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...

An algorithm for synthesizing color textures from a small set of parameters is presented in this paper. The synthesis algorithm is based on the 2-D moving average model, and realistic textures resembling many real textures can be synthesized using this algorithm. A maximum likelihood estimation algorithm to estimate parameters from a sample texture is also presented. Using the estimated paramet...

We obtain the rate of growth of long strange segments and the rate of decay of infinite horizon ruin probabilities for a class of infinite moving average processes with exponentially light tails. The rates are computed explicitly. We show that the rates are very similar to those of an i.i.d. process as long as moving average coefficients decay fast enough. If they do not, then the rates are sig...

This paper investigates the (conditional) quasi-likelihood ratio test for the threshold in MA models. Under the hypothesis of no threshold, it is shown that the test statistic converges weakly to a function of the centred Gaussian process. Under local alternatives, it is shown that this test has nontrivial asymptotic power. The results are based on a new weak convergence of a linear marked empi...

The standardized precipitation index (SPI) was used to quantify the classification of drought in the Guanzhong Plain, China. The autoregressive integrated moving average (ARIMA) models were developed to fit and forecast the SPI series. Most of the selected ARIMA models are seasonal models (SARIMA). The forecast results show that the forecasting power of the ARIMA models increases with the incre...

In this paper, we propose a time series based method for analyzing and predicting personal medical data. First, we introduce an auto-regressive integrated moving average model which is good for all time series processes. Second, we describe how to identify a personalized time series model based on the patient’s history information, followed by estimating the parameters in the model. Furthermore...