# first-order difference

## first-order difference

[¦fərst ¦ȯrd·ər ′dif·rəns]
(mathematics)
A member of a sequence that is formed from a given sequence by subtracting each term of the original sequence from the next succeeding term.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Thus, in this paper, we intend to propose a novel method for short-term traffic prediction based on the energetically grey Verhulst prediction algorithm and the first-order difference exponential smoothing technique to solve the problem of low prediction accuracy caused by traffic event-triggering strong fluctuation.
The test results in Table 1 show that level value of the three sequences is nonstationary, and further test indicates that cp, op, and gdp sequences are first-order difference stationary.
This dynamic element is described by linear time-invariant first-order difference equation; see [11, 12].
The test results of the unit root of the variable show that most of the data unit root tests are not significant, so we have a first-order difference unit root test for these data, the sequence of the first order difference unit root test results are obtained.
The results of the unit root test for first-order difference variables, except for that ofthe price index logarithm and trade liberalization logarithm, are shown in Table 2.
Mathematical topics covered include Markov chains, matrix algebra and linear and nonlinear first-order difference equations.
Non-stationary time series data are normally predictive only within a shorter episode, hence are not considered the an appropriate tool in forecasting (Gujarati and Porter, (10)) If the original time series is non-stationary, the first-order difference often becomes stationary.
However, they said, "It seems clear that there is a first-order difference in the nature of Earth surface Cr cycling" before and after the rise of animals."
The edge E with the first-order difference is defined as E ([x.sub.0], [y.sub.0])
At first, the first-order difference sequence of the PA data is calculated:
Hypothesis 1a: The first-order difference of the slope function with respect to time will be negative until [T.sub.2], that is, [s.sub.T+1] - [s.sub.T] = [DELTA]([s.sub.T]) < 0, where T [member of] [[T.sub.0], [T.sub.2]] .
So we should firstly implement difference on the series to get the first-order difference series graph (see figure 2).

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