Time domain analysis

thumb|300px|right|Above: A plot of a series of 100 random numbers concealing a sine function. Below: Its [[correlogram plots the autocorrelation function (ACF) of the series on the y-axis for every lag on the x-axis. Peaks occur at lags where the series is highly correlated with itself. Peaks to the right of the initial peak at lag 0 indicate periodicity in the series and help estimate the concealed sine's period.]] thumb|400px|Visual comparison of convolution, cross-correlation, and autocorrelation. For the operations involving function , and assuming the height of is 1.0, the value of the re

a dynamic system's output when inputted with a brief input signal, used to parameterize the dynamic behavior of the system

analysis of math functions with respect to time

mathematical term

thumb|400px|Visual comparison of convolution, cross-correlation and [[autocorrelation. For the operations involving function , and assuming the height of is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point. Also, the vertical symmetry of is the reason f*g and f \star g are identical in this example.]]

mathematical model of system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance

statistical test

In probability and statistics, given two stochastic processes \left\{X_t\right\} and \left\{Y_t\right\}, the cross-covariance is a function that gives the covariance of one process with the other at pairs of time points. With the usual notation \operatorname E for the expectation operator, if the processes have the mean functions \mu_X(t) = \operatorname \operatorname E[X_t] and \mu_Y(t) = \operatorname E[Y_t], then the cross-covariance is given by

partial correlation of a time series with its lagged values