In this paper the asymptotic properties of ARMA processes with complex-conjugate unit roots in the AR lag polynomial are studied. These processes behave quite di¤erently from regular unit root processes (with a single root equal to 1). In particular, the asymptotic properties of a standardized version of the periodogram for such processes are analyzed, and a nonparametric test of the complex un...

There has been increased interest in time series data mining recently. In some cases, approaches of real-time segmenting time series are necessary in time series similarity search and data mining, and this is the focus of this paper. A real-time iterative algorithm that is based on time series prediction is proposed in this paper. Proposed algorithm consists of three modular steps. (1) Modeling...

To solve the problem in which the conventional ARMA modeling methods for gyro random noise require a large number of samples and converge slowly, an ARMA modeling method using a robust Kalman filtering is developed. The ARMA model parameters are employed as state arguments. Unknown time-varying estimators of observation noise are used to achieve the estimated mean and variance of the observatio...

The Normalized Prediction Error, or NPE, can be used for the evaluation of the fit of AR models, which are estimated from signals that are generated by an AR process. The NPE does not only provide a measure of the time domain fit, but also of the frequency domain fit of an estimated model. Therefore, it is a measure that can very well be used for comparison of different estimates. In this paper...

In this paper, we propose a cumulant-based estimator for ARMA systems. The polyspectra, cumulants, and various other related statistics, such as bicepstra and bicoherence are all used to develop cumulant-based algorithms for estimating the parameters of linear (e.g. ARMA) or nonlinear processes. The use of cumulant-based estimator is useful: (1) if the additive noise is Gaussian and the signal ...

The well-known prediction-error-based maximum likelihood (PEML) method can only handle minimum phase ARMA models. This likelihood (BFML) method, which can handle nonminimum phase and noncausal ARMA models. The BFML method is identical to the PEML method in the case of a minimum phase ARMA model, and it turns out that the BFML method incorporates a noncausal ARMA filter with poles outside the un...

We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller ...

The time histories of stochastic ocean wave-related processes are simulated by means of computatlonally efficient parametric models The parametric models utdlzed here include the autoregresslve and moving averages (ARMA) algorithms for the simulation of wave height fluctuations, discrete convolution models for linear transformations of given time histories, discrete differentlatmn models for ob...

A feasibility study of using of Dynamic Bayesian Networks in combination with ARMA modeling in exchange rate prediction is presented. A new algorithm (ARMA-DBN) is constructed and applied to the exchange rate forecast of RMB. Results show that the improved dynamic Bayesian forecast algorithm has better performance than the standard ARMA model.

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...