The auto-covariance and cross-covariance functions are like their correlation equivalents, but unscaled; it's the same difference as between covariance and correlation.

I have calculated autocorrelation on time series data on the patterns of movement of a fish based on its positions: X (x.ts) and Y (y.ts). By using R, I ran the following functions and produced the

I am reading through Dangers and uses of cross-correlation in analyzing time series in perception, performance, movement, and neuroscience: The importance of constructing transfer function autoregressive models by Dean and Dunsmuir, and they mention time series that are "individually autocorrelated". What does this term mean?

I just started with time series analysis and I would like to know whether there is a formular for calculating the autocorrelation function (ACF) and the partial autocorrelation function (PACF) for time series data.

EDIT: Apparently I was not thorough enough in my search for previous questions on this topic. This is pretty much the same question, and has been answered: Auto-correlation vs Auto-covariance The a...

7 I am trying to plot the auto and cross correlation of the bitstream that is obtained from a nonlinear dynamical system. The graph is the Auto and cross-correlation for the bitstream obtained from the same nonlinear dyanamical system. I am not sure how to interpret the graph. Whether the program is incorrect or not.

9 I have been working with some time-series theory and I noticed something that I can understand "mathematically", but not based on the intuitive explanations of what the partial auto-correlation function (PACF) is supposed to represent: The correlation between points of a given lag with the effects of smaller correlations removed.

Usually either random effects or autocorrelation should be modeled by the same grouping indicator but not both. If you already have a random intercept varying by whale, it already captures the correlation between multiple measurements taken from the same whale, so it will be redundant to use autocorrelation.

All references, which i found so far only explain how to generate random samples with a single correlation-coefficent, but not with a auto-correlation function. For my auto-correlation i have 30 lags with the corresponding value of my e-function which approximates the auto-correlation-function.

The ARMA.autocov function takes an auto-regression vector ar and a moving-average vector ma (so long as the AR polynomial is for a stationary model) and gives the auto-correlation or auto-covariance function up to any specified length n.