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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TLDR
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
Has the EMS reduced member-country exchange rate volatility?
Francis X. Diebold,Peter Pauly +1 more
TL;DR: This paper found that the stochastic structure of the percentage changes in both the Franc/DM and Lira/DM rates is well described by a low order autoregression with ARCH disturbances.
Book ChapterDOI
The Importance of Size-Dependent Processes in the Ecology of Deposit-Feeding Benthos
TL;DR: The comprehensive study of developmental changes in functional morphology and critical physiological rate processes should provide valuable insights into the adaptation and design of deposit-feeding benthos.
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Non-Parametric Nonlinear System Identification: A Data-Driven Orthogonal Basis Function Approach
TL;DR: A data driven orthogonal basis function approach is proposed for non-parametric FIR nonlinear system identification because the basis functions are not fixed a priori and match the structure of the unknown system automatically.
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Carbon markets in times of VUCA: a weak-form efficiency investigation of the phase II EU ETS
TL;DR: In this article, the weak-form efficiency status of the European carbon market over periods of sustained volatility, uncertainty, complexity and ambiguity was examined using 1,035 daily spot price data observations from the Phase II ETS from 2008 to 2012, along with random walk and trading rule profitability tests.
Journal ArticleDOI
Some Empirical Evidence on the Properties of Daily Cash Flow
TL;DR: In this paper, the authors used the Cash Management personnel of the firms that provided data for analysis, as well as 0.0.Cogger, Kenneth 0.1.Johnson, and Dileep Mehta for their advice.
References
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Book
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.
Journal ArticleDOI
Time Series Analysis Forecasting and Control
TL;DR: This revision of a classic, seminal, and authoritative book explores the building of stochastic models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control.
Journal ArticleDOI
A Note on the Generation of Random Normal Deviates
Journal ArticleDOI
Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables
TL;DR: In this paper, it is shown that the asymptotic distribution of the serial correlation coefficient calculated from the least-squares residuals differs from that of the true disturbances in a regression model where some of the regressors are lagged dependent variables.
Journal ArticleDOI
On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers
TL;DR: In this article, a curve representing a simple harmonic function of the time, and superposing on the ordinates small random errors, is shown to make the graph somewhat irregular, leaving the suggestion of periodicity still quite clear to the eye.