@ARTICLE{18276160_1970,
author = {Box, George E.P. and Pierce, D. A.},
keywords = {autoregressive models, statistical model, time series, авторегрессионная модель, модель авторегрессии-скользящего среднего, статистическая модель},
title = {Distribution of Residual Autocorrelations in
Autoregressive-Integrated Moving Average Time Series Models },
journal = {Journal of the American Statistical Association},
year = {1970},
month = {},
volume = {65},
number = {332},
pages = {1509-1526},
url = {http://ecsocman.hse.ru/text/18276160/},
publisher = {},
language = {ru},
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. },
annote = {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. }
}