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Statistics 248 D.R. Brillinger

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.

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Statistics 248 D.R. Brillinger

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  1. 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, ...

  2. 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)

  3. Tufte (1983). Perhaps 10th or 11th century movement of planets and sun

  4. Elephant seal dives 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

  5. Connected. Good for smooth series individual data points not unambiguously displayed irregular sampling can be unclear plot(type="l",

  6. Both. Points and line segments plot(type="b",

  7. Both. Points on top of connected plot(type="o",

  8. plot(type="n" points(pch="*"

  9. plot(type="n" lines(type=3

  10. plot(type="h" Good when need to see individual values when series long about centralvalue (next) Not good when strong trend

  11. Amazon River at Manaus plot(type="h",...) Amazon T = 32875 Good about central value

  12. Mississippi Locks

  13. Vector ts case matplot(type="l" use several line types colors use to provide comparison

  14. 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)

  15. Computer software R CRAN 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.

  16. 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

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