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on Econometric Time Series |
| By: | Stéphane Lhuissier |
| Abstract: | We examine Markov-switching autoregressive models where the commonly used Gaussian assumption for disturbances is replaced with a skew-normal distribution. This allows us to detect regime changes not only in the mean and the variance of a specified time series, but also in its skewness. A Bayesian framework is developed based on Markov chain Monte Carlo sampling. Our informative prior distributions lead to closed-form full conditional posterior distributions, whose sampling can be efficiently conducted within a Gibbs sampling scheme. The usefulness of the methodology is illustrated with a real-data example from U.S. stock markets. |
| Keywords: | Regime switching, Skewness, Gibbs-sampler, time series analysis, upside and downside risks. |
| JEL: | C01 C11 C2 G11 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:bfr:banfra:726&r=all |
| By: | Du Nguyen |
| Abstract: | We show Vector Autoregressive Moving Average models with scalar Moving Average components could be estimated by generalized least square (GLS) for each fixed moving average polynomial. The conditional variance of the GLS model is the concentrated covariant matrix of the moving average process. Under GLS the likelihood function of these models has similar format to their VAR counterparts. Maximum likelihood estimate can be done by optimizing with gradient over the moving average parameters. These models are inexpensive generalizations of Vector Autoregressive models. We discuss a relationship between this result and the Borodin-Okounkov formula in operator theory. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.00386&r=all |
| By: | Yixiao Li; Gloria Lin; Thomas Lau; Ruochen Zeng |
| Abstract: | The objective of the change-point detection is to discover the abrupt property changes lying behind the time-series data. In this paper, we firstly summarize the definition and in-depth implication of the changepoint detection. The next stage is to elaborate traditional and some alternative model-based changepoint detection algorithms. Finally, we try to go a bit further in the theory and look into future research directions. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.07136&r=all |
| By: | Tore Selland Kleppe; Roman Liesenfeld; Guilherme Valle Moura; Atle Oglend |
| Abstract: | We propose a factor state-space approach with stochastic volatility to model and forecast the term structure of future contracts on commodities. Our approach builds upon the dynamic 3-factor Nelson-Siegel model and its 4-factor Svensson extension and assumes for the latent level, slope and curvature factors a Gaussian vector autoregression with a multivariate Wishart stochastic volatility process. Exploiting the conjugacy of the Wishart and the Gaussian distribution, we develop a computationally fast and easy to implement MCMC algorithm for the Bayesian posterior analysis. An empirical application to daily prices for contracts on crude oil with stipulated delivery dates ranging from one to 24 months ahead show that the estimated 4-factor Svensson model with two curvature factors provides a good parsimonious representation of the serial correlation in the individual prices and their volatility. It also shows that this model has a good out-of-sample forecast performance. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.07798&r=all |
| By: | Yang Hu (University of Waikato); Yang (Greg) Hou (University of Waikato); Les Oxley (University of Waikato) |
| Abstract: | This paper investigates the causal relationships, cointegration and price discovery between spot and futures markets of Bitcoin using the daily data from a time-varying perspective for the first time in the literature. We apply the time-varying Granger causality test of Shi et al. (2018) to explore the causal relationship between spot and futures markets and find that futures prices Granger cause spot prices. We identify the existence of a cointegration relationship under the consideration of a time-varying cointegrating coefficient between spot and futures prices based on the Park and Hahn (1999) test. We also explore the time-varying price discovery process and find that futures prices dominate in the process, implying a leading informational role. |
| Keywords: | Bitcoin; futures; time-varying; causality; cointegration; price discovery |
| JEL: | C5 G12 G13 G14 |
| Date: | 2019–08–31 |
| URL: | http://d.repec.org/n?u=RePEc:wai:econwp:19/13&r=all |
| By: | Peter Carr; Sander Willems |
| Abstract: | This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts around a constant level, with a speed of mean reversion that is affine in the instantaneous volatility level. The steady-state distribution of the instantaneous volatility belongs to the class of Generalized Inverse Gaussian distributions. We show that the quadratic term in the drift is crucial to avoid moment explosions and to preserve the martingale property of the stock price process. Using a conveniently chosen change of measure, we relate the model to the class of polynomial diffusions. This remarkable relation allows us to develop a highly accurate option price approximation technique based on orthogonal polynomial expansions. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.07417&r=all |