Mandelbrot (1971, 1972) was one of the first to formally recognize the possibility and the implications of long-term persistent
statistical dependence. The author indicates that these series are characterized by distinct, but non-periodic, cyclical patterns and relates the processes of long memory with the fractional integration.
The basic case of statistical dependence consists in simple dependence, the dependence between two random quantities, X and Y.
However, this is not a realistic description of statistical dependence. In view of the random character of dependence, the points do not lie directly on the line, but are instead around it.
The
statistical dependence between values of the family farm income and the net investment value was also low, the determination coefficient was equal to 0.243 (fig.
Dr Ibrahim Elfadel, head of Masdar Institute's Centre for Microelectronics, said: "The goal of the chip is to measure the
statistical dependence of circuit performance on process variations.
We will see that statistical dependence between characteristics is what is important for inferences from passive observation.
It is well known among scientists, statisticians, and philosophers that statistical dependence is a necessary but not a sufficient requirement for a causal relationship-that is, that correlation does not imply causation.
Short-term dependent time series include standard autoregressive moving average and Markov processes and have the property that observations far apart exhibit little or no
statistical dependence.