Modeling process asymmetries with Laplace moving average

Modeling process asymmetries with Laplace moving average

Many records in environmental science exhibit asymmetries: for example in shallow water and with variable bathymetry, the sea wave time series shows front–back asymmetries and different shapes for crests and troughs. In such situation, numerical models are available but their computational cost and complexity are high. A stochastic process aimed at modeling such asymmetries has recently been pr...

Moving Average Processes with Infinite Variance

The sample autocorrelation function (acf) of a stationary process has played a central statistical role in traditional time series analysis, where the assumption is made that the marginal distribution has a second moment. Now, the classical methods based on acf are not applicable in heavy tailed modeling. Using the codifference function as dependence measure for such processes be shown it be as...

Fault Detection in the Semiconductor Etch Process Using the Seasonal Autoregressive Integrated Moving Average Modeling

In this paper, we investigated the use of seasonal autoregressive integrated moving average (SARIMA) time series models for fault detection in semiconductor etch equipment data. The derivative dynamic time warping algorithm was employed for the synchronization of data. The models were generated using a set of data from healthy runs, and the established models were compared with the experimental...

Complete Convergence for Moving Average Process of Martingale Differences

A Moving Average Exponential Point Process ( Ema 1 )

A construction is given for a stationary sequence of random variables {X.} which have exponential marginal distributions and are random linear combinations of order one of an i.i.d. exponential sequence {e.}. The Joint and trivariate exponential distributions of X.,, X. and X... are studied, as well as the Intensity function, point spectrum and variance time curve for the point process which ha...