Data and Data Tapers for Stat/EE 520
Here are some links to data sets and data tapers.
-
nine time series used extensively as examples in the book
-
three other time series used as examples in the book
- St. Paul temperatures (Figure 9)
- Golden Gate Bridge traffic (Figure 195)
- 20 points from
rotation of earth series.
These numbers are listed on page 287 and are used in Figure 288
to illustrate the computational pathways depicted in Figure 285.
Figure 288 has six rows of plots.
Each row has two plots.
The left-hand plot is the time (or lag) domain
representation
of a certain quantity,
while the right-hand plot is the corresponding frequency
domain representation.
Each representation consists of 64 numbers,
which you can download (along with some comments)
via the following six items
(one for each row in the figure).
- centered time series
(padded with 44 zeros)
and
its DFT
- Slepian (dpss) data taper with NW=4
(padded with 44 zeros)
and
its DFT
- tapered time series
(padded with 44 zeros)
and
its DFT
- acvs of tapered series
(circularly wrapped)
and
its DFT
(unnormalized direct spectral estimate)
- Parzen lag window
(circularly wrapped)
and
its DFT
- lag windowed acvs of tapered series
(circularly wrapped)
and
its DFT
(unnormalized lag window spectral estimate)
Second example of calculation of a lag window estimate
for the 20 points from the
rotation of earth series,
similar to the one displayed in Figure 288,
but now using a Hanning data taper
(rather than a Slepian data taper)
and a Daniell lag window with m=5
(rather than a Parzen lag window):
- centered time series
(padded with 44 zeros)
and
its DFT
- Hanning data taper
(padded with 44 zeros)
and
its DFT
- tapered time series
(padded with 44 zeros)
and
its DFT
- acvs of tapered series
(circularly wrapped)
and
its DFT
(unnormalized direct spectral estimate)
- Daniell lag window
(circularly wrapped)
and
its DFT
- lag windowed acvs of tapered series
(circularly wrapped)
and
its DFT
(unnormalized lag window spectral estimate)
- computation of zeroth order dpss data tapers via Equation (386)
- modified Bessel function I_0(x), Abramowitz and Stegun (1964), p. 378:
-
N=16, NW=1 test case
-
N=20, NW=4 test case (can be used to help reproduce Figure 288)
-
N=64, NW=3 test case
-
N=128, NW=4 test case
- dpss multitaper test cases
- Figure 106:
k=0,
k=1,
k=2
and
k=3
tapers for N=32 and NW=4
- Figure 108:
k=0,
k=1,
k=2
and
k=3
tapers for N=99 and NW=4
- another simulated AR(4) series
created from a
simulated white noise sequence
consisting of 1024 computer-generated
pseudo-random deviates from a Gaussian distribution
with zero mean and unit variance (the coefficients for the AR(4) process
are as listed on page 46, namely, 2.7607, -3.8106, 2.6535 and -0.9238).
These two series can be used for testing a computer implementation
of a recipe for simulating AR process available
in
html,
LaTeX,
PostScript
and
PDF
formats.
- numerical example that can be used to test the implementation
of the Yule-Walker method
for estimating the parameters of an autoregressive process
- numerical example that can be used to test the implementation
of Burg's algorithm
for estimating the parameters of an autoregressive process
- time series used in forthcoming second volume of SAPA
Also, here is a
description of -- and access to -- the
sapaclisp archive,
a collection of Common Lisp functions that implement most of the
procedures in the book
(an
older version
of this archive is on
StatLib).
Return to home page for
Stat/EE 520.