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In this paper, we propose some tests in the time domain to check the equality of autocorrelation structure of multiple (M>2) independent stationary time series. To develop the tests, multiple time series are divided into two groups in different ways. Given that k time series are in one group and M−k time series are in the other group, test statistics TM,k, k=1,2,…,⌊M/2⌋ are the maximum Mahalanobis difference between 2 groups of time series over all possible ways of such grouping. The asymptotic distributions under the null are derived. An extensive simulation is conducted to check the finite sample properties of the test statistics. Suggestion is given on the selection of test statistics under different situations based on the simulation. The paper provides some options to compare multiple time series when the length of time series is relatively short and M is relatively large. An application of the tests on vibrational data analysis is discussed.

Time series where the mean-level changes with time are known as non-stationary processes or processes having a unit root. In this context, for a series to be stationary it needs to be differentiated a sufficient number of times, where the number of differences is known as the integration order I(d). Classical tests for unit root processes consider an integer order of integration, where the null and alternative hypotheses are I(1) and I(0), respectively. However, recently, some research has shown a refinement of these hypotheses where 0≤d≤1. This kind of analysis can be obtained through fractional processes, also known as long-memory models. In this work, we propose, for testing unit roots, the use of the semi-parametric estimator of the fractional parameter of the ARFIMA model suggested by Geweke and Porter-Hudak [Geweke, J. and Porter-Hudak, S., 1983, The estimation and application of long memory time series model. Journal of Time Series Analysis, 4(4), 221–238.], GPH, and a bootstrap version of this tes...

In the traditional Box–Jenkins modelling procedure, we use the sample autocorrelation function as a tool for identifying the plausible models for empirical data. In this paper, we consider the sample normalized codifference as a new tool for the preliminary order identification of pure univariate Gaussian moving average process. From simulation studies, we find that when the number of observations are large (more than 100), the proposed method may be superior than a similar identification procedure which is based on the sample autocorrelation function. Simulation results also indicate that the proposed method may perform as well as Gallagher’s procedure [Gallagher, C., 2002, Order identifi-cation for Gaussian moving averages using the Covariation. Journal of the Statistical Computation and Simulations, 72(4), 279–283.].

This paper presents a trend analysis of monthly riverflows recorded at the Apalachicola River at Chattahoochee, FL during the 1930–2001 water years. The environmental concern is that increasing urbanization upstream (Atlanta and Columbus, GA) increases downstream riverflows. In statistical terms, our objective is to test whether there are months in which riverflows are significantly increasing. For this purpose, a parsimonious periodic autoregressive moving-average time series model is fitted to the error structure of the series. The covariances of this time series model are then used to assess the significance of monthly and yearly linear trend estimators. In the end, we do not find strong evidence of increasing riverflows.

This paper discusses extensions of the popular methods proposed by Geweke and Porter-Hudak [Geweke, J. and Porter-Hudak, S., 1983, The estimation and application of long memory times series models. Journal of Time Series Analysis, 4(4), 221–238.] and Fox and Taqqu [Fox, R. and Taqqu, M.S., 1986, Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Annals of Statistics, 14, 517–532.] for estimating the long-memory parameter of autoregressive fractionally integrated moving average models to the estimation of long-range dependent models with seasonal components. The proposed estimates are obtained from a selection of harmonic frequencies chosen between the seasonal frequencies. The maximum likelihood method given in Beran [Beran, J., 1994, Statistic for Long-Memory Processes (New York: Chapman & Hall).] and the semi-parametric approaches introduced by Arteche and Robinson [Arteche, J. and Robinson, P.M., 2000, Semiparametric inference in seasonal and cyclical...

This article deals with Bayesian analysis of quarter plane moving average (MA) models observed on a rectangular part of a lattice. We present some properties concerning the autocorrelation function of MA models. These properties relate correlation parameters with the original model parameters providing much more understandable interpretation of results concerning the model. Simulation experiment is developed to explore the sensitivity of the posterior distribution when the process is contaminated with innovation and additive contamination. We show by simulation that the correlation structure of the model is seriously affected when the process contains additive contamination. We then propose a more general class of MA models which automatically deals with the contamination phenomenon [contaminated MA (CMA) model]. Also, we establish theoretical properties of the correlation function analogous with those in the previous model. Finally, we consider two applications of the CMA model. The results obtained in n...

In this paper we propose a new identification method based on the residual white noise autoregressive criterion (Pukkila et al., 1990) to select the order of VARMA structures. Results from extensive simulation experiments based on different model structures with varying number of observations and number of component series are used to demonstrate the performance of this new procedure. We also use economic and business data to compare the model structures selected by this order selection method with those identified in other published studies.

In the traditional Box-Jenkins procedure for fitting ARMA time series models to data, the first step is order identification. The sample autocorrelation function can be used to identify pure moving average behavior. In this paper we consider using the autocovariation function identify the order of a univariate Gaussian time series. Simulation evidence indicates the suggested method may be a superior order identification tool when at least 100 observations are taken.

Three implementations of the direct method of obtaining the asymptotic maximum likelihood estimate of a Gaussian Moving Average Process are described. A number of examples are given, some show the general use of the method, the remainder illustrate the rarely appreciated limitations of estimating a Moving Average Process. A listing of one implementation is also given.