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on Econometric Time Series |
| By: | Jannik Kreye; Philipp Sibbertsen |
| Abstract: | We propose a test to detect a forecast accuracy breakdown in a long memory time series and provide theoretical and simulation evidence on the memory transfer from the time series to the forecast residuals. The proposed method uses a double sup-Wald test against the alternative of a structural break in the mean of an out-of-sample loss series. To address the problem of estimating the long-run variance under long memory, a robust estimator is applied. The corresponding breakpoint results from a long memory robust CUSUM test. The finite sample size and power properties of the test are derived in a Monte Carlo simulation. A monotonic power function is obtained for the fixed forecasting scheme. In our practical application, we find that the global energy crisis that began in 2021 led to a forecast break in European electricity prices, while the results for the U.S. are mixed. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.07087 |
| By: | Li, D.; Linton, O. B.; Zhang, H. |
| Abstract: | We propose a new estimator of high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure from noisy and asynchronous high-frequency data collected for an ultra-large number of assets. The noise processes are allowed to be temporally correlated, heteroskedastic, asymptotically vanishing and dependent on the efficient prices. We define a kernel-weighted pre-averaging method to jointly tackle the microstructure noise and asynchronicity issues, and we obtain uniformly consistent estimates for latent prices. We impose a continuous-time factor model with time-varying factor loadings on the price processes, and estimate the common factors and loadings via a local principal component analysis. Assuming a uniform sparsity condition on the idiosyncratic volatility structure, we combine the POET and kernel-smoothing techniques to estimate the spot volatility matrices for both the latent prices and idiosyncratic errors. Under some mild restrictions, the estimated spot volatility matrices are shown to be uniformly consistent under various matrix norms. We provide Monte-Carlo simulation and empirical studies to examine the numerical performance of the developed estimation methodology. |
| Keywords: | Continuous Semimartingale, Kernel Smoothing, Microstructure Noise, PCA, Spot Volatility, Time-Varying Factor Models |
| JEL: | G12 G14 C14 |
| Date: | 2024–09–19 |
| URL: | https://d.repec.org/n?u=RePEc:cam:camdae:2454 |
| By: | Li, D.; Linton, O. B.; Zhang, H. |
| Abstract: | We propose a new estimator of high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure from noisy and asynchronous high-frequency data collected for an ultra-large number of assets. The noise processes are allowed to be temporally correlated, heteroskedastic, asymptotically vanishing and dependent on the efficient prices. We define a kernel-weighted pre-averaging method to jointly tackle the microstructure noise and asynchronicity issues, and we obtain uniformly consistent estimates for latent prices. We impose a continuous-time factor model with time-varying factor loadings on the price processes, and estimate the common factors and loadings via a local principal component analysis. Assuming a uniform sparsity condition on the idiosyncratic volatility structure, we combine the POET and kernel-smoothing techniques to estimate the spot volatility matrices for both the latent prices and idiosyncratic errors. Under some mild restrictions, the estimated spot volatility matrices are shown to be uniformly consistent under various matrix norms. We provide Monte-Carlo simulation and empirical studies to examine the numerical performance of the developed estimation methodology. |
| Keywords: | Continuous Semimartingale, Kernel Smoothing, Microstructure Noise, PCA, Spot Volatility, Time-Varying Factor Models |
| JEL: | G12 G14 C14 |
| Date: | 2024–09–19 |
| URL: | https://d.repec.org/n?u=RePEc:cam:camjip:2424 |
| By: | Jean-Marie Dufour; Endong Wang |
| Abstract: | This paper introduces a novel two-stage estimation and inference procedure for generalized impulse responses (GIRs). GIRs encompass all coefficients in a multi-horizon linear projection model of future outcomes of y on lagged values (Dufour and Renault, 1998), which include the Sims' impulse response. The conventional use of Least Squares (LS) with heteroskedasticity- and autocorrelation-consistent covariance estimation is less precise and often results in unreliable finite sample tests, further complicated by the selection of bandwidth and kernel functions. Our two-stage method surpasses the LS approach in terms of estimation efficiency and inference robustness. The robustness stems from our proposed covariance matrix estimates, which eliminate the need to correct for serial correlation in the multi-horizon projection residuals. Our method accommodates non-stationary data and allows the projection horizon to grow with sample size. Monte Carlo simulations demonstrate our two-stage method outperforms the LS method. We apply the two-stage method to investigate the GIRs, implement multi-horizon Granger causality test, and find that economic uncertainty exerts both short-run (1-3 months) and long-run (30 months) effects on economic activities. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.10820 |
| By: | Endong Wang |
| Abstract: | We propose a structural model-free methodology to analyze two types of macroeconomic counterfactuals related to policy path deviation: hypothetical trajectory and policy intervention. Our model-free approach is built on a structural vector moving-average (SVMA) model that relies solely on the identification of policy shocks, thereby eliminating the need to specify an entire structural model. Analytical solutions are derived for the counterfactual parameters, and statistical inference for these parameter estimates is provided using the Delta method. By utilizing external instruments, we introduce a projection-based method for the identification, estimation, and inference of these parameters. This approach connects our counterfactual analysis with the Local Projection literature. A simulation-based approach with nonlinear model is provided to add in addressing Lucas' critique. The innovative model-free methodology is applied in three counterfactual studies on the U.S. monetary policy: (1) a historical scenario analysis for a hypothetical interest rate path in the post-pandemic era, (2) a future scenario analysis under either hawkish or dovish interest rate policy, and (3) an evaluation of the policy intervention effect of an oil price shock by zeroing out the systematic responses of the interest rate. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.09577 |
| By: | Tomás E. Caravello; Alisdair McKay; Christian K. Wolf |
| Abstract: | In a rich family of linearized structural macroeconomic models, the counterfactual evolution of the macro-economy under alternative policy rules is pinned down by just two objects: first, reduced-form projections with respect to a large information set; and second, the dynamic causal effects of policy shocks. In particular, no assumptions about the structural shocks affecting the economy are needed. We propose to recover these two sufficient statistics using a ``VAR-Plus'' approach, and apply it to evaluate several monetary policy counterfactuals. |
| JEL: | E32 E58 E61 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32988 |
| By: | Silvana Tiedemann (Centre for Sustainability, Hertie School); Jorge Sanchez Canales (Centre for Sustainability, Hertie School); Felix Schur (Department of Mathematics, ETH Zurich); Raffaele Sgarlato (Centre for Sustainability, Hertie School); Lion Hirth (Centre for Sustainability, Hertie School); Oliver Ruhnau (Department of Economics and Institute of Energy Economics, University of Cologne); Jonas Peters (Department of Mathematics, ETH Zurich) |
| Abstract: | The price elasticity of demand can be estimated from observational data using instrumental variables (IV). However, naive IV estimators may be inconsistent in settings with autocorrelated time series. We argue that causal time graphs can simplify IV identification and help select consistent estimators. To do so, we propose to first model the equilibrium condition by an unobserved confounder, deriving a directed acyclic graph (DAG) while maintaining the assumption of a simultaneous determination of prices and quantities. We then exploit recent advances in graphical inference to derive valid IV estimators, including estimators that achieve consistency by simultaneously estimating nuisance effects. We further argue that observing significant differences between the estimates of presumably valid estimators can help to reject false model assumptions, thereby improving our understanding of underlying economic dynamics. We apply this approach to the German electricity market, estimating the price elasticity of demand on simulated and real-world data. The findings underscore the importance of accounting for structural autocorrelation in IV-based analysis. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.15530 |
| By: | Giuseppe Cavaliere; Iliyan Georgiev; Edoardo Zanelli |
| Abstract: | 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. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.12611 |