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