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The notation () indicates an autoregressive model of order p.The AR(p) model is defined as = = + where , …, are the parameters of the model, and is white noise. [1] [2] This can be equivalently written using the backshift operator B as
The model is usually denoted ARMA(p, q), where p is the order of AR and q is the order of MA. The general ARMA model was described in the 1951 thesis of Peter Whittle , Hypothesis testing in time series analysis , and it was popularized in the 1970 book by George E. P. Box and Gwilym Jenkins .
Polynomials of the lag operator can be used, and this is a common notation for ARMA (autoregressive moving average) models. For example, = = = (=) specifies an AR(p) model.A polynomial of lag operators is called a lag polynomial so that, for example, the ARMA model can be concisely specified as
Non-seasonal ARIMA models are usually denoted ARIMA(p, d, q) where parameters p, d, q are non-negative integers: p is the order (number of time lags) of the autoregressive model, d is the degree of differencing (the number of times the data have had past values subtracted), and q is the order of the moving-average model.
The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a particular ...
Since the parent ion can only be 2 P 1/2 or 2 P 3/2, the notation can be shortened to [] or ′ [], where nℓ means the parent ion is in 2 P 3/2 while nℓ′ is for the parent ion in 2 P 1/2 state. Paschen notation is a somewhat odd notation; it is an old notation made to attempt to fit an emission spectrum of neon to a hydrogen-like theory.
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics , science , and engineering for representing complex concepts and properties in a concise ...
lnp1 – natural logarithm plus 1 function. ln1p – natural logarithm plus 1 function. log – logarithm. (If without a subscript, this may mean either log 10 or log e.) logh – natural logarithm, log e. [6] LST – language of set theory. lub – least upper bound. [1] (Also written sup.)