Def.: Time Series Time series is a collection or sequence of numbers that represent the state of any...

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

e.g., Bottom Temperature

(almost periodic)

(transient)

Vector Time Series Data

Speed (length of “stick”) and direction (orientation of “stick”)

as a function of time

Ocean Currents

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 patternsthat vary with time

MEASUREMENT

=

SIGNAL

+

NOISEHow to separate?

Ensembles are a set of realizations xi(t) of a random process {x(t)}

Experiment-4

Experiment-3

Experiment-2

Experiment-1

t t+τ Time t and lag τ

tree-1, drifter-1

tree-2, drifter-2

tree-3, drifter-3

tree-4, drifter-4

x1(t)

x2(t)

x4(t)

x3(t)

Qualities of time series:

Sine wave

Sine wave plus random noise

Narrow-band random noise

Wide-band random noise

Probability Density Functions:

Sine wave




(histograms)

Auto-correlation functions

Sine wave




0

Lag Time

Lag

ged

Aut

o-C

orre

lati

on R

xx(

)

Auto-spectral Density

Sine wave




Def.: Time Series Time series is a collection or sequence of numbers that represent the state of any...

Documents

Transcript of Def.: Time Series Time series is a collection or sequence of numbers that represent the state of any...