Showing papers in "Journal of Time Series Analysis in 1980"
TL;DR: Generation and estimation of these models are considered and applications on generated and real data presented, showing potentially useful long-memory forecasting properties.
Abstract: . The idea of fractional differencing is introduced in terms of the infinite filter that corresponds to the expansion of (1-B)d. When the filter is applied to white noise, a class of time series is generated with distinctive properties, particularly in the very low frequencies and provides potentially useful long-memory forecasting properties. Such models are shown to possibly arise from aggregation of independent components. Generation and estimation of these models are considered and applications on generated and real data presented.
3,250 citations
TL;DR: In this paper, the authors describe statistical tests for testing the assumption that the series conforms to a linear model, based on the bispectral density function, and demonstrate these tests with two real time series and four simulated time series.
Abstract: . A standard assumption that is often made in time series analysis is that the series conforms to a linear model. The object of this paper is to describe statistical tests for testing this assumption. The tests are constructed from the bispectral density function, and depend on the application of Hotelling T2. These tests are illustrated with two real time series and four simulated time series. Some guidelines about the choice of the parameters are also included.
318 citations
TL;DR: A sequential type of recursive algorithm for identifying state‐dependent models is described, and it is shown how such models may be used for forecasting and for indicating specific types of non‐linear behaviour.
Abstract: . We construct a general class of non-linear models, called ‘state-dependent models’, which have a very flexible non-linear structure and which contain, as special cases, bilinear, threshold autoregressive, and exponential autoregressive models. We describe a sequential type of recursive algorithm for identifying state-dependent models, and show how such models may be used for forecasting and for indicating specific types of non-linear behaviour.
289 citations
TL;DR: In this paper, the basic ideas underlying the construction of a newly introduced seasonal adjustment procedure by a Bayesian modeling are discussed in detail, with particular emphasis on the use of the concept of the likelihood of a bayesian model for model selection.
Abstract: The basic ideas underlying the construction of a newly introduced seasonal adjustment procedure by a Bayesian modeling are discussed in detail. Particular emphasis is placed on the use of the concept of the likelihood of a Bayesian model for model selection. The performance of the procedure is illustrated by a numerical example.
149 citations
TL;DR: In this paper, a two-stage regression procedure is used to estimate the unknown parameters of a class of random coefficient autoregressive models, and the estimates are shown to satisfy a central limit theorem.
Abstract: . This paper is concerned with autoregressive models in which the coefficients are assumed to be not constant but subject to random perturbations so that we are considering a class of random coefficient autoregressive models. By means of a two stage regression procedure estimates of the unknown parameters of these models are obtained. The estimates are shown to be strongly consistent and to satisfy a central limit theorem. A number of Monte Carlo experiments was carried out to illustrate the estimation procedure and their results are reported.
74 citations
TL;DR: In this article, it was shown that the empirical distribution of a set of observations from a stationary time series with spectral density f(ω) converges almost surely to the distribution with density exp(-x) under appropriate conditions, and the same methods were used to prove the convergence of an estimate of the prediction error variance constructed from the I(ωj) and the complex empirical distribution function based on the Fourier coefficients.
Abstract: . The empirical distribution function of yi=I(ωj)/{2πf(ωj)}, ωj= 2πj/T, where I(ω) is the periodogram for a set of observations from a stationary time series with spectral density f(ω), is shown to converge, almost surely, to the distribution with density exp(- x), under appropriate conditions. The same methods are used to prove the convergence, almost surely, of an estimate of the prediction error variance constructed from the I(ωj) and of the complex empirical distribution function based on the Fourier coefficients.
57 citations
TL;DR: In this article, the theoretical relationship between the skewness and kurtosis of an ARMA process and the corresponding parameters of its generating noise series and the implications of these results are considered.
Abstract: . ARMA processes with non-normal residuals have applications in surface metrology and have recently been shown by Nelson and Granger (1979) to occur in modelling economic time series. In this paper we obtain the theoretical relationship between the skewness and kurtosis of an ARMA process and the corresponding parameters of its generating noise series and consider some of the implications of these results. Simulation methods for any ARMA process with given skewness and kurtosis, using Johnson transformations are briefly discussed.
41 citations
TL;DR: In this paper, the third-order periodogram is used for the estimation of frequency triples with ω3 = 2ω -ω1ω2, ω2.
Abstract: . Given a stretch of time series values, the third-order periodogram is investigated as a criterion for use in the estimation of bifrequencies, that is of frequency triples (ω1ω2, ω3) with ω3= 2ω -ω1ω2. The least squares estimates of such frequencies are compared with estimates derived by maximizing the modulus of the third-order periodogram. It is found that neither estimation procedure is uniformly better than the other.
36 citations
TL;DR: In this article, for finite order normal autoregressive models, sufficient conditions for the existence of maximum likelihood estimates are given, and some cases not satisfying the conditions are studied. But they do not cover all cases where maximum likelihood does not always exist.
Abstract: . In finite order normal moving average models the maximum likelihood estimates always exist. For finite order normal autoregressive models sufficient conditions for the existence of maximum likelihood estimates is given. Some cases not satisfying the conditions are studied.
13 citations
TL;DR: In this paper, the authors examined the difficulties in fitting simple non-seasonal models to seasonally adjusted time series data and found that the fitting of such models can be difficult.
Abstract: . This paper examines, with reference to some well known data, possible difficulties in the fitting of simple non-seasonal models to seasonally adjusted time series data.
9 citations
TL;DR: In this article, a time-lag interpretation is given for the group delay between continuous-time weakly-stationary stochastic processes, and a corresponding time-lag relationship between continuous time weaklystationary processes is revealed.
Abstract: . A time-lag interpretation is given for the group delay between continuous-time weakly-stationary stochastic processes, and a corresponding time-lag relationship between stochastic processes is revealed. The group delay for discrete-time processes and its relationship to time leakage are also discussed.
TL;DR: In the last few years, there has been considerable interest in the accounting literature in time series methods as mentioned in this paper, and a survey of the areas of accounting in which time series analysis has proved useful.
Abstract: . In the last few years there has been considerable interest in the accounting literature in time series methods. This paper briefly surveys those areas of accounting in which time series analysis has proved useful and discusses the analytical procedures that have been employed.
TL;DR: This article developed a test of the natural-rate hypothesis that does not require strong assumptions about the structure of the economy or how the public anticipates inflation, and applied this test to U.S. data.
Abstract: . This paper develops a test of the natural-rate hypothesis that does not require strong assumptions about the structure of the economy or how the public anticipates inflation. The paper then applies this test to U.S. data, finding that one cannot reject the natural-rate hypothesis.