226 research outputs found
Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes with infinite variance
We discuss joint temporal and contemporaneous aggregation of independent
copies of random-coefficient AR(1) process driven by i.i.d. innovations in the
domain of normal attraction of an -stable distribution, , as both and the time scale tend to infinity, possibly at a
different rate. Assuming that the tail distribution function of the random
autoregressive coefficient regularly varies at the unit root with exponent
, we show that, for , the joint aggregate
displays a variety of stable and non-stable limit behaviors with stability
index depending on , and the mutual increase rate of and
. The paper extends the results of Pilipauskait\.e and Surgailis (2014) from
to
M-estimation of linear models with dependent errors
We study asymptotic properties of -estimates of regression parameters in
linear models in which errors are dependent. Weak and strong Bahadur
representations of the -estimates are derived and a central limit theorem is
established. The results are applied to linear models with errors being
short-range dependent linear processes, heavy-tailed linear processes and some
widely used nonlinear time series.Comment: Published at http://dx.doi.org/10.1214/009053606000001406 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Information Ranking and Power Laws on Trees
We study the situations when the solution to a weighted stochastic recursion
has a power law tail. To this end, we develop two complementary approaches, the
first one extends Goldie's (1991) implicit renewal theorem to cover recursions
on trees; and the second one is based on a direct sample path large deviations
analysis of weighted recursive random sums. We believe that these methods may
be of independent interest in the analysis of more general weighted branching
processes as well as in the analysis of algorithms
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Quantile autoregressive distributed lag model with an application to house price returns
This paper studies quantile regression in an autoregressive dynamic framework with exogenous stationary covariates. Hence, we develop a quantile autoregressive distributed lag model (QADL). We show that these estimators are consistent and asymptotically normal. Inference based on Wald and Kolmogorov-Smirnov tests for general linear restrictions is proposed. An extensive Monte Carlo simulation is conducted to evaluate the properties of the estimators. We demonstrate the potential of the QADL model with an application to house price returns in the United Kingdom. The results show that house price returns present a heterogeneous autoregressive behavior across the quantiles. The real GDP growth and interest rates also have an asymmetric impact on house prices variations
Testing for Changes in Kendall's Tau
For a bivariate time series we want to detect
whether the correlation between and stays constant for all . We propose a nonparametric change-point test statistic based on
Kendall's tau and derive its asymptotic distribution under the null hypothesis
of no change by means a new U-statistic invariance principle for dependent
processes. The asymptotic distribution depends on the long run variance of
Kendall's tau, for which we propose an estimator and show its consistency.
Furthermore, assuming a single change-point, we show that the location of the
change-point is consistently estimated. Kendall's tau possesses a high
efficiency at the normal distribution, as compared to the normal maximum
likelihood estimator, Pearson's moment correlation coefficient. Contrary to
Pearson's correlation coefficient, it has excellent robustness properties and
shows no loss in efficiency at heavy-tailed distributions. We assume the data
to be stationary and P-near epoch dependent on an
absolutely regular process. The P-near epoch dependence condition constitutes a
generalization of the usually considered -near epoch dependence, , that does not require the existence of any moments. It is therefore very
well suited for our objective to efficiently detect changes in correlation for
arbitrarily heavy-tailed data
Subsampling confidence intervals for the autoregressive root
In this paper, we propose a new method for constructing confidence intervals for the autoregressive parameter of an AR(I) model. Our method works when the parameter equals one, is close to one, or is far away from one and is therefore more general than previous procedures. The crux of the method is to recompute the OLS t-statistics for the AR(I) parameter on smaller blocks of the observed sequence, according to the subsampling approach of Politis and Romano (1994). Some simulation studies show good finite sample properties of our intervals
HAR Inference: Recommendations for Practice
The classic papers by Newey and West (1987) and Andrews (1991) spurred a large body of work on how to improve heteroscedasticity- and autocorrelation-robust (HAR) inference in time series regression. This literature finds that using a larger-than-usual truncation parameter to estimate the long-run variance, combined with Kiefer-Vogelsang (2002, 2005) fixed-b critical values, can substantially reduce size distortions, at only a modest cost in (size-adjusted) power. Empirical practice, however, has not kept up. This article therefore draws on the post-Newey West/Andrews literature to make concrete recommendations for HAR inference. We derive truncation parameter rules that choose a point on the size-power tradeoff to minimize a loss function. If Newey-West tests are used, we recommend the truncation parameter rule S = 1.3T 1/2 and (nonstandard) fixed-b critical values. For tests of a single restriction, we find advantages to using the equal-weighted cosine (EWC) test, where the long run variance is estimated by projections onto Type II cosines, using ν = 0.4T 2/3 cosine terms; for this test, fixed-b critical values are, conveniently, tν or F. We assess these rules using first an ARMA/GARCH Monte Carlo design, then a dynamic factor model design estimated using a 207 quarterly U.S. macroeconomic time series
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