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on Econometric Time Series |
| By: | Ziwei Mei; Zhentao Shi |
| Abstract: | In a high dimensional linear predictive regression where the number of potential predictors can be larger than the sample size, we consider using LASSO, a popular L1-penalized regression method, to estimate the sparse coefficients when many unit root regressors are present. Consistency of LASSO relies on two building blocks: the deviation bound of the cross product of the regressors and the error term, and the restricted eigenvalue of the Gram matrix of the regressors. In our setting where unit root regressors are driven by temporal dependent non-Gaussian innovations, we establish original probabilistic bounds for these two building blocks. The bounds imply that the rates of convergence of LASSO are different from those in the familiar cross sectional case. In practical applications given a mixture of stationary and nonstationary predictors, asymptotic guarantee of LASSO is preserved if all predictors are scale-standardized. In an empirical example of forecasting the unemployment rate with many macroeconomic time series, strong performance is delivered by LASSO when the initial specification is guided by macroeconomic domain expertise. |
| Date: | 2022–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2212.07052&r=ets |
| By: | Meyer-Gohde, Alexander; Shabalina, Ekaterina |
| Abstract: | In this paper, we propose a new method to forecast macroeconomic variables that combines two existing approaches to mixed-frequency data in DSGE models. The first existing approach estimates the DSGE model in a quarterly frequency and uses higher frequency auxiliary data only for forecasting (see Giannone, Monti and Reichlin (2016)). The second method transforms a quarterly state space into a monthly frequency and applies, e.g., the Kalman filter when faced missing observations (see Foroni and Marcellino (2014)). Our algorithm combines the advantages of these two existing approaches, using the information from monthly auxiliary variables to inform in-between quarter DSGE estimates and forecasts. We compare our new method with the existing methods using simulated data from the textbook 3-equation New Keynesian model (see, e.g., Galí (2008)) and real-world data with the Smets and Wouters (2007) model. With the simulated data, our new method outperforms all other methods, including forecasts from the standard quarterly model. With real world data, incorporating auxiliary variables as in our method substantially decreases forecasting errors for recessions, but casting the model in a monthly frequency delivers better forecasts in normal times. |
| Keywords: | Mixed-frequency data, DSGE models, Forecasting, Estimation, Temporal aggregation |
| JEL: | E12 E17 E37 E44 C61 C68 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:imfswp:175&r=ets |
| By: | Jiaqi Li; Likai Chen; Kun Ho Kim; Tianwei Zhou |
| Abstract: | We introduce a new methodology to conduct simultaneous inference of non-parametric trend in a partially linear time series regression model where the trend is a multivariate unknown function. In particular, we construct a simultaneous confidence region (SCR) for the trend function by extending the high-dimensional Gaussian approximation to dependent processes with continuous index sets. Our results allow for a more general dependence structure compared to previous works and are widely applicable to a variety of linear and non-linear auto-regressive processes. We demonstrate the validity of our proposed inference approach by examining the finite-sample performance in the simulation study. The method is also applied to a real example in time series: the forward premium regression, where we construct the SCR for the foreign exchange risk premium in the exchange rate data. |
| Date: | 2022–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2212.10359&r=ets |
| By: | Ke-Li Xu (Indiana University, Department of Economics) |
| Abstract: | This paper provides the uniform asymptotic theory for local projection (LP) regression when the true lag order of the model is unknown, possibly in nity. The theory allows for various persistence levels of the data, growing response horizons, and general conditionally heteroskedastic shocks. Based on the theory, we make two contributions. First, we show that LPs are semiparametrically efficient under classical assumptions on data and horizons if the controlled lag order diverges. Thus the commonly perceived efficiency loss of running LPs is asymptotically negligible with many controls. Second, we propose LP-based inferences for (individual and cumulated) impulse responses with robustness properties not shared by other existing methods. Inference methods using two different standard errors are considered, and neither involves HAR-type correction. The uniform validity for the first method depends on a zero fourth moment condition on shocks, while the validity for the second holds more generally for martingale-difference heteroskedastic shocks. |
| Keywords: | Impulse response; local projection; persistence; semiparametric efficiency; uniform inference |
| Date: | 2023–01 |
| URL: | http://d.repec.org/n?u=RePEc:inu:caeprp:2023001&r=ets |