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on Econometric Time Series |
| By: | Daniel Dzikowski; Carsten Jentsch |
| Abstract: | While seasonality inherent to raw macroeconomic data is commonly removed by seasonal adjustment techniques before it is used for structural inference, this approach might distort valuable information contained in the data. As an alternative method to commonly used structural vector autoregressions (SVAR) for seasonally adjusted macroeconomic data, this paper offers an approach in which the periodicity of not seasonally adjusted raw data is modeled directly by structural periodic vector autoregressions (SPVAR) that are based on periodic vector autoregressions (PVAR) as the reduced form model. In comparison to a VAR, the PVAR does allow not only for periodically time-varying intercepts, but also for periodic autoregressive parameters and innovations variances, respectively. As this larger flexibility leads also to an increased number of parameters, we propose linearly constrained estimation techniques. Overall, SPVARs allow to capture seasonal effects and enable a direct and more refined analysis of seasonal patterns in macroeconomic data, which can provide useful insights into their dynamics. Moreover, based on such SPVARs, we propose a general concept for structural impulse response analyses that takes seasonal patterns directly into account. We provide asymptotic theory for estimators of periodic reduced form parameters and structural impulse responses under flexible linear restrictions. Further, for the construction of confidence intervals, we propose residual-based (seasonal) bootstrap methods that allow for general forms of seasonalities in the data and prove its bootstrap consistency. A real data application on industrial production, inflation and federal funds rate is presented, showing that useful information about the data structure can be lost when using common seasonal adjustment methods. |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2401.14545&r=ets |
| By: | Xuanling Yang; Dong Li; Ting Zhang |
| Abstract: | Economic and financial time series can feature locally explosive behavior when a bubble is formed. The economic or financial bubble, especially its dynamics, is an intriguing topic that has been attracting longstanding attention. To illustrate the dynamics of the local explosion itself, the paper presents a novel, simple, yet useful time series model, called the stochastic nonlinear autoregressive model, which is always strictly stationary and geometrically ergodic and can create long swings or persistence observed in many macroeconomic variables. When a nonlinear autoregressive coefficient is outside of a certain range, the model has periodically explosive behaviors and can then be used to portray the bubble dynamics. Further, the quasi-maximum likelihood estimation (QMLE) of our model is considered, and its strong consistency and asymptotic normality are established under minimal assumptions on innovation. A new model diagnostic checking statistic is developed for model fitting adequacy. In addition two methods for bubble tagging are proposed, one from the residual perspective and the other from the null-state perspective. Monte Carlo simulation studies are conducted to assess the performances of the QMLE and the two bubble tagging methods in finite samples. Finally, the usefulness of the model is illustrated by an empirical application to the monthly Hang Seng Index. |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2401.07038&r=ets |
| By: | Christis Katsouris |
| Abstract: | This article studies identification and estimation for the network vector autoregressive model with nonstationary regressors. In particular, network dependence is characterized by a nonstochastic adjacency matrix. The information set includes a stationary regressand and a node-specific vector of nonstationary regressors, both observed at the same equally spaced time frequencies. Our proposed econometric specification correponds to the NVAR model under time series nonstationarity which relies on the local-to-unity parametrization for capturing the unknown form of persistence of these node-specific regressors. Robust econometric estimation is achieved using an IVX-type estimator and the asymptotic theory analysis for the augmented vector of regressors is studied based on a double asymptotic regime where both the network size and the time dimension tend to infinity. |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2401.04050&r=ets |
| By: | Efthymios Pavlidis |
| Abstract: | Periodically collapsing bubbles, if they exist, induce asymmetric dynamics in asset prices. In this paper, I show that unit root quantile autoregressive models can approximate such dynamics by allowing the largest autoregressive root to take values below unity at low quantiles, which correspond to price crashes, and above unity at upper quantiles, that correspond to bubble expansions. On this basis, I employ two unit root tests based on quantile regressions to detect bubbles. Monte Carlo simulations suggest that the two tests have good size and power properties, and can outperform recursive least-squares-based tests that allow for time variation in persistence. The merits of the two tests are further illustrated in three empirical applications that examine Bitcoin, U.S. equity and U.S. housing markets. In the empirical applications, special attention is given to the issue of controlling for economic fundamentals. The estimation results indicate the presence of asymmetric dynamics that closely match those of the simulated bubble processes. |
| Keywords: | rational bubbles, unit root quantile autoregressions, cryptocurrencies, U.S. house prices, S&P 500 |
| JEL: | C12 C22 G10 R30 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:lan:wpaper:404203101&r=ets |
| By: | Makoto Takahashi; Yuta Yamauchi; Toshiaki Watanabe; Yasuhiro Omori |
| Abstract: | Forecasting volatility and quantiles of financial returns is essential for accurately measuring financial tail risks, such as value-at-risk and expected shortfall. The critical elements in these forecasts involve understanding the distribution of financial returns and accurately estimating volatility. This paper introduces an advancement to the traditional stochastic volatility model, termed the realized stochastic volatility model, which integrates realized volatility as a precise estimator of volatility. To capture the well-known characteristics of return distribution, namely skewness and heavy tails, we incorporate three types of skew-t distributions. Among these, two distributions include the skew-normal feature, offering enhanced flexibility in modeling the return distribution. We employ a Bayesian estimation approach using the Markov chain Monte Carlo method and apply it to major stock indices. Our empirical analysis, utilizing data from US and Japanese stock indices, indicates that the inclusion of both skewness and heavy tails in daily returns significantly improves the accuracy of volatility and quantile forecasts. |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2401.13179&r=ets |
| By: | Zongwu Cai (Department of Economics, University of Kansa, Lawrence, KS 66045, USA); Ying Fang (The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China); Dingshi Tian (Department of Statistics, School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei 430073, China) |
| Abstract: | The estimation and model selection of conditional autoregressive value at risk (CAViaR) model may be computationally intensive and even impractical when the true order of the quantile autoregressive components or the dimension of the other regressors are high. On the other hand, automatic variable selection methods cannot be directly applied to this problem because the quantile lag components are latent. In this paper, we propose to identify the optimal CAViaR model using a two-step approach. The estimation procedure consists of an approximation of the conditional quantile in the first step, followed by an adaptive Lasso penalized quantile regression of the regressors as well as the estimated quantile lag components in the second step. We show that under some mild regularity conditions, the proposed adaptive Lasso penalized quantile estimators enjoy the oracle properties. Finally, the proposed method is illustrated by Monte Carlo simulation study and applied to analyzing the daily data of the S&P500 return series. |
| Keywords: | CAViaR model; Adaptive Lasso; Model selection; Tail risk. |
| JEL: | C32 C51 C58 |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:202403&r=ets |
| By: | Xinshuai Dong; Haoyue Dai; Yewen Fan; Songyao Jin; Sathyamoorthy Rajendran; Kun Zhang |
| Abstract: | Financial data is generally time series in essence and thus suffers from three fundamental issues: the mismatch in time resolution, the time-varying property of the distribution - nonstationarity, and causal factors that are important but unknown/unobserved. In this paper, we follow a causal perspective to systematically look into these three demons in finance. Specifically, we reexamine these issues in the context of causality, which gives rise to a novel and inspiring understanding of how the issues can be addressed. Following this perspective, we provide systematic solutions to these problems, which hopefully would serve as a foundation for future research in the area. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2401.05414&r=ets |