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on Econometric Time Series |
| By: | Silvia Goncalves; Ana María Herrera; Lutz Kilian; Elena Pesavento |
| Abstract: | We study the construction of nonlinear impulse responses in structural dynamic models that include nonlinearly transformed regressors. Such models have played an important role in recent years in capturing asymmetries, thresholds and other nonlinearities in the responses of macroeconomic variables to exogenous shocks. The conventional approach to estimating nonlinear responses is by Monte Carlo integration. We show that the population impulse responses in this class of models may instead be derived analytically from the structural model. We use this insight to study under what conditions linear projection (LP) estimators may be used to recover the population impulse responses. We find that, unlike in vector autoregressive models, the asymptotic equivalence between estimators based on the structural model and LP estimators breaks down. Only in one important special case can the population impulse response be consistently estimated by LP methods. The construction of this LP estimator, however, differs from the LP approach currently used in the literature. Simulation evidence suggests that the modified LP estimator is less accurate in finite samples than estimators based on the structural model, when both are valid. |
| Keywords: | local projection; structural model; censored regressor; nonlinear transformation; nonlinear responses; Monte Carlo integration |
| JEL: | C22 C32 C51 |
| Date: | 2020–06–30 |
| URL: | http://d.repec.org/n?u=RePEc:fip:feddwp:88270&r=all |
| By: | Zongwu Cai (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA); Ted Juhl (School of Business, The University of Kansas, Lawrence, KS 66045, USA) |
| Abstract: | We find the asymptotic distribution for rolling linear regression models various window widths. The limiting distribution depends on using the width of the rolling window, and on a Òbias processÓ that is typically ignored in practice. Based on the distribution, we tabulate critical values used to find uniform confidence intervals for the average values of regression parameters over the windows. We propose a corrected rolling regression technique that removes the bias process by rolling over smoothed parameter estimates. The procedure is illustrated using a series of Monte Carlo experiments. The paper includes an empirical example to show the how the confidence bands suggest alternative conclusions about the persistence of inflation. |
| Keywords: | Asymptotic distribution; Bias correction; Nonparametric estimation; Rolling regressions; Time-varying parameters. |
| JEL: | C14 C22 |
| Date: | 2020–08 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:202013&r=all |
| By: | Robert Adamek; Stephan Smeekes; Ines Wilms |
| Abstract: | The desparsified lasso is a high-dimensional estimation method which provides uniformly valid inference. We extend this method to a time series setting under Near-Epoch Dependence (NED) assumptions allowing for non-Gaussian, serially correlated and heteroskedastic processes, where the number of regressors can possibly grow faster than the time dimension. We first derive an oracle inequality for the (regular) lasso, relaxing the commonly made exact sparsity assumption to a weaker alternative, which permits many small but non-zero parameters. The weak sparsity coupled with the NED assumption means this inequality can also be applied to the (inherently misspecified) nodewise regressions performed in the desparsified lasso. This allows us to establish the uniform asymptotic normality of the desparsified lasso under general conditions. Additionally, we show consistency of a long-run variance estimator, thus providing a complete set of tools for performing inference in high-dimensional linear time series models. Finally, we perform a simulation exercise to demonstrate the small sample properties of the desparsified lasso in common time series settings. |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2007.10952&r=all |
| By: | Paolo Andreini; Cosimo Izzo; Giovanni Ricco |
| Abstract: | We propose a novel deep neural net framework - that we refer to as Deep Dynamic Factor Model (D2FM) -, to encode the information available, from hundreds of macroeconomic and financial time-series into a handful of unobserved latent states. While similar in spirit to traditional dynamic factor models (DFMs), differently from those, this new class of models allows for nonlinearities between factors and observables due to the deep neural net structure. However, by design, the latent states of the model can still be interpreted as in a standard factor model. In an empirical application to the forecast and nowcast of economic conditions in the US, we show the potential of this framework in dealing with high dimensional, mixed frequencies and asynchronously published time series data. In a fully real-time out-of-sample exercise with US data, the D2FM improves over the performances of a state-of-the-art DFM. |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2007.11887&r=all |
| By: | Denis Belomestny; Ekaterina Krymova; Andrey Polbin |
| Abstract: | The main goal of this paper is to develop a methodology for estimating time varying parameter vector auto-regression (TVP-VAR) models with a timeinvariant long-run relationship between endogenous variables and changes in exogenous variables. We propose a Gibbs sampling scheme for estimation of model parameters as well as time-invariant long-run multiplier parameters. Further we demonstrate the applicability of the proposed method by analyzing examples of the Norwegian and Russian economies based on the data on real GDP, real exchange rate and real oil prices. Our results show that incorporating the time invariance constraint on the long-run multipliers in TVP-VAR model helps to significantly improve the forecasting performance. |
| Date: | 2020–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2008.00718&r=all |
| By: | Stephan Smeekes; Ines Wilms |
| Abstract: | Unit root tests form an essential part of any time series analysis. We provide practitioners with a single, unified framework for comprehensive and reliable unit root testing in the R package bootUR. The package's backbone is the popular augmented Dickey-Fuller (ADF) test, which can be performed directly on single time series or multiple (including panel) time series. Accurate inference is ensured through the use of bootstrap methods. The package addresses the needs of both novice users, by providing user-friendly and easy-to-implement functions with sensible default options, as well as expert users, by giving full user-control to adjust the tests to one's desired settings. Our OpenMP-parallelized efficient C++ implementation ensures that all unit root tests are scalable to datasets containing many time series. |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2007.12249&r=all |
| By: | Philippe Goulet Coulombe; Maxime Leroux; Dalibor Stevanovic; St\'ephane Surprenant |
| Abstract: | From a purely predictive standpoint, rotating the predictors' matrix in a low-dimensional linear regression setup does not alter predictions. However, when the forecasting technology either uses shrinkage or is non-linear, it does. This is precisely the fabric of the machine learning (ML) macroeconomic forecasting environment. Pre-processing of the data translates to an alteration of the regularization -- explicit or implicit -- embedded in ML algorithms. We review old transformations and propose new ones, then empirically evaluate their merits in a substantial pseudo-out-sample exercise. It is found that traditional factors should almost always be included in the feature matrix and moving average rotations of the data can provide important gains for various forecasting targets. |
| Date: | 2020–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2008.01714&r=all |
| By: | Jushan Bai; Serena Ng |
| Abstract: | Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section dependence. This paper presents simplified proofs for the estimates by using alternative rotation matrices, exploiting properties of low rank matrices, as well as the singular value decomposition of the data in addition to its covariance structure. These simplifications facilitate interpretation of results and provide a more friendly introduction to researchers new to the field. New results are provided to allow linear restrictions to be imposed on factor models. |
| Date: | 2020–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2008.00254&r=all |