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on Econometric Time Series |
| By: | Fresoli, Diego Eduardo; Poncela Blanco, Maria Pilar; Ruiz Ortega, Esther |
| Abstract: | In economics, Principal Components, its generalized version that takes into account heteroscedasticity, and Kalman filter and smoothing procedures are among the most popular procedures for factor extraction in the context of Dynamic Factor Models. This paper analyses the consequences on point and interval factor estimation of using these procedures when the idiosyncratic components are wrongly assumed to be cross-sectionally uncorrelated. We show that not taking into account the presence of cross-sectional dependence increases the uncertainty of point estimates of the factors. Furthermore, the Mean Square Errors computed using the usual expressions based on asymptotic approximations, are underestimated and may lead to prediction intervals with extremely low coverages. |
| Keywords: | EM Algorithm; Kalman Filter; Principal Components; State-Space Model |
| JEL: | C32 C38 C55 |
| Date: | 2022–12–12 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:36251&r=ets |
| By: | Wagner, Martin (Department of Economics University of Klagenfurt, Austria, Bank of Slovenia Ljubljana, Slovenia and Institute for Advanced Studies Vienna, Austria) |
| Abstract: | We consider fully modified least squares estimation for systems of cointegrating polynomial regressions, i. e., systems of regressions that include deterministic variables, integrated processes and their powers as regressors. The errors are allowed to be correlated across equations, over time and with the regressors. Whilst, of course, fully modified OLS and GLS estimation coincide – for any regular weighting matrix – without restrictions on the parameters and with the same regressors in all equations, this equivalence breaks down, in general, in case of parameter restrictions and/or different regressors across equations. Consequently, we discuss in detail restricted fully modified GLS estimators and inference based upon them. |
| Keywords: | Fully Modified Estimation, Cointegrating Polynomial Regression, Generalized, Least Squares, Hypothesis Testing |
| JEL: | C12 C13 Q20 |
| Date: | 2023–01 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihswps:44&r=ets |
| By: | Niko Hauzenberger; Florian Huber; Gary Koop; James Mitchell |
| Abstract: | In light of widespread evidence of parameter instability in macroeconomic models, many time-varying parameter (TVP) models have been proposed. This paper proposes a nonparametric TVP-VAR model using Bayesian additive regression trees (BART). The novelty of this model stems from the fact that the law of motion driving the parameters is treated nonparametrically. This leads to great flexibility in the nature and extent of parameter change, both in the conditional mean and in the conditional variance. In contrast to other nonparametric and machine learning methods that are black box, inference using our model is straightforward because, in treating the parameters rather than the variables nonparametrically, the model remains conditionally linear in the mean. Parsimony is achieved through adopting nonparametric factor structures and use of shrinkage priors. In an application to US macroeconomic data, we illustrate the use of our model in tracking both the evolving nature of the Phillips curve and how the effects of business cycle shocks on inflationary measures vary nonlinearly with movements in uncertainty. |
| Keywords: | Bayesian Vector Autoregression; Time-varying Parameters; Nonparametric Modeling; Machine Learning; Regression Trees; Phillips Curve; Business Cycle Shocks |
| JEL: | C11 C32 C51 E32 |
| Date: | 2023–01–11 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwq:95470&r=ets |
| By: | Yicong Lin (Vrije Universiteit Amsterdam); Hanno Reuvers (Erasmus University Rotterdam) |
| Abstract: | We study a set of fully modified (FM) estimators in multivariate cointegrating polynomial regressions. Such regressions allow for deterministic trends, stochastic trends, and integer powers of stochastic trends to enter the cointegrating relations. A new feasible generalized least squares estimator is proposed. Our estimator incorporates: (1) the inverse autocovariance matrix of multidimensional errors and (2) second-order bias corrections. The resulting estimator has the intuitive interpretation of applying a weighted least squares objective function to filtered data series. Moreover, the required second-order bias corrections are convenient byproducts of our approach and lead to a conventional asymptotic inference. Based on different FM estimators, multiple multivariate KPSS-type of tests for the null of cointegration are constructed. We then undertake a comprehensive Monte Carlo study to compare the performance of the FM estimators and the related tests. We find good performance of the proposed estimator and the implied test statistics for linear hypotheses and cointegration. |
| Keywords: | Cointegrating Polynomial Regression, Cointegration Testing, Fully Modified Estimation, Generalized Least Squares |
| JEL: | C12 C13 C32 |
| Date: | 2022–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20220093&r=ets |
| By: | Jan Pablo Burgard; Matthias Neuenkirch; Dennis Umlandt |
| Abstract: | Recursively identified vector autoregressive (VAR) models often lead to a counterintuitive response of prices (and output) shortly after a monetary policy shock. To overcome this problem, we propose to estimate the VAR parameters under the restriction that economic theory is not violated, while the shocks are still recursively identified. We solve this optimization problem under non-linear constraints using an augmented Lagrange solution approach, which adjusts the VAR coefficients to meet the theoretical requirements. In a generalization, we allow for a (minimal) rotation of the Cholesky matrix in addition to the parameter restrictions. Based on a Monte Carlo study and an empirical application, we show that particularly the "almost recursively identified approach with parameter restrictions" leads to a solution that avoids an estimation bias, generates theory-consistent impulse responses, and is as close as possible to the recursive scheme. |
| Keywords: | Monetary Policy Transmission, Non-Linear Optimization, Price Puzzle, Recursive Identification, Rotation, Sign Restrictions |
| JEL: | C32 E52 E58 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:trr:qfrawp:202301&r=ets |
| By: | Julien Hambuckers; Li Sun; Luca Trapin |
| Abstract: | We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root predictors to appropriately capture the time-varying behaviour of the distribution of high-frequency extreme losses. To characterize trading activity and market uncertainty, we consider several volatility and liquidity predictors, and propose a two-step adaptive $L_1$-regularized maximum likelihood estimator to select the most appropriate ones. We establish the oracle property of the proposed estimator for selecting both stationary and local unit-root predictors, and show its good finite sample properties in an extensive simulation study. Studying the high-frequency extreme losses of nine large liquid U.S. stocks using 42 liquidity and volatility predictors, we find the severity of extreme losses to be well predicted by low levels of price impact in period of high volatility of liquidity and volatility. |
| Date: | 2023–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2301.01362&r=ets |