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on Econometrics |
| By: | Francq, Christian; Zakoian, Jean-Michel |
| Abstract: | We investigate the problem of testing finiteness of moments for a class of semi-parametric augmented GARCH models encompassing most commonly used specifications. The existence of positive-power moments of the strictly stationary solution is characterized through the Moment Generating Function (MGF) of the model, defined as the MGF of the logarithm of the random autoregressive coefficient in the volatility dynamics. We establish the asymptotic distribution of the empirical MGF, from which tests of moments are deduced. Alternative tests relying on the estimation of the Maximal Moment Exponent (MME) are studied. Power comparisons based on local alternatives and the Bahadur approach are proposed. We provide an illustration on real financial data, showing that semi-parametric estimation of the MME offers an interesting alternative to Hill's nonparametric estimator of the tail index. |
| Keywords: | APARCH model; Bahadur slopes; Hill's estimator; Local asymptotic power; Maximal moment exponent; Moment generating function |
| JEL: | C12 C58 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:110511&r= |
| By: | Yuefeng Han; Cun-Hui Zhang; Rong Chen |
| Abstract: | Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CP decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.15517&r= |
| By: | Alexander Krei{\ss}; Christoph Rothe |
| Abstract: | We study regression discontinuity designs in which many covariates, possibly much more than the number of observations, are available. We provide a two-step algorithm which first selects the set of covariates to be used through a localized Lasso-type procedure, and then, in a second step, estimates the treatment effect by including the selected covariates into the usual local linear estimator. We provide an in-depth analysis of the algorithm's theoretical properties, showing that, under an approximate sparsity condition, the resulting estimator is asymptotically normal, with asymptotic bias and variance that are conceptually similar to those obtained in low-dimensional settings. Bandwidth selection and inference can be carried out using standard methods. We also provide simulations and an empirical application. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.13725&r= |
| By: | Daniel Wilhelm (Daniel Wilhelm); Magne Mogstad (Magne Mogstad); Azeem Shaikh (Azeem M. Shaikh) |
| Abstract: | It is common to rank different categories by means of preferences that are revealed through data on choices. A prominent example is the ranking of political candidates or parties using the estimated share of support each one receives in surveys or polls about political attitudes. Since these rankings are computed using estimates of the share of support rather than the true share of support, there may be considerable uncertainty concerning the true ranking of the political candidates or parties. In this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each category. We consider both the problem of constructing marginal confidence sets for the rank of a particular category as well as simultaneous confidence sets for the ranks of all categories. A distinguishing feature of our analysis is that we exploit the multinomial structure of the data to develop confidence sets that are valid in finite samples. We additionally develop confidence sets using the bootstrap that are valid only approximately in large samples. We use our methodology to rank political parties in Australia using data from the 2019 Australian Election Survey. We find that our finite-sample confidence sets are informative across the entire ranking of political parties, even in Australian territories with few survey respondents and/or with parties that are chosen by only a small share of the survey respondents. In contrast, the bootstrap-based confidence sets may sometimes be considerably less informative. These findings motivate us to compare these methods in an empirically-driven simulation study, in which we conclude that our finite-sample confidence sets often perform better than their large-sample, bootstrap-based counterparts, especially in settings that resemble our empirical application. |
| Keywords: | Confidence sets, Multinomial Data, Multiple Testing, Polls, Ranks, Surveys |
| JEL: | C12 C14 D31 I20 J62 |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:crm:wpaper:2132&r= |
| By: | Zhan, Ruohan (Institute for Computational and Mathematical Engineering, Stanford University); Hadad, Vitor (Stanford University); Hirshberg, David A. (Stanford University); Athey, Susan (Stanford University) |
| Abstract: | It has become increasingly common for data to be collected adaptively, for example using contextual bandits. Historical data of this type can be used to evaluate other treatment assignment policies to guide future innovation or experiments. However, policy evaluation is challenging if the target policy differs from the one used to collect data, and popular estimators, including doubly robust (DR) estimators, can be plagued by bias, excessive variance, or both. In particular, when the pattern of treatment assignment in the collected data looks little like the pattern generated by the policy to be evaluated, the importance weights used in DR estimators explode, leading to excessive variance. In this paper, we improve the DR estimator by adaptively weighting observations to control its variance. We show that a t-statistic based on our improved estimator is asymptotically normal under certain conditions, allowing us to form confidence intervals and test hypotheses. Using synthetic data and public benchmarks, we provide empirical evidence for our estimator’s improved accuracy and inferential properties relative to existing alternatives. |
| Date: | 2021–06 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:3970&r= |
| By: | Shi, Chengchun; Xu, Tianlin; Bergsma, Wicher; Li, Lexin |
| Abstract: | In this article, we study the problem of high-dimensional conditional independence testing, a key building block in statistics and machine learning. We propose an inferential procedure based on double generative adversarial networks (GANs). Specifically, we first introduce a double GANs framework to learn two generators of the conditional distributions. We then integrate the two generators to construct a test statistic, which takes the form of the maximum of generalized covariance measures of multiple transformation functions. We also employ data-splitting and cross-fitting to minimize the conditions on the generators to achieve the desired asymptotic properties, and employ multiplier bootstrap to obtain the corresponding p-value. We show that the constructed test statistic is doubly robust, and the resulting test both controls type-I error and has the power approaching one asymptotically. Also notably, we establish those theoretical guarantees under much weaker and practically more feasible conditions compared to the existing tests, and our proposal gives a concrete example of how to utilize some state-of-the-art deep learning tools, such as GANs, to help address a classical but challenging statistical problem. We demonstrate the efficacy of our test through both simulations and an application to an anti-cancer drug dataset. |
| Keywords: | conditional independence; double-robustness; generalized covariance measure; generative adversarial networks; multiplier bootstrap |
| JEL: | C1 |
| Date: | 2021–11–02 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:112550&r= |
| By: | Brendan Kline; Ariel Pakes; Elie Tamer |
| Abstract: | We review approaches to identification and inference on models in Industrial Organization with partial identification and/or moment inequalities. Often, such approaches are intentionally built directly on assumptions of optimizing behavior that are credible in Industrial Organization settings, while avoiding the use of strong modeling and measurement assumptions that may not be warranted. The result is an identified set for the object of interest, reflecting what the econometrician can learn from the data and assumptions. The chapter formally defines identification, reviews the assumptions underlying the identification argument, and provides examples of their use in Industrial Organization settings. We then discuss the corresponding statistical inference problem paying particular attention to practical implementation issues. |
| JEL: | C18 L22 L25 |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:29409&r= |
| By: | Graziano Moramarco |
| Abstract: | This paper proposes an approach for enhancing density forecasts of non-normal macroeconomic variables using Bayesian Markov-switching models. Alternative views about economic regimes are combined to produce flexible forecasts, which are optimized with respect to standard objective functions of density forecasting. The optimization procedure explores both forecast combinations and Bayesian model averaging. In an application to U.S. GDP growth, the approach is shown to achieve good accuracy in terms of average predictive densities and to produce well-calibrated forecast distributions. The proposed framework can be used to evaluate the contribution of economists' views to density forecast performance. In the empirical application, we consider views derived from the Fed macroeconomic scenarios used for bank stress tests. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.13761&r= |
| By: | Pratha Khandelwal; Philip Nadler; Rossella Arcucci; William Knottenbelt; Yi-Ke Guo |
| Abstract: | The nature of available economic data has changed fundamentally in the last decade due to the economy's digitisation. With the prevalence of often black box data-driven machine learning methods, there is a necessity to develop interpretable machine learning methods that can conduct econometric inference, helping policymakers leverage the new nature of economic data. We therefore present a novel Variational Bayesian Inference approach to incorporate a time-varying parameter auto-regressive model which is scalable for big data. Our model is applied to a large blockchain dataset containing prices, transactions of individual actors, analyzing transactional flows and price movements on a very granular level. The model is extendable to any dataset which can be modelled as a dynamical system. We further improve the simple state-space modelling by introducing non-linearities in the forward model with the help of machine learning architectures. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.14346&r= |
| By: | Leonardo Nogueira Ferreira |
| Abstract: | This paper explores the complementarity between traditional econometrics and machine learning and applies the resulting model – the VAR-teXt – to central bank communication. The VAR-teXt is a vector autoregressive (VAR) model augmented with information retrieved from text, turned into quantitative data via a Latent Dirichlet Allocation (LDA) model, whereby the number of topics (or textual factors) is chosen based on their predictive performance. A Markov chain Monte Carlo (MCMC) sampling algorithm for the estimation of the VAR-teXt that takes into account the fact that the textual factors are estimates is also provided. The approach is then extended to dynamic factor models (DFM) generating the DFM-teXt. Results show that textual factors based on Federal Open Market Committee (FOMC) statements are indeed useful for forecasting. |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:bcb:wpaper:559&r= |
| By: | Ali Hortacsu (University of Chicago and NBER); Olivia R. Natan (University of California, Berkeley); Hayden Parsley (University of Texas, Austin); Timothy Schwieg (University of Chicago, Booth); Kevin R. Williams (Cowles Foundation, Yale University) |
| Abstract: | We propose an approach to modeling and estimating discrete choice demand that allows for a large number of zero sale observations, rich unobserved heterogeneity, and endogenous prices. We do so by modeling small market sizes through Poisson arrivals. Each of these arriving consumers then solves a standard discrete choice problem. We present a Bayesian IV estimation approach that addresses sampling error in product shares and scales well to rich data environments. The data requirements are traditional market-level data and measures of consumer search intensity. After presenting simulation studies, we consider an empirical application of air travel demand where product-level sales are sparse. We ï¬ nd considerable variation in demand over time. Periods of peak demand feature both larger market sizes and consumers with higher willingness to pay. This ampliï¬ es cyclicality. However, observed frequent price and capacity adjustments offset some of this compounding effect. |
| Keywords: | Discrete Choice Modeling, Demand Estimation, Zeros, Bayesian Methods, Cyclical Demand, Airline Markets |
| JEL: | C10 C11 C13 C18 L93 |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2313&r= |
| By: | Lingxiao Huang (Huawei TCS Lab); K. Sudhir (Cowles Foundation and Yale School of Management); Nisheeth Vishnoi (Cowles Foundation and Yale Department of Computer Science) |
| Abstract: | We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors for real-time measurement and rapid drop in storage costs. In particular, we consider the setting where the time series data on N entities is generated from a Gaussian mixture model with autocorrelations over k clusters in Rd. Our main contribution is an algorithm to construct coresets for the maximum likelihood objective for this mixture model. Our algorithm is efficient, and, under a mild assumption on the covariance matrices of the Gaussians, the size of the coreset is independent of the number of entities N and the number of observations for each entity, and depends only polynomially on k, d and 1/ε, where ε is the error parameter. We empirically assess the performance of our coresets with synthetic data. |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2310&r= |
| By: | Zouhaier Dhifaoui (Department of family and community medicine, Faculty of medicine of Sousse, Mohamed Karoui street 4002, Tunisia) |
| Abstract: | The computation of the bivariate Hurst exponent constitutes an important technique to test the power-law cross-correlation of time series. For this objective, the detrended cross-correlation analysis method represents the most used one. In this article, we prove the robustness of the detrended cross-correlation analysis method, where the trend is estimated using the polynomial fitting, to estimate the bivariate Hurst exponent when time series are corrupted by outliers observations. On the other hand, we give the exact polynomial order and a regression region for computing a detrended cross-correlation function to obtain a least-square estimator of bivariate Hurst exponent. Our theoretical results are shown by a simulation study on a two-fractional Gaussian noise process corrupted by outliers observations. Additionally, our results are applied to financial time series. The empirical findings results are accompanied by interpretations. |
| Keywords: | Power-law cross-correlation,detrended cross-correlation function,bivariate Hurst exponent,two-fractional Gaussian noise process |
| Date: | 2021–11–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03411380&r= |
| By: | Hossein Babaei; Sina Alemohammad; Richard Baraniuk |
| Abstract: | The first step towards investigating the effectiveness of a treatment is to split the population into the control and the treatment groups, then compare the average responses of the two groups to the treatment. In order to ensure that the difference in the two groups is only caused by the treatment, it is crucial for the control and the treatment groups to have similar statistics. The validity and reliability of trials are determined by the similarity of two groups' statistics. Covariate balancing methods increase the similarity between the distributions of the two groups' covariates. However, often in practice, there are not enough samples to accurately estimate the groups' covariate distributions. In this paper, we empirically show that covariate balancing with the standardized means difference covariate balancing measure is susceptible to adversarial treatment assignments in limited population sizes. Adversarial treatment assignments are those admitted by the covariate balance measure, but result in large ATE estimation errors. To support this argument, we provide an optimization-based algorithm, namely Adversarial Treatment ASsignment in TREatment Effect Trials (ATASTREET), to find the adversarial treatment assignments for the IHDP-1000 dataset. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.13262&r= |
| By: | Krishnamurthy, Sanath Kumar (Stanford University); Hadad, Vitor (Stanford University); Athey, Susan (Stanford University) |
| Abstract: | Computationally efficient contextual bandits are often based on estimating a predictive model of rewards given contexts and arms using past data. However, when the reward model is not well-specified, the bandit algorithm may incur unexpected regret, so recent work has focused on algorithms that are robust to misspecification. We propose a simple family of contextual bandit algorithms that adapt to misspecification error by reverting to a good safe policy when there is evidence that misspecification is causing a regret increase. Our algorithm requires only an offline regression oracle to ensure regret guarantees that gracefully degrade in terms of a measure of the average misspecification level. Compared to prior work, we attain similar regret guarantees, but we do not rely on a master algorithm, and do not require more robust oracles like online or constrained regression oracles [e.g., Foster et al. (2020a); Krishnamurthy et al. (2020)]. This allows us to design algorithms for more general function approximation classes. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:3951&r= |