摘要:

Abstract.This paper considers a mean shift with an unknown shift point in a linear process and estimates the unknown shift point (change point) by the method of least squares. Pre‐shift and post‐shift means are estimated concurrently with the change point. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained when the magnitude of shift is small. It is shown that serial correlation affects the variance of the change point estimator via the sum of the coefficients of the linear process. When the underlying process is autoregressive moving average, a mean shift causes overestimation of its order. A simple procedure is suggested to mitigate the bias in order estimat

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00204.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Abstract.In this paper we consider the estimation of the degree of differencingdin the fractionally integrated autoregressive moving‐average time series model ARFIMA (p, d, q). Using lag window spectral density estimators we develop a regression type estimator ofdwhich is easy to calculate and does not require prior knowledge ofpandq.Some large sample properties of the estimator are studied and the performance of the estimator for small samples is investigated using the simulation method for a range of commonly used lag windows. Some practical recommendations on the choice of lag windows and the choice of the window parameters are provide

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00205.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Abstract.A hidden Markov regime is a Markov process that governs the time or space dependent distributions of an observed stochastic process. We propose a recursive algorithm for parameter estimation in a switching autoregressive process governed by a hidden Markov chain. A common approach to the recursive estimation problem is to base the estimation on suboptimal modifications of Kalman filtering techniques. The main idea in this paper is to use the maximum likelihood method and from this develop a recursive EM algorithm.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00206.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Abstract.Kudo (On the testing of outlying observations.Sankhya17 (1956), 67–73) has derived an optimal invariant detector of a single additive outlier of unknown position in the context of an underlying Gaussian process consisting of independent and identically distributed random variables. We show how this author's arguments can be extended to derive an invariant detector of an additive outlier of unknown position for an underlying zero‐mean Gaussian stochastic process. This invariant detector depends on the parameters of this process; its properties are analysed further for the particular case of an underlying zero‐mean Gaussian AR(p) process. It provides an upper bound on the performance of any invariant detector based solely on the data and it may be ‘bootstrapped’ to provide an invariant detector based solely on the data. A plausibility argument is presented in favour of the proposition that the bootstrapped detector is nearly optimal for sufficiently large data lengthn.The truth of this proposition has been confirmed by simulation results for zero‐mean Gaussian AR(1) and AR(2) processes (for certain sets of possible outlier positions). The bootstrapped detector is shown to be closely related to the detector based on the approximate likelihood ratio criteria of Fox (Outliers in time series.J. Roy. Statist. Soc. Ser. B34 (1972), 350–63) and the leave‐one‐out diagnostic of Bruce and Martin (Leave‐k‐out diagnostics in time series.J. Roy. Statist. Soc. Ser B51 (1989), 363–424). It is also shown how the case of an underlying Gaussian process with arbitrary mean can be reduced to the case of an underlying zer

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00207.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Abstract.In this paper we develop a very general Markov switching model for analysis of economic time series. Our general set‐up allows us to assess the effects of a variety of model and prior assumptions on the results. The growth rates of US quarterly real gross national product are used to illustrate the proposed analysis. We find that although the evidence is not strong the analysis does not support the model in which the dynamic behavior is constant and that allowing the dynamic structure to change affects the results. We also find that the results are sensitive to the prior specificatio

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00208.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Abstract.The assumption of a linear autoregressive model for time series has often been justified on the basis of a maximum entropy principle. The purpose of this short note is to point out that the class of nonlinear autoregressions is also characterized by a maximum entropy property.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00209.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Abstract.In this paper we propose the order determination quantity (ODQ) as a new way to solve order estimation problems in time series analysis. We estimate orders according to ODQ>0 or ODQ<0 instead of by minimizing. Theoretical analysis and simulation have shown that the ODQ has higher identifiability for unknown true orders, provides clear separation points and requires less computational effort than the existing order estimation criteria such as Akaike's information criterion (AIC), Bayes information criterion (BIC),φand predictive least squares (PLS)

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00210.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Abstract.A sign error in the proof of Theorem 3 of the paper by Grayet al.(1989) slightly changes a result of that theorem. In this correction we note the error along with the resulting changes that should be made in the results and the proof of the theorem. Additionally, another minor error in the proof is noted which does not effect the result.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00211.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY