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on Econometric Time Series |
| By: | Zongwu Cai (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA); Gunawan (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA) |
| Abstract: | Structural breaks in time series forecasting can cause inconsistency in the conventional OLS estimator. Recent research suggests combining pre and post-break estimators for a linear model can yield an optimal estimator for weak breaks. However, this approach is limited to linear models only. In this paper, we propose a weighted local linear estimator for a nonlinear model. This estimator assigns a weight based on both the distance of observations to the predictor covariates and their location in time. We investigate the asymptotic properties of the proposed estimator and choose the optimal tuning parameters using multifold cross-validation to account for the dependence structure in time series data. Additionally, we use a nonparametric method to estimate the break date. Our Monte Carlo simulation results provide evidence for the forecasting outperformance of our estimator over the regular nonparametric post-break estimator. Finally, we apply our proposed estimator to forecast GDP growth for nine countries and demonstrate its superior performance compared to the conventional estimator using Diebold-Mariano tests. |
| Keywords: | Combination Forecasting; Local Linear Fitting; Multifold Cross-Validation; Nonparametric Model; Structural Break Model |
| JEL: | C14 C22 C53 |
| Date: | 2023–09 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:202310&r=ets |
| By: | Eric A. Beutner (Vrije Universiteit Amsterdam); Yicong Lin (Vrije Universiteit Amsterdam); Andre Lucas (Vrije Universiteit Amsterdam) |
| Abstract: | We study the in-fill asymptotics of score-driven time series models. For general forms of model mis-specification, we show that score-driven filters are consistent for the Kullback-Leibler (KL) optimal time-varying parameter path, which minimizes the pointwise KL divergence between the statistical model and the unknown dynamic data generating process. This directly implies that for a correctly specified predictive conditional density, score-driven filters consistently estimate the time-varying parameter path even if the model is mis-specified in other respects. We also obtain distributional convergence results for the filtering errors and derive the filter that minimizes the asymptotic filter error variance. Score-driven filters turn out to be optimal under correct specification of the predictive conditional density. The results considerably generalize earlier findings on the continuous-time consistency of volatility filters under mis-specification: they apply to biased filters, use weaker assumptions, allow for more general forms of mis-specification, and consider general time-varying parameters in non-linear time series models beyond the volatility case. Several examples are used to illustrate the theory, including time-varying tail shape models, dynamic copulas, and time-varying regression models. |
| Keywords: | score-driven models, information theoretic optimality, Kullback-Leibler divergence, pseudo true time-varying parameters, in-fill asymptotics. |
| JEL: | C22 C32 |
| Date: | 2023–08–30 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20230051&r=ets |
| By: | German Rodikov; Nino Antulov-Fantulin |
| Abstract: | This paper introduces the $\sigma$-Cell, a novel Recurrent Neural Network (RNN) architecture for financial volatility modeling. Bridging traditional econometric approaches like GARCH with deep learning, the $\sigma$-Cell incorporates stochastic layers and time-varying parameters to capture dynamic volatility patterns. Our model serves as a generative network, approximating the conditional distribution of latent variables. We employ a log-likelihood-based loss function and a specialized activation function to enhance performance. Experimental results demonstrate superior forecasting accuracy compared to traditional GARCH and Stochastic Volatility models, making the next step in integrating domain knowledge with neural networks. |
| Date: | 2023–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2309.01565&r=ets |
| By: | Yicong Lin (Vrije Universiteit Amsterdam); Mingxuan Song (Vrije Universiteit Amsterdam) |
| Abstract: | We propose two robust bootstrap-based simultaneous inference methods for time series models featuring time-varying coefficients and conduct an extensive simulation study to assess their performance. Our exploration covers a wide range of scenarios, encompassing serially correlated, heteroscedastic, endogenous, nonlinear, and nonstationary error processes. Additionally, we consider situations where the regressors exhibit unit roots, thus delving into a nonlinear cointegration framework. We find that the proposed moving block bootstrap and sieve wild bootstrap methods show superior, robust small sample performance, in terms of empirical coverage and length, compared to the sieve bootstrap introduced by Friedrich and Lin (2022) for stationary models. We then revisit two empirical studies: herding effects in the Chinese new energy market and consumption behaviors in the U.S. Our findings strongly support the presence of herding behaviors before 2016, aligning with earlier studies. However, we diverge from previous research by finding no substantial herding evidence between around 2018 and 2021. In the second example, we find a time-varying cointegrating relationship between consumption and income in the U.S. |
| Keywords: | time-varying models, bootstrap inference, simultaneous confidence bands, energy market, nonlinear cointegration. |
| JEL: | C14 C22 C63 Q56 |
| Date: | 2023–08–23 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20230049&r=ets |
| By: | Amilcar Velez |
| Abstract: | This paper contributes to a growing literature on confidence interval construction for impulse response coefficients based on the local projection (LP) approach. We propose an LP-residual bootstrap method to construct confidence intervals for the impulse response coefficients of AR(1) models. The method uses the LP approach and a residual bootstrap procedure to compute critical values. We present two theoretical results. First, we prove the uniform consistency of the LP-residual bootstrap under general conditions, which implies that the proposed confidence intervals are uniformly asymptotically valid. Second, we show that the LP-residual bootstrap can provide asymptotic refinements to the confidence intervals under certain conditions. We illustrate our results with a simulation study. |
| Date: | 2023–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2309.01889&r=ets |
| By: | Eva F. Janssens; Sean McCrary |
| Abstract: | This paper proposes a novel finite-state Markov chain approximation method for Markov processes with continuous support, providing both an optimal grid and transition probability matrix. The method can be used for multivariate processes, as well as non-stationary processes such as those with a life-cycle component. The method is based on minimizing the information loss between a Hidden Markov Model and the true data-generating process. We provide sufficient conditions under which this information loss can be made arbitrarily small if enough grid points are used. We compare our method to existing methods through the lens of an asset-pricing model, and a life-cycle consumption-savings model. We find our method leads to more parsimonious discretizations and more accurate solutions, and the discretization matters for the welfare costs of risk, the marginal propensities to consume, and the amount of wealth inequality a life-cycle model can generate. |
| Keywords: | numerical methods; Kullback–Leibler divergence; misspecified model; earnings process |
| JEL: | C63 C68 D15 E21 |
| Date: | 2023–05–19 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:96642&r=ets |