Def Time Series Time series is a collection

Def. : Time Series Time series is a collection or sequence of numbers that represent the state of any system as a function of time or space or any other “ordering” independent variable.

Scalar Time Series Data e. g. , Sealevel Pressure (almost periodic) e. g. , Bottom Temperature (transient)

Vector Time Series Data Ocean Currents Speed (length of “stick”) and direction (orientation of “stick”) as a function of time

Matrix Time Series Data Spatial pattern of “some scalar” Reflectance at 645 nm (red part of visible spectrum) of ice, water, and land from MODIS July-26, 2009 11: 40 UTC

Matrix Time Series Data Spatial patterns that vary with time

MEASUREMENT = SIGNAL + NOISE How to separate?

Ensembles are a set of realizations xi(t) of a random process {x(t)} x 1(t) Experiment-1 tree-1, drifter-1 x 2(t) Experiment-2 tree-2, drifter-2 x 3(t) Experiment-3 tree-3, drifter-3 x 4(t) Experiment-4 tree-4, drifter-4 t t+τ Time t and lag τ

Qualities of time series: Sine wave plus random noise Narrow-band random noise Wide-band random noise

Probability Density Functions: (histograms) Sine wave plus random noise Narrow-band random noise Wide-band random noise

Lagged Auto-Correlation Rxx( ) Auto-correlation functions Sine wave plus random noise Narrow-band random noise Wide-band random noise 0 Lag Time

Auto-spectral Density Sine wave plus random noise Narrow-band random noise Wide-band random noise