Statistics 248 D.R. Brillinger
Process data
indexed values Y(), : time, space, set, function
curves, surfaces, shapes, measures, images, sequences, scatter, spirals, trajectories, mosaics - and they may be moving
Random process data
Put process datums in an urn and pick one,
Y(;), a random variable
time series, point processes, marked point processes, spatial processes, spatial-temporal processes, categorical-valueds, hybrids, ...
Time series data.
t: time (but could be space)
0 t T (continuous)
t = 0,...,T-1 (discrete)
t = 1 ,..., N unequally spaced, missings
(unique) value Y(t)
Y in R
{0,1}
Rp
N, category, [0, 2)
Tufte (1983). Perhaps 10th or 11th century movement of planets and sun
Symbol graph. Good for long term behavior
cannot appreciate middle and high frequency behavior
irregular sampling can be unclear
plot(type="p",...) seals T = 940
Elephant seal dives
Connected. Good for smooth series
individual data points not unambiguously displayed
irregular sampling can be unclear
plot(type="l",
Both. Points and line segments
plot(type="b",
Both. Points on top of connected
plot(type="o",
plot(type="n"
points(pch="*"
plot(type="n"
lines(type=3
plot(type="h"
Good when need to see individual values
when series long
about centralvalue (next)
Not good when strong trend
plot(type="h",...) Amazon T = 32875
Good about central value
Amazon River at Manaus
Mississippi Locks
Vector ts case matplot(type="l"
use several line types
colors
use to provide comparison
Hipel K. W. McLeod A. I. (1994). Time Series Modelling of Water Resources and Environmental Systems Elsevier
Buys-Ballot
Useful when there is special period P
t=nP+p, p=0,...,P-1
n=0,1,2,...
Yn(p)=Y(nP+p)
Computer software
Ross Ihaka is one the originators of R, a software package for statistical computing that has had phenomenal uptake internationally. It can be downloaded free and easily customised for a very wide variety of applications. The package and the paper introducing it have been cited over 1700 times, by far the highest for publications in the mathematical sciences over the last ten years, worldwide. It is now disseminated from over 75 internet sites in 30 countries.
R
CRAN
The package is used both for teaching and research by hundreds of universities around the world, including Stanford, Oxford, Cambridge and Berkeley. There are over 40 books written about, or featuring, the use of R.
http://www.nytimes.com/2009/01/07/technology/business-computing/07program.html?scp=2&sq=ihaka&st=cse
