ON THE IDENTIFICATION OF SOME BILINEAR TIME SERIES MODELS (original) (raw)

On the Structure of Third Order Moment and Identification of Bilinear Time Series Model

Calcutta Statistical Association Bulletin, 1988

Kumar(l986) has proposed the criterion of third order moment for the identification of bilinear time series model and discussed its properties with respect to a simple bilinear model, In this paper, we have derived the explicit expressions of third order moment with respect to two terms diagonal model and discussed their properties in identifying the structure of a diagonal model.

Zero-lag white noise vector bilinear autoregressive time series models

The non linear part of a mixed bilinear time series structure seems to pose difficulty if we are to extract the pure autoregressive (AR) bilinear form from the mixed process with the condition that the outcome of such extraction clearly defines itself as an extension from its parent linear AR model. It is therefore of immense interest to address a ' bilinear' situation where the same " order " identified in the linear AR processes are extended to cover the linear and non linear components of a bilinear process with an exception that the lagged white noise process is allowed to remain in its present state. This research focused on these two innovations where the white noise is lagged zero to isolate a pure vector AR bilinear model from a mixed process based on the distribution of autocorrelation and partial autocorrelation function of the different series involved in a vector process, and the extension of the linear 'orders' to bilinear 'orders'. To achieve the aforementioned, we formulated a matrix for a general case of n-dimensional vector for an AR process and then considered a special case of zero lag of white noise. With given conditions, and introduction of diagonal matrix of lagged vector elements, special bilinear expressions reflecting the same 'orders' of the corresponding linear forms emerged. The zero lagged white noise denoted by  it-0 clearly defined our models as pure AR bilinear models since the lag l = 0 and is equivalent to the current state white noise  t of the linear AR process. These gave a brilliant meaning to vector bilinear AR processes in terms of linear AR 'orders'. The workability of these special bilinear models was assessed by applying them to revenue series and the result showed that the models gave a good fit, in support of our idea.

Characterizations of the Moments of the Purely Diagonal Bilinear Time Series Model of Order One

In this paper, we study the similarities and dissimilarities between a purely diagonal bilinear process of order one [PDB(1)] and a moving average process of order one [MA(1)] by comparing their first, second and fourth order moments. The well known similarity between their covariance structure was discovered to be true only when 16. 0 0 1 < < ρ. With respect to the fourth moments, the PDB(1) process identifies as an autoregressive moving average process of order 1 1 = = q and p while the equivalent non-zero mean MA(1) process identifies as an MA(1) process.

On the Autocorrelation Structure and Identification of Some Bilinear Time Series

Journal of Time Series Analysis, 1984

For the bilinear time series X , = pX,-,e,-, + en k P 1, formulas for the first k-1 autocorrelations of X : are obtained. These results fill in a gap in Granger and Andersen (1978). Simulation experiments are used to study the applicability of theoretical results and to investigate some more general situations. It is found that if p is not too small, k and 1 may be identified using the autocorrelations of X:. Application to more general situations is also briefly discussed.

Covariance analysis of the squares of the purely diagonal bilinear time series models

Brazilian Journal of Probability and Statistics, 2011

The covariance structure among other properties of the square of the purely diagonal bilinear time series model is obtained. The time series properties of these squares are compared with those of the linear moving average time series model. It was discovered that the square of a linear moving average process is also identified as a moving average process whereas, while

On The Identification of the Simple Bilinear White Noise Process

2017

Moments of the squares of simple bilinear process were determined under second order analysis for the purpose of identification and discriminating between bilinear process and linear white noise process. We showed how the variance of the bilinear white noise process can be used to distinguish it from the linear white noise process. The simulation results showed that the squared data of the bilinear white noise series fitted the ARMA(2, 1) model better than ARMA(1, 1) and MA(1)) models respectively.

On the Third-Order Moment Structure and Bispectral Analysis of Some Bilinear Time Series

Journal of Time Series Analysis, 1988

For the bilinear time series model X, = p X ,-k et-, + e , , k 1, k = 1 and k i 1 formulae for the third-order theoretical moments and an expression for the bispectral density function are obtained. These results can be used to distinguish between bilinear models and white noise and, in general, linear models. Furthermore, they give an indication of the type combination (k, Q in the above model. The modulus of the bispectral density function of the above bilinear time series model for different combinations of (k, Q and values of /? are computed and the properties are studied.

On the Bilinear Time Series Models Provided by Garch White Noise: Estimation and Simulation

Advances in Mathematics: Scientific Journal, 2020

This work proposes the estimation of a sample of bilinear time series models mixed by a GARCH white noise, where GARCH model was followed by time varying coefficients. The study allows demonstrating some properties and remarks depending on the behavior of the estimators. Moreover, this work will be validated by a simulations study and digital illustrations using the Matlab software.

On the Existence of Some Bilinear Time Series Models

Journal of Time Series Analysis, 1983

The existence of a multivariate strictly stationary stochastic process conform-Keywords. Bilinear time series models, stationary processes, Kronecker product of ing to a certain bilinear time series model is discussed. matrices, spectral radius of a matrix. for every t =. . .-1,O, 1,. .. , for some constants { a l , a2,. .. , a,} and {bij, 1 S i s p , 1 s j s q } and for some sequence {e,, t =. . .-1, 0,1,. . .}of independent identically distributed random variables defined on (fl,B, P) with common mean zero and common variance cr2 < CO. In the notation of Granger and Andersen (1978), the above model is denoted by BARMA (p , 0, p , q). In the notation used by Subba Rao (1981, p. 244), the above model is denoted by BL (p , O,p, q). If 0143-978~/83/02 0095-16 io2.so/o

Subsetting and Identification of Optimal Models in One-Dimensional Bilinear Time Series Modelling

2010

To date, significant efforts have been made to study the theory of bilinear time series models, especially simple bilinear models. Much less efforts, however, have been made to identify optimal models. Focused on optimal model identification, this study attempts to fill this gap. Full and subset one-dimensional bilinear models are proposed and shown to be robust in achieving stationarity for all non-linear series. The parameters of the models are estimated using robust nonlinear least-square method and Newton-Raphson iterative method, and statistical properties of the derived estimates are investigated. An algorithm is proposed to eliminate redundant parameters from full order bilinear models.