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on Econometric Time Series |
| By: | Christis Katsouris |
| Abstract: | These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional dependent data which is relevant to covariance matrix structures as well as to dependent time series sequences. Second, we present main aspects of the asymptotic theory related to time series regression models with many covariates. Third, we discuss various applications of statistical learning methodologies for time series analysis purposes. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.16192&r=ets |
| By: | Christis Katsouris |
| Abstract: | This article discusses recent developments in the literature of quantile time series models in the cases of stationary and nonstationary underline stochastic processes. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.06617&r=ets |
| By: | Dante Amengual (CEMFI, Centro de Estudios Monetarios y Financieros); Xinyue Bei (Duke University); Enrique Sentana (CEMFI, Centro de Estudios Monetarios y Financieros) |
| Abstract: | We develop tests for neglected serial correlation when the information matrix is repeatedly singular under the null. Specifically, we consider white noise against a multiplicative seasonal AR model, and a local-level model against a nesting UCARIMA one. Our proposals, which involve higher-order derivatives, are asymptotically equivalent to the likelihood ratio test but only require estimation under the null. Remarkably, we show that our proposed tests effectively check that certain autocorrelations of the observations are 0, so their asymptotic distribution is standard. We conduct Monte Carlo exercises that study their finite sample size and power properties, comparing them to alternative approaches. |
| Keywords: | Generalized extremum tests, higher-order identifiability, likelihood ratio test. |
| JEL: | C22 C32 C52 C12 |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:cmf:wpaper:wp2023_2302&r=ets |
| By: | Anna Mikusheva; Mikkel S{\o}lvsten |
| Abstract: | This paper studies linear time series regressions with many regressors. Weak exogeneity is the most used identifying assumption in time series. Weak exogeneity requires the structural error to have zero conditional expectation given the present and past regressor values, allowing errors to correlate with future regressor realizations. We show that weak exogeneity in time series regressions with many controls may produce substantial biases and even render the least squares (OLS) estimator inconsistent. The bias arises in settings with many regressors because the normalized OLS design matrix remains asymptotically random and correlates with the regression error when only weak (but not strict) exogeneity holds. This bias's magnitude increases with the number of regressors and their average autocorrelation. To address this issue, we propose an innovative approach to bias correction that yields a new estimator with improved properties relative to OLS. We establish consistency and conditional asymptotic Gaussianity of this new estimator and provide a method for inference. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.08958&r=ets |
| By: | Daniel Buncic; Adrian Pagan; Tim Robinson |
| Abstract: | Many key macroeconomic variables such as the NAIRU, potential GDP, and the neutral real rate of interest—which are needed for policy analysis—are latent. Collectively, these latent variables are known as ‘stars’ and are typically estimated using the Kalman filter or smoother from models that can be expressed in State Space form. When these models contain more shocks than observed variables, they are ‘short’, and potentially create issues in recovering the star variable of interest from the observed data. Recovery issues can occur when the model is correctly specified and its parameters are known. In this paper, we summarize the literature on shock recovery and demonstrate its implications for estimating stars in a number of widely used models in policy analysis. The ability of many popular and recent models to recover stars is shown to be limited. We suggest ways this can be addressed. |
| Keywords: | Kalman filter and smoother, State Space models, shock recovery, short systems, natural rate of interest, macroeconomic policy, Beveridge-Nelson decomposition |
| JEL: | C22 C32 E58 |
| Date: | 2023–09 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2023-43&r=ets |
| By: | Kejin Wu; Sayar Karmakar |
| Abstract: | In this work, we further explore the forecasting ability of a recently proposed normalizing and variance-stabilizing (NoVaS) transformation after wrapping exogenous variables. In practice, especially in the area of financial econometrics, extra knowledge such as fundamentals- and sentiments-based information could be beneficial to improve the prediction accuracy of market volatility if they are incorporated into the forecasting process. In a classical approach, people usually apply GARCHX-type methods to include the exogenous variables. Being a Model-free prediction method, NoVaS has been shown to be more accurate and stable than classical GARCH-type methods. We are interested in whether the novel NoVaS method can also sustain its superiority after exogenous covariates are taken into account. We provide the NoVaS transformation based on GARCHX model and then claim the corresponding prediction procedure with exogenous variables existing. Also, simulation studies verify that the NoVaS method still outperforms traditional methods, especially for long-term time aggregated predictions. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.13346&r=ets |
| By: | Junting Duan; Markus Pelger; Ruoxuan Xiong |
| Abstract: | This paper develops a novel method to estimate a latent factor model for a large target panel with missing observations by optimally using the information from auxiliary panel data sets. We refer to our estimator as target-PCA. Transfer learning from auxiliary panel data allows us to deal with a large fraction of missing observations and weak signals in the target panel. We show that our estimator is more efficient and can consistently estimate weak factors, which are not identifiable with conventional methods. We provide the asymptotic inferential theory for target-PCA under very general assumptions on the approximate factor model and missing patterns. In an empirical study of imputing data in a mixed-frequency macroeconomic panel, we demonstrate that target-PCA significantly outperforms all benchmark methods. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.15627&r=ets |
| By: | Cameron Cornell; Lewis Mitchell; Matthew Roughan |
| Abstract: | Methodologies to infer financial networks from the price series of speculative assets vary, however, they generally involve bivariate or multivariate predictive modelling to reveal causal and correlational structures within the time series data. The required model complexity intimately relates to the underlying market efficiency, where one expects a highly developed and efficient market to display very few simple relationships in price data. This has spurred research into the applications of complex nonlinear models for developed markets. However, it remains unclear if simple models can provide meaningful and insightful descriptions of the dependency and interconnectedness of the rapidly developed cryptocurrency market. Here we show that multivariate linear models can create informative cryptocurrency networks that reflect economic intuition, and demonstrate the importance of high-influence nodes. The resulting network confirms that node degree, a measure of influence, is significantly correlated to the market capitalisation of each coin ($\rho=0.193$). However, there remains a proportion of nodes whose influence extends beyond what their market capitalisation would imply. We demonstrate that simple linear model structure reveals an inherent complexity associated with the interconnected nature of the data, supporting the use of multivariate modelling to prevent surrogate effects and achieve accurate causal representation. In a reductive experiment we show that most of the network structure is contained within a small portion of the network, consistent with the Pareto principle, whereby a fraction of the inputs generates a large proportion of the effects. Our results demonstrate that simple multivariate models provide nontrivial information about cryptocurrency market dynamics, and that these dynamics largely depend upon a few key high-influence coins. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.15769&r=ets |
| By: | Xiaohong Chen; Sokbae Lee; Yuan Liao; Myung Hwan Seo; Youngki Shin; Myunghyun Song |
| Abstract: | We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular Hansen (1982) (offline) GMM, and offers fast and scalable implementation with the ability to handle streaming datasets in real time. We establish the almost sure convergence, and the (functional) central limit theorem for the inefficient online 2SLS and the efficient SGMM. Moreover, we propose online versions of the Durbin-Wu-Hausman and Sargan-Hansen tests that can be seamlessly integrated within the SGMM framework. Extensive Monte Carlo simulations show that as the sample size increases, the SGMM matches the standard (offline) GMM in terms of estimation accuracy and gains over computational efficiency, indicating its practical value for both large-scale and online datasets. We demonstrate the efficacy of our approach by a proof of concept using two well known empirical examples with large sample sizes. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.13564&r=ets |