We propose a Cramer-von Mises type test for diagnostic checking of weak vector autoregressive models, in which the errors are assumed to be uncorrelated but not necessarily independent. The test statistic is constructed from the integrated squared distance between the sample periodogram of the residuals and a constant spectrum. Unlike time domain portmanteau tests, which rely on the first residual autocorrelations, the proposed spectral test is sensitive to correlations at all lags. We study the asymptotic behavior of the test statistic and show that, due to the dependent structure of the errors and the effect of parameter estimation, the limiting distribution is not asymptotically pivotal. To address this issue, we employ a blockwise random weighting bootstrap to approximate critical values and establish its asymptotic validity. Finite sample performance is assessed through extensive Monte Carlo simulations and illustrated with a real data application.
We consider the problem of nonparametric testing for rough volatility, using high-frequency data with a fixed time span, in a setting where the price is purely discontinuous. More specifically, we analyze the asymptotic properties of a test we developed in previous work in a pure-jump setting. We show that the asymptotic behavior of the test remains unchanged, regardless of whether the underlying price contains a diffusion or is of purely discontinuous type. This adaptive nature of the test is very convenient from an empirical point of view as it implies that no pretest for the underlying features of the price process, that is, whether it contains a diffusion, is needed when testing for rough volatility. A Monte Carlo study shows good finite sample behavior of the test in purely discontinuous price settings.
This paper studies -penalized estimation for location models , where is defined by a possibly non-Markovian recursion and is a martingale difference sequence with possibly time-varying conditional variance. In such settings, standard LS/QML criteria are typically non-convex. A two-step plug-in scheme is considered: a first-step estimator (e.g., WLS or QMLE) is assumed to be strongly consistent, its fitted recursions are frozen, and a weighted least-squares criterion with an penalty is minimized in a second step. The resulting objective is convex and compatible with standard LASSO algorithms. Under mild regularity conditions, the second-step estimator is strongly consistent as soon as the penalties attached to the nonzero coordinates of the true parameter vanish. For penalties of order , its asymptotic distribution is derived, and adaptive penalties yield selection consistency and an oracle property. The second-step estimator is unconstrained and, when combined with an unconstrained first-step estimator, it yields a standard Gaussian limit with a tractable covariance matrix, in contrast with the non-standard limits that typically arise for QMLE when some components of the true parameter are zero. The general results are specialized to several time-series models and illustrated by Monte Carlo experiments and a real-data application to interest rates.
This note develops a rigorous analytical framework for computing exact MA() coefficients of mixed causal-noncausal autoregressive MAR processes. While analytical solutions exist only for the MAR specification in the existing literature (Gouri & eacute;roux and Jasiak, 2016), general MAR processes are typically handled through recursive approximation algorithms that suffer from numerical approximations. Using complex contour integration and the residue theorem, we derive explicit closed-form expressions valid for arbitrary orders . The derived expressions enable direct simulation algorithms, eliminating the recursive approximation bias while retaining only the standard truncation error inherent to any finite-order approximation, and facilitate implementation of forecasting methodologies. Numerical comparisons with existing recursive methods demonstrate improvements in accuracy, and an experiment with -stable innovations illustrate the empirical relevance of our results.
