As we have remarked, dependence is very common in time series observations. To model this time series dependence, we start with univariate ARMA models. To motivate the model, basically we can track two lines of thinking. First, for a series xt, we can model that the level of its current observations depends on the level of its lagged observations. For example, if we observe a high GDP realizati...

Using the multiple threshold autoregressive and moving average (TARMA) model we analyze the nonlinearities in the dynamics of realized volatilities of daily stock returns of 30 companies in the Dow Jones index. We find that the realized volatility processes can be characterized by the high, moderate, and low regimes and that the persistence, variance and ARMA error term change with each regime....

Autoregressive moving average (ARMA) models are a fundamental tool in time series analysis that offer intuitive modeling capability and efficient predictors. Unfortunately, the lack of globally optimal parameter estimation strategies for these models remains a problem: application studies often adopt the simpler autoregressive model that can be easily estimated by maximizing (a posteriori) like...

An analytically simple and tractable formula for the start-up autocovariances of periodic ARMA (P ARMA) models is provided.

Autoregressive moving average (ARMA) models are useful statistical tools to examine the dynamical characteristics of ecological time-series data. Here, we illustrate the utility and challenges of applying ARMA (p,q) models, where p is the dimension of the autoregressive component of the model, and q is the dimension of the moving average component. We focus on parameter estimation and model sel...