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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. - PowerPoint PPT Presentation
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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
Sine wave plus random noise
Narrow-band random noise
Wide-band random noise
(histograms)
Auto-correlation functions
Sine wave
Sine wave plus random noise
Narrow-band random noise
Wide-band random noise
0
Lag Time
Lag
ged
Aut
o-C
orre
lati
on R
xx(
)
Auto-spectral Density
Sine wave
Sine wave plus random noise
Narrow-band random noise
Wide-band random noise
