BIOL 335 Lecture Notes - Lecture 5: Uncorrelated Random Variables, Stationary Process, Stochastic Calculus
Document Summary
Introduction: suppose a time series is thought to contain a periodic sinusoidal component, then a simple underlying model could be: Xt = r cos( t + ) + zt, Is the (angular) frequency (# radians per unit time: de ne f := . 2 to be the frequency of the model (# cycles per unit time - a more natural interpretation in data analysis) Example: sales might uctuate at di erent frequencies, e. g. , weakly (high), monthly (medium), yearly (low), and other: a natural extension of the above model is. Question: is the process {xt} in (1) stationary, in general: yes, no, don"t know. Rj cos( j t + j ) + zt, {xt} in (1) is stationary if either: {rj ; j = 1, . , k} are uncorrelated random variables with mean zero; or: j unif (0, 2 ), j = 1, . , k, and these variables are xed for each realization of the process (check!)
