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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Wavelet coherence analysis of returns, volatility and interdependence of the US and the EU money markets: Pre & post crisis
TL;DR: In this paper, the authors analyze the US and the EU money markets interdependence from 2004 to 2018 and find that correlation rises in periods when countries are exposed to the same external shocks as global financial crisis.
Journal ArticleDOI
Time Series Modeling of Sunspot Numbers Using Long-Range Cyclical Dependence
TL;DR: In this paper, the analysis of the sunspot number time series using a new technique based on cyclical long-range dependence is presented, which shows that sunspot numbers have a periodicity of 130 months but, more importantly, that the series is highly persistent, with an order of cyclical fractional integration slightly above 0.30.
Journal ArticleDOI
Coronavirus Disease 2019 (COVID-19): Forecast of an Emerging Urgency in Pakistan
Rabia Mushtaq Chaudhry,Asif Hanif,Muhammad Chaudhary,Sadia Minhas,Khalid Mirza,Tahira Asif,Syed Amir Gilani,Muhammad Kashif +7 more
TL;DR: There is now an alarming increase in the number of COVID-19 patients in Pakistan, despite a contained spread in the beginning, so it is crucial for governing bodies, administrators, and researchers to re-evaluate the current situation, designed policies, and implemented strategies.
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StockNet - GRU based stock index prediction
TL;DR: In this paper , the authors proposed a new data augmentation approach in their GRU based StockNet model consisting of two modules: Injection module to prohibit overfitting and investigation module for stock index forecasting.
A forecasting model based on time series analysis applied to electrical energy consumption
TL;DR: This paper presents a Time Series Analysis Model and its application to the electricity consumption of public transportation in Sofia (Bulgaria) in 2011, 2012 and 2013, and shows a strongly periodic pattern that will be reconstructed with three different seasonal coefficients.
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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A Note on the Generation of Random Normal Deviates
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On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers
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