Journal ArticleDOI
Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models
George E. P. Box,David A. Pierce +1 more
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In this paper, it is shown that the residual autocorrelations are to a close approximation representable as a singular linear transformation of the auto-correlations of the errors so that they possess a singular normal distribution.Abstract:
Many statistical models, and in particular autoregressive-moving average time series models, can be regarded as means of transforming the data to white noise, that is, to an uncorrelated sequence of errors. If the parameters are known exactly, this random sequence can be computed directly from the observations; when this calculation is made with estimates substituted for the true parameter values, the resulting sequence is referred to as the "residuals," which can be regarded as estimates of the errors. If the appropriate model has been chosen, there will be zero autocorrelation in the errors. In checking adequacy of fit it is therefore logical to study the sample autocorrelation function of the residuals. For large samples the residuals from a correctly fitted model resemble very closely the true errors of the process; however, care is needed in interpreting the serial correlations of the residuals. It is shown here that the residual autocorrelations are to a close approximation representable as a singular linear transformation of the autocorrelations of the errors so that they possess a singular normal distribution. Failing to allow for this results in a tendency to overlook evidence of lack of fit. Tests of fit and diagnostic checks are devised which take these facts into account.read more
Citations
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Journal ArticleDOI
Towards an improved Adaboost algorithmic method for computational financial analysis
TL;DR: The use of the proposed machine learning algorithm; an Adaptive Boosting (Adaboost) algorithm, in analyzing and forecasting financial nonstationary data, and demonstrating its feasibility in financial trading is presented.
Proceedings ArticleDOI
Timing of Autonomous Driving Software: Problem Analysis and Prospects for Future Solutions
Miguel Alcon,Hamid Tabani,Leonidas Kosmidis,Enrico Mezzetti,Jaume Abella,Francisco J. Cazorla +5 more
TL;DR: This work statistically characterize its observed execution time variability and reason on the sources behind it and shows the main traits for the acceptability of statistical timing analysis techniques as a feasible path for Apollo timing analysis.
Journal ArticleDOI
Spatial forecasting of solar radiation using ARIMA model
TL;DR: In this paper, the seasonal ARIMA (SARIMA) model is used for simulating and forecasting time series of insolation data from NASA's POWER (Prediction of Worldwide Energy Resources) data archive.
Journal ArticleDOI
Forecasting crude oil price: Does exist an optimal econometric model?
Vinicius Phillipe de Albuquerquemello,Rennan Kertlly de Medeiros,Cássio da Nóbrega Besarria,Sinézio Fernandes Maia +3 more
TL;DR: In this article, a Self-Exciting Threshold Auto-regressive (SETAR) model was proposed, which automatically allows for regime switching after a threshold, hence achieving a Root Mean Square Error (RMSE) of 2%.
Journal ArticleDOI
Testing the adaptive market hypothesis as an evolutionary perspective on market efficiency: Evidence from the crude oil prices
TL;DR: In this paper, the authors examined the existence of the adaptive market hypothesis (AMH) as an evolutionary alternative to the efficient market hypothesis by applying daily returns on the three benchmark crude oils.
References
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Time series analysis, forecasting and control
TL;DR: In this article, a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970 is presented, focusing on practical techniques throughout, rather than a rigorous mathematical treatment of the subject.
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Journal ArticleDOI
A Note on the Generation of Random Normal Deviates
Journal ArticleDOI
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Journal ArticleDOI
On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers
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