The Estimation of the Order of an ARMA Process
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In this article, strong consistency of estimates of the maximum lags of an autoregressive moving average process is established under general conditions, and a theorem on weak consistency is also proved and in certain cases where consistency does not hold the probability of overestimation of a maximum lag is evaluated.Abstract:
Under general conditions strong consistency of certain estimates of the maximum lags of an autoregressive moving average process is established. A theorem on weak consistency is also proved and in certain cases where consistency does not hold the probability of over-estimation of a maximum lag is evaluated.read more
Citations
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Conditional heteroskedasticity in asset returns: a new approach
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Regression and time series model selection in small samples
TL;DR: In this article, a bias correction to the Akaike information criterion, called AICC, is derived for regression and autoregressive time series models, which is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample sample size.
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Introduction to Time Series and Forecasting.
TL;DR: A general approach to Time Series Modelling and ModeLLing with ARMA Processes, which describes the development of a Stationary Process in Terms of Infinitely Many Past Values and the Autocorrelation Function.
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Statistical Analysis in Climate Research
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Introduction to time series and forecasting
TL;DR: In this paper, the authors present a general approach to time series analysis based on simple time series models and the Autocorrelation Function (AFF) and the Wold Decomposition.
References
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TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.
Estimating the dimension of a model
TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.
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TL;DR: The number of digits it takes to write down an observed sequence x1,...,xN of a time series depends on the model with its parameters that one assumes to have generated the observed data.
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The determination of the order of an autoregression
E. J. Hannan,Barry G. Quinn +1 more
TL;DR: In this article, it was shown that a strongly consistent estimation procedure for the order of an autoregression can be based on the law of the iterated logarithm for the partial autocorrelations.