model to the time series of daily overnight money market network in the UK 2003–2012. The results show that our model can successfully accommodate the numerous structural breaks arising from changes to the monetary framework and captures well the dynamics of the interbank lending relationships in this period.
Journal Article
STATIONARY INTEGRATED ARCH(∞) AND AR(∞) PROCESSES WITH FINITE VARIANCE
We prove the long standing conjecture of Ding and Granger (1996) about the existence of a stationary Long Memory ARCH model with finite fourth moment. This result follows from the necessary and sufficient conditions for the existence of covariance stationary integrated AR(∞), ARCH(∞), and FIGARCH models obtained in the present article. We also prove that such processes always have long memory.
Journal Article
ASYMPTOTIC NORMALITY FOR WEIGHTED SUMS OF LINEAR PROCESSES
We establish asymptotic normality of weighted sums of linear processes with general triangular array weights and when the innovations in the linear process are martingale differences. The results are obtained under minimal conditions on the weights and innovations. We also obtain weak convergence of weighted partial sum processes. The results are applicable to linear processes that have short or long memory or exhibit seasonal long memory behavior. In particular, they are applicable to GARCH and ARCH(∞) models and to their squares. They are also useful in deriving asymptotic normality of kernel-type estimators of a nonparametric regression function with short or long memory moving average errors.
Journal Article
On asymptotic distributions of weighted sums of periodograms
We establish asymptotic normality of weighted sums of periodograms of a stationary linear process where weights depend on the sample size. Such sums appear in numerous statistical applications and can be regarded as a discretized versions of quadratic forms involving integrals of weighted periodograms. Conditions for asymptotic normality of these weighted sums are simple, minimal, and resemble Lindeberg–Feller condition for weighted sums of independent and identically distributed random variables. Our results are applicable to a large class of short, long or negative memory processes. The proof is based on sharp bounds derived for Bartlett type approximation of these sums by the corresponding sums of weighted periodograms of independent and identically distributed random variables.
Journal Article
AGGREGATION OF THE RANDOM COEFFICIENT GLARCH(1,1) PROCESS
The paper discusses contemporaneous aggregation of the Linear ARCH (LARCH) model as defined in (1), which was introduced in Robinson (1991) and studied in Giraitis, Robinson, and Surgailis (2000) and other works. We show that the limiting aggregate of the (G)eneralized LARCH(1,1) process in (3)–(4) with random Beta distributed coefficient β exhibits long memory. In particular, we prove that squares of the limiting aggregated process have slowly decaying correlations and their partial sums converge to a self-similar process of a new type.
Journal Article
A TEST FOR STATIONARITY VERSUS TRENDS AND UNIT ROOTS FOR A WIDE CLASS OF DEPENDENT ERRORS
We suggest a rescaled variance type of test for the null hypothesis of
stationarity against deterministic and stochastic trends (unit roots). The
deterministic trend can be represented as a general function in time
(e.g., nonparametric, linear, or polynomial regression, abrupt changes in
the mean). Under the null, the asymptotic distribution of the test is
derived, and critical values are tabulated for a wide class of stationary
processes with short, long, or negative dependence structure. A simulation
study examines the performance of the test in terms of size and power. The
empirical performance of the test is illustrated using the S&P 500
data.The authors thank the editor, the
referees, and Karim Abadir for helpful comments and Alfredas
Račkauskas for drawing our attention to the criterion of Cremers
and Kadelka (1986). The first author's work
was supported by the ESRC grants R000238212 and R000239538. The last two
authors were supported by a cooperation agreement CNRS/LITHUANIA
(4714) and by a bilateral Lithuania-France research project
Gilibert.
Journal Article