arXiv subjects

Giuseppe Cavaliere

Publications and source records attributed to Giuseppe Cavaliere.

At least 19 recordsLinked to original sources

arXiv2026

Bootstrap inference in autoregressive duration models

This paper develops bootstrap inference for autoregressive conditional duration (ACD) models observed over a fixed calendar span, so that the number of durations is random. We study recursive schemes that either fix the calendar span or the realized event count. For the fixed-count bootstrap, we establish consistency when the duration tail index satisfies $\kappa\geq1$. When $0<\kappa<1$, classical consistency fails because the estimator has a mixed-normal limit, but the bootstrap reproduces its conditional Gaussian component. Consequently, basic percentile intervals remain first-order valid and bootstrap $t$-statistics are asymptotically standard normal. Monte Carlo experiments show accurate finite-sample inference across finite- and infinite-mean regimes and robustness to non-exponential innovations. An application to cryptocurrency ETF transaction durations finds strong persistence and illustrates the practical difference between fixed-count and random-count inference.

econ.EM↗

arXiv2026

Global factors for local shocks in a data-scarce environment: with an application to regional fiscal multipliers in Italy

We propose a novel econometric methodology for Structural Vector Autoregressions with external instruments (`proxy-SVARs' or `SVAR-IVs') in panel data characterized by strong cross-sectional dependence, dynamic heterogeneity, and limited availability of direct external instruments for the shocks of interest. For each unit, we specify a Factor-Augmented proxy-SVAR (`proxy-FA-SVAR') that incorporates factors summarizing cross-sectional information from the non-policy variables of the system. The effects of the policy shocks are then recovered indirectly by estimating unit-specific policy reaction functions through a Minimum Distance approach. Identification relies on global instruments for the non-policy shocks; that is, proxies common to all units in the panel, internally constructed from a separate SVAR estimated on factors for the policy and non-policy variables. These global instruments can be complemented with local (idiosyncratic) instruments constructed from auxiliary unit-level SVARs. Their joint use renders the proxy-FA-SVARs overidentified and therefore statistically testable. We illustrate the methodology by estimating government spending multipliers for Italian NUTS-2 regions using annual data. The global and local instruments for the regional output shocks are obtained from Blanchard-Perotti-type SVARs.

econ.EM↗

arXiv2026

Improved inference for nonparametric regression and regression-discontinuity designs

Nonparametric regression and regression-discontinuity designs suffer from smoothing bias that distorts conventional confidence intervals. Solutions based on robust bias correction (RBC) are now central to the economist's toolbox. In this paper, we establish a novel connection between RBC methods and bootstrap prepivoting. Revisiting RBC through the lens of bootstrapping allows us to develop a novel bias correction procedure which delivers improved nonparametric inference. The resulting confidence intervals are 17% shorter than the usual intervals employed in curve estimation and regression discontinuity designs, without compromising asymptotic coverage. This holds regardless of evaluation point location, bandwidth choice, or regressor and error distribution.

econ.EM↗

arXiv2025

Bootstrap Diagnostic Tests

Violation of the assumptions underlying classical (Gaussian) limit theory often yields unreliable statistical inference. This paper shows that the bootstrap can detect such violations by delivering simple and powerful diagnostic tests that (a) induce no pre-testing bias, (b) use the same critical values across applications, and (c) are consistent against deviations from asymptotic normality. The tests compare the conditional distribution of a bootstrap statistic with the Gaussian limit implied by valid specification and assess whether the resulting discrepancy is large enough to indicate failure of the asymptotic Gaussian approximation. The method is computationally straightforward and only requires a sample of i.i.d. draws of the bootstrap statistic. We derive sufficient conditions for the randomness in the data to mix with the randomness in the bootstrap repetitions in a way such that (a), (b) and (c) above hold. We demonstrate the practical relevance and broad applicability of bootstrap diagnostics by considering several scenarios where the asymptotic Gaussian approximation may fail, including weak instruments, non-stationarity, parameters on the boundary of the parameter space, infinite variance data and singular Jacobian in applications of the delta method. An illustration drawn from the empirical macroeconomic literature concludes.

econ.EM↗

arXiv2025

Uniform Critical Values for Likelihood Ratio Tests in Boundary Problems

Limit distributions of likelihood ratio statistics are well-known to be discontinuous in the presence of nuisance parameters at the boundary of the parameter space, which lead to size distortions when standard critical values are used for testing. In this paper, we propose a new and simple way of constructing critical values that yields uniformly correct asymptotic size, regardless of whether nuisance parameters are at, near or far from the boundary of the parameter space. Importantly, the proposed critical values are trivial to compute and at the same time provide powerful tests in most settings. In comparison to existing size-correction methods, the new approach exploits the monotonicity of the two components of the limiting distribution of the likelihood ratio statistic, in conjunction with rectangular confidence sets for the nuisance parameters, to gain computational tractability. Uniform validity is established for likelihood ratio tests based on the new critical values, and we provide illustrations of their construction in two key examples: (i) testing a coefficient of interest in the classical linear regression model with non-negativity constraints on control coefficients, and, (ii) testing for the presence of exogenous variables in autoregressive conditional heteroskedastic models (ARCH) with exogenous regressors. Simulations confirm that the tests have desirable size and power properties. A brief empirical illustration demonstrates the usefulness of our proposed test in relation to testing for spill-overs and ARCH effects.

econ.EM↗

arXiv2025

Beyond the Mean: Limit Theory and Tests for Infinite-Mean Autoregressive Conditional Durations

Integrated autoregressive conditional duration (ACD) models serve as natural counterparts to the well-known integrated GARCH models used for financial returns. However, despite their resemblance, asymptotic theory for ACD is challenging and also not complete, in particular for integrated ACD. Central challenges arise from the facts that (i) integrated ACD processes imply durations with infinite expectation, and (ii) even in the non-integrated case, conventional asymptotic approaches break down due to the randomness in the number of durations within a fixed observation period. Addressing these challenges, we provide here unified asymptotic theory for the (quasi-) maximum likelihood estimator for ACD models; a unified theory which includes integrated ACD models. Based on the new results, we also provide a novel framework for hypothesis testing in duration models, enabling inference on a key empirical question: whether durations possess a finite or infinite expectation. We apply our results to high-frequency cryptocurrency ETF trading data. Motivated by parameter estimates near the integrated ACD boundary, we assess whether durations between trades in these markets have finite expectation, an assumption often made implicitly in the literature on point process models. Our empirical findings indicate infinite-mean durations for all the five cryptocurrencies examined, with the integrated ACD hypothesis rejected -- against alternatives with tail index less than one -- for four out of the five cryptocurrencies considered.

econ.EM↗

arXiv2025

Factor Network Autoregressions

We propose a factor network autoregressive (FNAR) model for time series with complex network structures. The coefficients of the model reflect many different types of connections between economic agents ("multilayer network"), which are summarized into a smaller number of network matrices ("network factors") through a novel tensor-based principal component approach. We provide consistency and asymptotic normality results for the estimation of the factors, their loadings, and the coefficients of the FNAR, as the number of layers, nodes and time points diverges to infinity. Our approach combines two different dimension-reduction techniques and can be applied to high-dimensional datasets. Simulation results show the goodness of our estimators in finite samples. In an empirical application, we use the FNAR to investigate the cross-country interdependence of GDP growth rates based on a variety of international trade and financial linkages. The model provides a rich characterization of macroeconomic network effects as well as good forecasts of GDP growth rates.

econ.EM↗

arXiv2024

Parameters on the boundary in predictive regression

We consider bootstrap inference in predictive (or Granger-causality) regressions when the parameter of interest may lie on the boundary of the parameter space, here defined by means of a smooth inequality constraint. For instance, this situation occurs when the definition of the parameter space allows for the cases of either no predictability or sign-restricted predictability. We show that in this context constrained estimation gives rise to bootstrap statistics whose limit distribution is, in general, random, and thus distinct from the limit null distribution of the original statistics of interest. This is due to both (i) the possible location of the true parameter vector on the boundary of the parameter space, and (ii) the possible non-stationarity of the posited predicting (resp. Granger-causing) variable. We discuss a modification of the standard fixed-regressor wild bootstrap scheme where the bootstrap parameter space is shifted by a data-dependent function in order to eliminate the portion of limiting bootstrap randomness attributable to the boundary, and prove validity of the associated bootstrap inference under non-stationarity of the predicting variable as the only remaining source of limiting bootstrap randomness. Our approach, which is initially presented in a simple location model, has bearing on inference in parameter-on-the-boundary situations beyond the predictive regression problem.

econ.EM↗

arXiv2023

Bootstrap inference in the presence of bias

We consider bootstrap inference for estimators which are (asymptotically) biased. We show that, even when the bias term cannot be consistently estimated, valid inference can be obtained by proper implementations of the bootstrap. Specifically, we show that the prepivoting approach of Beran (1987, 1988), originally proposed to deliver higher-order refinements, restores bootstrap validity by transforming the original bootstrap p-value into an asymptotically uniform random variable. We propose two different implementations of prepivoting (plug-in and double bootstrap), and provide general high-level conditions that imply validity of bootstrap inference. To illustrate the practical relevance and implementation of our results, we discuss five examples: (i) inference on a target parameter based on model averaging; (ii) ridge-type regularized estimators; (iii) nonparametric regression; (iv) a location model for infinite variance data; and (v) dynamic panel data models.

econ.EM↗

arXiv2023

An identification and testing strategy for proxy-SVARs with weak proxies

When proxies (external instruments) used to identify target structural shocks are weak, inference in proxy-SVARs (SVAR-IVs) is nonstandard and the construction of asymptotically valid confidence sets for the impulse responses of interest requires weak-instrument robust methods. In the presence of multiple target shocks, test inversion techniques require extra restrictions on the proxy-SVAR parameters other those implied by the proxies that may be difficult to interpret and test. We show that frequentist asymptotic inference in these situations can be conducted through Minimum Distance estimation and standard asymptotic methods if the proxy-SVAR can be identified by using `strong' instruments for the non-target shocks; i.e. the shocks which are not of primary interest in the analysis. The suggested identification strategy hinges on a novel pre-test for the null of instrument relevance based on bootstrap resampling which is not subject to pre-testing issues, in the sense that the validity of post-test asymptotic inferences is not affected by the outcomes of the test. The test is robust to conditionally heteroskedasticity and/or zero-censored proxies, is computationally straightforward and applicable regardless of the number of shocks being instrumented. Some illustrative examples show the empirical usefulness of the suggested identification and testing strategy.

econ.EM↗

arXiv2023

Asymptotics for the Generalized Autoregressive Conditional Duration Model

Engle and Russell (1998, Econometrica, 66:1127--1162) apply results from the GARCH literature to prove consistency and asymptotic normality of the (exponential) QMLE for the generalized autoregressive conditional duration (ACD) model, the so-called ACD(1,1), under the assumption of strict stationarity and ergodicity. The GARCH results, however, do not account for the fact that the number of durations over a given observation period is random. Thus, in contrast with Engle and Russell (1998), we show that strict stationarity and ergodicity alone are not sufficient for consistency and asymptotic normality, and provide additional sufficient conditions to account for the random number of durations. In particular, we argue that the durations need to satisfy the stronger requirement that they have finite mean.

econ.EM↗

arXiv2022

The Econometrics of Financial Duration Modeling

We establish new results for estimation and inference in financial durations models, where events are observed over a given time span, such as a trading day, or a week. For the classical autoregressive conditional duration (ACD) models by Engle and Russell (1998, Econometrica 66, 1127-1162), we show that the large sample behavior of likelihood estimators is highly sensitive to the tail behavior of the financial durations. In particular, even under stationarity, asymptotic normality breaks down for tail indices smaller than one or, equivalently, when the clustering behaviour of the observed events is such that the unconditional distribution of the durations has no finite mean. Instead, we find that estimators are mixed Gaussian and have non-standard rates of convergence. The results are based on exploiting the crucial fact that for duration data the number of observations within any given time span is random. Our results apply to general econometric models where the number of observed events is random.

econ.EM↗

arXiv2022

Time-Varying Poisson Autoregression

In this paper we propose a new time-varying econometric model, called Time-Varying Poisson AutoRegressive with eXogenous covariates (TV-PARX), suited to model and forecast time series of counts. {We show that the score-driven framework is particularly suitable to recover the evolution of time-varying parameters and provides the required flexibility to model and forecast time series of counts characterized by convoluted nonlinear dynamics and structural breaks.} We study the asymptotic properties of the TV-PARX model and prove that, under mild conditions, maximum likelihood estimation (MLE) yields strongly consistent and asymptotically normal parameter estimates. Finite-sample performance and forecasting accuracy are evaluated through Monte Carlo simulations. The empirical usefulness of the time-varying specification of the proposed TV-PARX model is shown by analyzing the number of new daily COVID-19 infections in Italy and the number of corporate defaults in the US.

econ.EM↗

arXiv2022

Adaptive information-based methods for determining the co-integration rank in heteroskedastic VAR models

Standard methods, such as sequential procedures based on Johansen's (pseudo-)likelihood ratio (PLR) test, for determining the co-integration rank of a vector autoregressive (VAR) system of variables integrated of order one can be significantly affected, even asymptotically, by unconditional heteroskedasticity (non-stationary volatility) in the data. Known solutions to this problem include wild bootstrap implementations of the PLR test or the use of an information criterion, such as the BIC, to select the co-integration rank. Although asymptotically valid in the presence of heteroskedasticity, these methods can display very low finite sample power under some patterns of non-stationary volatility. In particular, they do not exploit potential efficiency gains that could be realised in the presence of non-stationary volatility by using adaptive inference methods. Under the assumption of a known autoregressive lag length, Boswijk and Zu (2022) develop adaptive PLR test based methods using a non-parameteric estimate of the covariance matrix process. It is well-known, however, that selecting an incorrect lag length can significantly impact on the efficacy of both information criteria and bootstrap PLR tests to determine co-integration rank in finite samples. We show that adaptive information criteria-based approaches can be used to estimate the autoregressive lag order to use in connection with bootstrap adaptive PLR tests, or to jointly determine the co-integration rank and the VAR lag length and that in both cases they are weakly consistent for these parameters in the presence of non-stationary volatility provided standard conditions hold on the penalty term. Monte Carlo simulations are used to demonstrate the potential gains from using adaptive methods and an empirical application to the U.S. term structure is provided.

econ.EM↗

arXiv2021

Bootstrap Inference for Hawkes and General Point Processes

Inference and testing in general point process models such as the Hawkes model is predominantly based on asymptotic approximations for likelihood-based estimators and tests. As an alternative, and to improve finite sample performance, this paper considers bootstrap-based inference for interval estimation and testing. Specifically, for a wide class of point process models we consider a novel bootstrap scheme labeled 'fixed intensity bootstrap' (FIB), where the conditional intensity is kept fixed across bootstrap repetitions. The FIB, which is very simple to implement and fast in practice, extends previous ideas from the bootstrap literature on time series in discrete time, where the so-called 'fixed design' and 'fixed volatility' bootstrap schemes have shown to be particularly useful and effective. We compare the FIB with the classic recursive bootstrap, which is here labeled 'recursive intensity bootstrap' (RIB). In RIB algorithms, the intensity is stochastic in the bootstrap world and implementation of the bootstrap is more involved, due to its sequential structure. For both bootstrap schemes, we provide new bootstrap (asymptotic) theory which allows to assess bootstrap validity, and propose a 'non-parametric' approach based on resampling time-changed transformations of the original waiting times. We also establish the link between the proposed bootstraps for point process models and the related autoregressive conditional duration (ACD) models. Lastly, we show effectiveness of the different bootstrap schemes in finite samples through a set of detailed Monte Carlo experiments, and provide applications to both financial data and social media data to illustrate the proposed methodology.

econ.EM↗

arXiv2021

Inference in heavy-tailed non-stationary multivariate time series

We study inference on the common stochastic trends in a non-stationary, $N$-variate time series $y_{t}$, in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail index, or even knowledge as to whether certain moments (such as the variance) exist or not, and develop an estimator of the number of stochastic trends $m$ based on the eigenvalues of the sample second moment matrix of $y_{t}$. We study the rates of such eigenvalues, showing that the first $m$ ones diverge, as the sample size $T$ passes to infinity, at a rate faster by $O\left(T \right)$ than the remaining $N-m$ ones, irrespective of the tail index. We thus exploit this eigen-gap by constructing, for each eigenvalue, a test statistic which diverges to positive infinity or drifts to zero according to whether the relevant eigenvalue belongs to the set of the first $m$ eigenvalues or not. We then construct a randomised statistic based on this, using it as part of a sequential testing procedure, ensuring consistency of the resulting estimator of $m$. We also discuss an estimator of the common trends based on principal components and show that, up to a an invertible linear transformation, such estimator is consistent in the sense that the estimation error is of smaller order than the trend itself. Finally, we also consider the case in which we relax the standard assumption of \textit{i.i.d.} innovations, by allowing for heterogeneity of a very general form in the scale of the innovations. A Monte Carlo study shows that the proposed estimator for $m$ performs particularly well, even in samples of small size. We complete the paper by presenting four illustrative applications covering commodity prices, interest rates data, long run PPP and cryptocurrency markets.

econ.EM↗

arXiv2021

MinP Score Tests with an Inequality Constrained Parameter Space

Score tests have the advantage of requiring estimation alone of the model restricted by the null hypothesis, which often is much simpler than models defined under the alternative hypothesis. This is typically so when the alternative hypothesis involves inequality constraints. However, existing score tests address only jointly testing all parameters of interest; a leading example is testing all ARCH parameters or variances of random coefficients being zero or not. In such testing problems rejection of the null hypothesis does not provide evidence on rejection of specific elements of parameter of interest. This paper proposes a class of one-sided score tests for testing a model parameter that is subject to inequality constraints. Proposed tests are constructed based on the minimum of a set of $p$-values. The minimand includes the $p$-values for testing individual elements of parameter of interest using individual scores. It may be extended to include a $p$-value of existing score tests. We show that our tests perform better than/or perform as good as existing score tests in terms of joint testing, and has furthermore the added benefit of allowing for simultaneously testing individual elements of parameter of interest. The added benefit is appealing in the sense that it can identify a model without estimating it. We illustrate our tests in linear regression models, ARCH and random coefficient models. A detailed simulation study is provided to examine the finite sample performance of the proposed tests and we find that our tests perform well as expected.

econ.EM↗

arXiv2021

Specification tests for GARCH processes

This paper develops tests for the correct specification of the conditional variance function in GARCH models when the true parameter may lie on the boundary of the parameter space. The test statistics considered are of Kolmogorov-Smirnov and Cramér-von Mises type, and are based on a certain empirical process marked by centered squared residuals. The limiting distributions of the test statistics are not free from (unknown) nuisance parameters, and hence critical values cannot be tabulated. A novel bootstrap procedure is proposed to implement the tests; it is shown to be asymptotically valid under general conditions, irrespective of the presence of nuisance parameters on the boundary. The proposed bootstrap approach is based on shrinking of the parameter estimates used to generate the bootstrap sample toward the boundary of the parameter space at a proper rate. It is simple to implement and fast in applications, as the associated test statistics have simple closed form expressions. A simulation study demonstrates that the new tests: (i) have excellent finite sample behavior in terms of empirical rejection probabilities under the null as well as under the alternative; (ii) provide a useful complement to existing procedures based on Ljung-Box type approaches. Two data examples are considered to illustrate the tests.

econ.EM↗