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仅用一阶滞后建模长记忆AI 解读

Two recent contributions have found conditions for large dimensional networks or systems to generate long memory in their individual components. We build on these and provide a multivariate methodology for modeling and forecasting series displaying long range dependence. We model long memory properties within a vector autoregressive system of order 1 and consider Bayesian estimation or ridge regression. For these, we derive a theory-driven parametric setting that informs a…

黏性无限隐马尔可夫切换自回归移动平均模型AI 解读

Markov-switching models are usually specified under the assumption that all the parameters change when a regime switch occurs. Relaxing this hypothesis and being able to detect which parameters evolve over time is relevant for interpreting the changes in the dynamics of the series, for specifying models parsimoniously, and may be helpful in forecasting. We propose the class of sticky infinite hidden Markov-switching autoregressive moving average models, in which we…

This paper compares the forecasting performance of models that have been proposed for forecasting in the presence of structural breaks. They differ in their treatment of the break process, the model applied in each regime and the out-of-sample probability of a break. In an extensive empirical evaluation, we demonstrate the presence of breaks and their importance for forecasting. We find no single model that consistently works best in the presence of breaks. In many cases,…

存在结构突变的长记忆过程预测AI 解读

We develop an easy-to-implement method for forecasting a stationary autoregressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an autoregressive (AR) model and suggest using an information criterion (AIC or Mallows’ Cp) to choose the order of the approximate AR model. Our method avoids…

马尔可夫切换 GARCH 模型的理论与推断AI 解读

We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling…