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on Econometric Time Series |
| By: | Jiti Gao; Bin Peng; Yayi Yan |
| Abstract: | This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this framework can be used to estimate shifts in the predictability of non-stationary variables, test whether economic theories hold periodically, etc. We first develop a time-varying Granger Representation Theorem, which facilitates the establishment of asymptotic properties for the model, and then propose estimation and inferential methods and theory for both short-run and long-run coefficients. We also propose an information criterion to estimate the lag length, a singular-value ratio test to determine the cointegration rank, and a hypothesis test to examine the parameter stability. To validate the theoretical findings, we conduct extensive simulations. Finally, we demonstrate the empirical relevance by applying the framework to investigate the rational expectations hypothesis of the U.S. term structure. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.17829&r=ets |
| By: | Giovanni Ballarin |
| Abstract: | Linear time series models are the workhorse of structural macroeconometric analysis. However, economic theory as well as data suggests that nonlinear and asymmetric effects might be important to study to understand the potential effects of policy makers' choices. Taking a dynamical system view, this paper compares known approaches to construct impulse responses in nonlinear time series models and proposes a new approach that more directly relies on the underlying model properties. Nonparametric estimation of autoregressive models is discussed under natural physical dependence assumptions as well as inference for structural impulse responses. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.19089&r=ets |
| By: | Christian Holberg; Susanne Ditlevsen |
| Abstract: | Uniformly valid inference for cointegrated vector autoregressive processes has so far proven difficult due to certain discontinuities arising in the asymptotic distribution of the least squares estimator. We show how asymptotic results from the univariate case can be extended to multiple dimensions and how inference can be based on these results. Furthermore, we show that the novel instrumental variable procedure proposed by [20] (IVX) yields uniformly valid confidence regions for the entire autoregressive matrix. The results are applied to two specific examples for which we verify the theoretical findings and investigate finite sample properties in simulation experiments. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.03632&r=ets |
| By: | Haiqi Li Author-Name-First: Haiqi (College of Finance and Statistics, Hunan University, Changsha, China); Jing Zhang (College of Finance and Statistics, Hunan University, Changsha, China); Chaowen Zheng (Department of Economics, University of Reading) |
| Abstract: | This paper proposes a generalized quantile cointegrating regressive model for nonstationary time series, allowing coefficients to be unknown functions of informative covariates at each quantile level. Using a local polynomial quantile regressive method, we obtain the estimator for the functional coefficients at each quantile level, which is shown to be nonparametrically super-consistent. To alleviate the endogeneity of the model, this paper proposes a fully modified local polynomial quantile cointegrating regressive estimator which is shown to follow a mixed normal distribution asymptotically. We then propose two types of test statistics related to functional coefficient quantile cointegrating model. The first is to test the stability of the cointegrating vector to determine whether the conventional fixed-coefficient cointegration model is appropriate or not. The second is to test the presence of the varying coefficient cointegrating relationship among the economic variables based on a modified quantile residual cumulative sum (MQCS) statistic. Monte Carlo simulation results show that the two tests perform quite well in finite samples. Finally, by using the proposed functional coefficient quantile cointegrating model, this paper examines the validity of the purchasing power parity (PPP) theory between China, Japan, South Korea and the United States, respectively. |
| Keywords: | bootstrap method, functional coefficient quantile cointegrating model, local polynomial approach, PPP theory |
| JEL: | C12 C13 |
| Date: | 2023–06–12 |
| URL: | http://d.repec.org/n?u=RePEc:rdg:emxxdp:em-dp2023-07&r=ets |
| By: | Christian Gourieroux; Quinlan Lee |
| Abstract: | The goal of this paper is to extend the method of estimating Impluse Response Functions (IRFs) by means of Local Projection (LP) in a nonlinear dynamic framework. We discuss the existence of a nonlinear autoregressive representation for a Markov process, and explain how their Impulse Response Functions are directly linked to the nonlinear Local Projection, as in the case for the linear setting. We then present a nonparametric LP estimator, and compare its asymptotic properties to that of IRFs obtained through direct estimation. We also explore issues of identification for the nonlinear IRF in the multivariate framework, which remarkably differs in comparison to the Gaussian linear case. In particular, we show that identification is conditional on the uniqueness of deconvolution. Then, we consider IRF and LP in augmented Markov models. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.18145&r=ets |
| By: | Eiji Kurozumi; Anton Skrobotov |
| Abstract: | In this study, we consider a four-regime bubble model under the assumption of time-varying volatility and propose the algorithm of estimating the break dates with volatility correction: First, we estimate the emerging date of the explosive bubble, its collapsing date, and the recovering date to the normal market under assumption of homoskedasticity; second, we collect the residuals and then employ the WLS-based estimation of the bubble dates. We demonstrate by Monte Carlo simulations that the accuracy of the break dates estimators improve significantly by this two-step procedure in some cases compared to those based on the OLS method. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.02977&r=ets |
| By: | Atsushi Inoue; \`Oscar Jord\`a; Guido M. Kuersteiner |
| Abstract: | An impulse response function describes the dynamic evolution of an outcome variable following a stimulus or treatment. A common hypothesis of interest is whether the treatment affects the outcome. We show that this hypothesis is best assessed using significance bands rather than relying on commonly displayed confidence bands. Under the null hypothesis, we show that significance bands are trivial to construct with standard statistical software using the LM principle, and should be reported as a matter of routine when displaying impulse responses graphically. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.03073&r=ets |
| By: | Andrew J. Patton; Yasin Simsek |
| Abstract: | We propose methods to improve the forecasts from generalized autoregressive score (GAS) models (Creal et. al, 2013; Harvey, 2013) by localizing their parameters using decision trees and random forests. These methods avoid the curse of dimensionality faced by kernel-based approaches, and allow one to draw on information from multiple state variables simultaneously. We apply the new models to four distinct empirical analyses, and in all applications the proposed new methods significantly outperform the baseline GAS model. In our applications to stock return volatility and density prediction, the optimal GAS tree model reveals a leverage effect and a variance risk premium effect. Our study of stock-bond dependence finds evidence of a flight-to-quality effect in the optimal GAS forest forecasts, while our analysis of high-frequency trade durations uncovers a volume-volatility effect. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.18991&r=ets |