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on Econometric Time Series |
| By: | Susana Campos-Martins (University of Oxford, University of Minho and NIPE); Cristina Amado (University of Minho and NIPE, CREATES and Aarhus University) |
| Abstract: | In this paper, we propose an additive time-varying (or partially time-varying) multivariate model of volatility, where a time-dependent component is added to the extended vector GARCH process for modelling the dynamics of volatility interactions. In our framework, co-dependence in volatility is allowed to change smoothly between two extreme states and second-moment interdependence is identified from these crisis-contingent strucural changes. The estimation of the new time-varying vector GARCH process is simplified using an equation-by-equation estimator for the volatility equations in the first step, and estimating the correlation matrix in the second step. A new Lagrange multiplier test is derived for testing the null hypothesis of constancy co-dependence volatility against a smoothly time-varying interdependence between financial markets. The test appears to be a useful statistical tool for evaluating the adequacy of GARCH equations by testing the presence of significant changes in cross-market volatility transmissions. Monte Carlo simulation experiments show that the test statistic has satisfactory empirical properties in finite samples. An application to sovereign bond yield returns illustrates the modelling strategy of the new specification. |
| Keywords: | Multivariate time-varying GARCH; Volatility spillovers; Time-variation;Lagrange multiplier test; Financial market interdependence. |
| JEL: | C12 C13 C32 C51 G15 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:nip:nipewp:12/2021&r= |
| By: | Lujia Bai; Weichi Wu |
| Abstract: | We consider the problem of testing for long-range dependence for time-varying coefficient regression models. The covariates and errors are assumed to be locally stationary, which allows complex temporal dynamics and heteroscedasticity. We develop KPSS, R/S, V/S, and K/S-type statistics based on the nonparametric residuals, and propose bootstrap approaches equipped with a difference-based long-run covariance matrix estimator for practical implementation. Under the null hypothesis, the local alternatives as well as the fixed alternatives, we derive the limiting distributions of the test statistics, establish the uniform consistency of the difference-based long-run covariance estimator, and justify the bootstrap algorithms theoretically. In particular, the exact local asymptotic power of our testing procedure enjoys the order $O( \log^{-1} n)$, the same as that of the classical KPSS test for long memory in strictly stationary series without covariates. We demonstrate the effectiveness of our tests by extensive simulation studies. The proposed tests are applied to a COVID-19 dataset in favor of long-range dependence in the cumulative confirmed series of COVID-19 in several countries, and to the Hong Kong circulatory and respiratory dataset, identifying a new type of 'spurious long memory'. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.08089&r= |
| By: | Jiti Gao; Bin Peng; Yayi Yan |
| Abstract: | Multivariate dynamic models are widely used in practical studies providing a tractable way to capture evolving interrelationships among multivariate time series, but not many studies focus on inferences. Along this line, a key question is that whether some coefficients (if not all) evolve with time. To settle this issue, the paper develops a Wald-type test statistic for detecting time-invariant parameters in a class of multivariate dynamic time-varying models. Since Gaussian/stationary approximation methods initially proposed for univariate time series settings are inapplicable to the setting under consideration in this paper, we develop an approximation method using a time-varying vector moving average infinity process. We show that the test statistic is asymptotically normal under both the null hypothesis and the local alternative. Simulation studies show that the proposed test has a desirable finite sample performance. |
| Keywords: | multivariate time series, parameter instability, specification testing, time-varying coefficient |
| JEL: | C12 C14 C32 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2021-11&r= |
| By: | Armin Pourkhanali; Jonathan Keith; Xibin Zhang |
| Abstract: | This paper proposes using Chebyshev polynomials to approximate time-varying parameters of a GARCH model, where polynomial coefficients are estimated via numerical optimization using the function gradient descent method. We investigate the asymptotic properties of the estimates of polynomial coefficients and the subsequent estimate of conditional variance. Monte Carlo studies are conducted to examine the performance of the proposed polynomial approximation. With empirical studies of modelling daily returns of the US 30-year T-bond daily closing price and daily returns of the gold futures closing price, we find that in terms of in-sample fitting and out-of-sample forecasting, our proposed time-varying model outperforms the constant-parameter counterpart and a benchmark time-varying model. |
| Keywords: | : Chebyshev polynomials, function gradient descent algorithm, loss function, one-day-ahead forecast |
| JEL: | C14 C58 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2021-15&r= |
| By: | Caporina, Massimiliano; Costola, Michele |
| Abstract: | Analysing causality among oil prices and, in general, among financial and economic variables is of central relevance in applied economics studies. The recent contribution of Lu et al. (2014) proposes a novel test for causality- the DCC-MGARCH Hong test. We show that the critical values of the test statistic must be evaluated through simulations, thereby challenging the evidence in papers adopting the DCC-MGARCH Hong test. We also note that rolling Hong tests represent a more viable solution in the presence of short-lived causality periods. |
| Keywords: | Granger Causality,Hong test,DCC-GARCH,Oil market,COVID-19 |
| JEL: | C10 C13 C32 C58 Q43 Q47 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:safewp:324&r= |
| By: | Curtis Nybo |
| Abstract: | Recently artificial neural networks (ANNs) have seen success in volatility prediction, but the literature is divided on where an ANN should be used rather than the common GARCH model. The purpose of this study is to compare the volatility prediction performance of ANN and GARCH models when applied to stocks with low, medium, and high volatility profiles. This approach intends to identify which model should be used for each case. The volatility profiles comprise of five sectors that cover all stocks in the U.S stock market from 2005 to 2020. Three GARCH specifications and three ANN architectures are examined for each sector, where the most adequate model is chosen to move on to forecasting. The results indicate that the ANN model should be used for predicting volatility of assets with low volatility profiles, and GARCH models should be used when predicting volatility of medium and high volatility assets. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.09489&r= |
| By: | Eiji Kurozumi; Anton Skrobotov |
| Abstract: | In this study, we extend the three-regime bubble model of Pang et al. (2021) to allow the forth regime followed by the unit root process after recovery. We provide the asymptotic and finite sample justification of the consistency of the collapse date estimator in the two-regime AR(1) model. The consistency allows us to split the sample before and after the date of collapse and to consider the estimation of the date of exuberation and date of recovery separately. We have also found that the limiting behavior of the recovery date varies depending on the extent of explosiveness and recovering. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.04500&r= |
| By: | Parley Ruogu Yang; Ryan Lucas; Camilla Schelpe |
| Abstract: | We formally introduce a time series statistical learning method, called Adaptive Learning, capable of handling model selection, out-of-sample forecasting and interpretation in a noisy environment. Through simulation studies we demonstrate that the method can outperform traditional model selection techniques such as AIC and BIC in the presence of regime-switching, as well as facilitating window size determination when the Data Generating Process is time-varying. Empirically, we use the method to forecast S&P 500 returns across multiple forecast horizons, employing information from the VIX Curve and the Yield Curve. We find that Adaptive Learning models are generally on par with, if not better than, the best of the parametric models a posteriori, evaluated in terms of MSE, while also outperforming under cross validation. We present a financial application of the learning results and an interpretation of the learning regime during the 2020 market crash. These studies can be extended in both a statistical direction and in terms of financial applications. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.11156&r= |
| By: | Jean-Pierre Florens; Anna Simoni |
| Abstract: | This paper studies the role played by identification in the Bayesian analysis of statistical and econometric models. First, for unidentified models we demonstrate that there are situations where the introduction of a non-degenerate prior distribution can make a parameter that is nonidentified in frequentist theory identified in Bayesian theory. In other situations, it is preferable to work with the unidentified model and construct a Markov Chain Monte Carlo (MCMC) algorithms for it instead of introducing identifying assumptions. Second, for partially identified models we demonstrate how to construct the prior and posterior distributions for the identified set parameter and how to conduct Bayesian analysis. Finally, for models that contain some parameters that are identified and others that are not we show that marginalizing out the identified parameter from the likelihood with respect to its conditional prior, given the nonidentified parameter, allows the data to be informative about the nonidentified and partially identified parameter. The paper provides examples and simulations that illustrate how to implement our techniques. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.09954&r= |
| By: | Jingtang Ma; Wensheng Yang; Zhenyu Cui |
| Abstract: | Rough volatility models have recently been empirically shown to provide a good fit to historical volatility time series and implied volatility smiles of SPX options. They are continuous-time stochastic volatility models, whose volatility process is driven by a fractional Brownian motion with Hurst parameter less than half. Due to the challenge that it is neither a semimartingale nor a Markov process, there is no unified method that not only applies to all rough volatility models, but also is computationally efficient. This paper proposes a semimartingale and continuous-time Markov chain (CTMC) approximation approach for the general class of rough stochastic local volatility (RSLV) models. In particular, we introduce the perturbed stochastic local volatility (PSLV) model as the semimartingale approximation for the RSLV model and establish its existence , uniqueness and Markovian representation. We propose a fast CTMC algorithm and prove its weak convergence. Numerical experiments demonstrate the accuracy and high efficiency of the method in pricing European, barrier and American options. Comparing with existing literature, a significant reduction in the CPU time to arrive at the same level of accuracy is observed. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.08320&r= |