Time-varying parameter auto-regressive models for autocovariance nonstationary time series

In this paper, autocovariance nonstationary time series is clearly defined on a family of time series. We propose three types of TVPAR (time-varying parameter auto-regressive) models: the full order TVPAR model, the time-unvarying order TVPAR model and the time-varying order TV-PAR model for autocovariance nonstationary time series. Related minimum AIC (Akaike information criterion) estimations are carried out.

Uniform Convergence Rate of Estimators of Autocovariances in Partly Linear Regression Models with Correlated Errors

Consider the partly linear regression model , where y i ’s are responses, are known and nonrandom design points, is a compact set in the real line , β = (β 1, ··· , β p )' is an unknown parameter vector, g(·) is an unknown function and {ε i } is a linear process, i.e., , where e j are i.i.d. random variables with zero mean and variance . Drawing upon B-spline estimation of g(·) and least squares estimation of β, we construct estimators of the autocovariances of {ε i }. The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {ε i } are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coeffcients of the process. Moreover, our result can be used to construct the asymptotically effcient estimators for parameters in the ARMA error process.

CONVERGENCE OF THE CLIPPED SAMPLE AUTOCORRELATION AND AUTOCOVARIANCE

Statistics composed of clipped binary sequences are not sensitive to the existence of outliers.We estimate the autocorrelation and autocovariance functions of a linear Gaussian stationary sequence by the clipped binary series, and show the law of the iterated logarithm and the central limit theorem for these statistics.

CHARACTERISTIC FUNCTIONS OF BILINEAR TIME SERIES MODEL

Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help of Volterra seriesexpansion,the impulse response function and frequency characteristic function of thegeneral bilinear time series model are also derived.

Origin of Dynamic Correlations of Words in Written Texts

In a previous study, we introduced dynamical aspects of written texts by regarding serial sentence number from the first to last sentence of a given text as discretized time. Using this definition of a textual timeline, we defined an autocorrelation function (ACF) for word occurrences and demonstrated its utility both for representing dynamic word correlations and for measuring word importance within the text. In this study, we seek a stochastic process governing occurrences of a given word having strong dynamic correlations. This is valuable because words exhibiting strong dynamic correlations play a central role in developing or organizing textual contexts. While seeking this stochastic process, we find that additive binary Markov chain theory is useful for describing strong dynamic word correlations, in the sense that it can reproduce characteristics of autocovariance functions (an unnormalized version of ACFs) observed in actual written texts. Using this theory, we propose a model for time-varying probability that describes the probability of word occurrence in each sentence in a text. The proposed model considers hierarchical document structures such as chapters, sections, subsections, paragraphs, and sentences. Because such a hierarchical structure is common to most documents, our model for occurrence probability of words has a wide range of universality for interpreting dynamic word correlations in actual written texts. The main contributions of this study are, therefore, finding usability of the additive binary Markov chain theory to analyze dynamic correlations in written texts and offering a new model of word occurrence probability in which common hierarchical structure of documents is taken into account.

Evaluating the eff ect of input variables on quantifying the spatial distribution of croaker Johnius belangerii in Haizhou Bay,China

A habitat model has been widely used to manage marine species and analyze relationship between species distribution and environmental factors.The predictive skill in habitat model depends on whether the models include appropriate explanatory variables.Due to limited habitat range,low density,and low detection rate,the number of zero catches could be very large even in favorable habitats.Excessive zeroes will increase the bias and uncertainty in estimation of habitat.Therefore,appropriate explanatory variables need to be chosen first to prevent underestimate or overestimate species abundance in habitat models.In addition,biotic variables such as prey data and spatial autocovariate(SAC)of target species are often ignored in species distribution models.Therefore,we evaluated the eff ects of input variables on the performance of generalized additive models(GAMs)under excessive zero catch(>70%).Five types of input variables were selected,i.e.,(1)abiotic variables,(2)abiotic and biotic variables,(3)abiotic variables and SAC,(4)abiotic,biotic variables and SAC,and(5)principal component analysis(PCA)based abiotic and biotic variables and SAC.Belanger’s croaker Johnius belangerii is one of the dominant demersal fish in Haizhou Bay,with a large number of zero catches,thus was used for the case study.Results show that the PCA-based GAM incorporated with abiotic and biotic variables and SAC was the most appropriate model to quantify the spatial distribution of the croaker.Biotic variables and SAC were important and should be incorporated as one of the drivers to predict species distribution.Our study suggests that the process of input variables is critical to habitat modelling,which could improve the performance of habitat models and enhance our understanding of the habitat suitability of target species.

Explicit bivariate rate functions for large deviations in AR(1)and MA(1)processes with Gaussian innovations

We investigate the large deviations properties for centered stationary AR(1)and MA(1)processes with independent Gaussian innovations,by giving the explicit bivariate rate functions for the sequence of two-dimensional random vectors.Via the Contraction Principle,we provide the explicit rate functions for the sample mean and the sample second moment.In the AR(1)case,we also give the explicit rate function for the sequence of two-dimensional random vectors(W_(n))n≥2=(n^(-1(∑_(k=1)^(n)X_(k),∑_(k=1)^(n)X_(k)^(2))))_(n∈N)n≥2,but we obtain an analytic rate function that gives different values for the upper and lower bounds,depending on the evaluated set and its intersection with the respective set of exposed points.A careful analysis of the properties of a certain family of Toeplitz matrices is necessary.The large deviations properties of three particular sequences of one-dimensional random variables will follow after we show how to apply a weaker version of the Contraction Principle for our setting,providing new proofs for two already known results on the explicit deviation function for the sample second moment and Yule-Walker estimators.We exhibit the properties of the large deviations of the first-order empirical autocovariance,its explicit deviation function and this is also a new result.

Development of a first order integrated moving average model corrupted with a Markov modulated convex combination of autoregressive moving average errors

With a view to providing a tool to accurately model time series processes which may be corrupted with errors such as measurement,round-off and data aggregation,this study developedan integrated moving average(IMA)model with a transition matrix for the errors resulting ina convex combination of two ARMA errors.Datasets on interest rates in the United States andNigeria were used to demonstrate the application of the formulated model.Basic tools such asthe autocovariance function,maximum likelihood method,Newton–Raphson iterative methodand Kolmogorov–Smirnov test statistic were employed to examine and fit the formulated specification to data.Test results showed that the proposed model provided a generalisation and amore flexible specification than the existing models of AR error and ARMA error in fitting timeseries processes in the presence of errors.