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unit root ：ウィキペディア英語版

unit root
A unit root is a feature of processes that evolve through time that can cause problems in statistical inference involving time series models.
A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. Such a process is non-stationary. If the other roots of the characteristic equation lie inside the unit circle—that is, have a modulus (absolute value) less than one—then the first difference of the process will be stationary.
==Definition==
Consider a discrete-time stochastic process

\

, and suppose that it can be written as an autoregressive process of order ''p'':
:

y_t=a_1 y_+a_2 y_ + \cdots + a_p y_+\varepsilon_t.

Here,

\

is a serially uncorrelated, zero-mean stochastic process with constant variance

\sigma^2

. For convenience, assume

y_0 = 0

. If

m=1

m^p - m^a_1 - m^a_2 - \cdots - a_p = 0

then the stochastic process has a unit root or, alternatively, is integrated of order one, denoted

I(1)

. If ''m'' = 1 is a root of multiplicity ''r'', then the stochastic process is integrated of order ''r'', denoted ''I''(''r'').

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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