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
Advertising Effects Under Consumer Heterogeneity – The Moderating Role of Brand Experience, Advertising Recall and Attitude
German Zenetti,Daniel Klapper +1 more
TL;DR: In this paper, the authors proposed an econometric framework for measuring the effects of advertising on consumers' purchase decisions by means of the widely used random coefficient logit model for aggregate sales and information about perceptions of advertising at the consumer level.
Journal ArticleDOI
Time series of scientific growth in Spanish doctoral theses (1848---2009)
TL;DR: The main finding is that Spanish output of doctoral theses appears to fit a quasi-logistic growth model in line with Price’s predictions, especially in the historical period from 1899 to 1939.
Journal ArticleDOI
Testing for Serial Correlation: Generalized Andrews–Ploberger Tests
John C. Nankervis,N.E. Savin +1 more
TL;DR: The GARCH(1, 1) model is a leading example of a model that generates serially uncorrelated but statistically dependent data as mentioned in this paper, and the generalized AP tests of serial correlation introduced by Andrews and Ploberger (1996, hereafter AP) are generalized for the purpose of testing the null hypothesis.
Journal ArticleDOI
Relation-aware dynamic attributed graph attention network for stocks recommendation
Shibo Feng,Ishizuka, Takashi,Chen Xu,Yu Zuo,Guo Chen,Fan Lin,Xiahou Jianbing,Xiahou Jianbing +7 more
TL;DR: The RA-AGAT architecture is capable of surpassing the previously applicable methods in the prediction and recommendation of stock return ratio and verified the practicality and applicability of the application of graph models in finance.
Journal ArticleDOI
Pareto Random Variables for Hydrological Modeling
Saralees Nadarajah,M. Masoom Ali +1 more
TL;DR: In this paper, the exact distributions of the sum X + Y, the product XY and the ratio X/(X + Y) are derived when X and Y are independent Pareto random variables.
References
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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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