Description Usage Arguments Details Value Author(s) References See Also Examples
The function creates a dlm representing a specified periodic component.
1 | dlmModTrig(s, q, om, tau, dV = 1, dW = 0, m0, C0)
|
s |
the period, if integer. |
q |
number of harmonics in the DLM. |
om |
the frequency. |
tau |
the period, if not an integer. |
dV |
variance of the observation noise. |
dW |
a single number expressing the variance of the system noise. |
m0 |
m0, the expected value of the pre-sample state vector. |
C0 |
C0, the variance matrix of the pre-sample state vector. |
The periodic component is specified by one and only one of s
,
om
, and tau
. When s
is given, the function
assumes that the period is an integer, while a period specified by
tau
is assumed to be noninteger. Instead of tau
,
the frequency om
can be specified. The argument q
specifies the number of harmonics to include in the model. When
tau
or omega
is given, then q
is required as
well, since in this case the implied Fourier representation has
infinitely many harmonics. On the other hand, if s
is given,
q
defaults to all the harmonics in the Fourier representation,
that is floor(s/2)
.
The system variance of the resulting dlm is dW
times the identity
matrix of the appropriate dimension.
An object of class dlm, representing a periodic component.
Giovanni Petris GPetris@uark.edu
Giovanni Petris (2010), An R Package for Dynamic Linear
Models. Journal of Statistical Software, 36(12), 1-16.
http://www.jstatsoft.org/v36/i12/.
Petris, Petrone, and Campagnoli, Dynamic Linear Models with
R, Springer (2009).
West and Harrison, Bayesian forecasting and
dynamic models (2nd ed.), Springer (1997).
dlmModSeas
, dlmModARMA
,
dlmModPoly
, dlmModReg
1 2 3 4 5 6 7 8 | dlmModTrig(s = 3)
dlmModTrig(tau = 3, q = 1) # same thing
dlmModTrig(s = 4) # for quarterly data
dlmModTrig(s = 4, q = 1)
dlmModTrig(tau = 4, q = 2) # a bad idea!
m1 <- dlmModTrig(tau = 6.3, q = 2); m1
m2 <- dlmModTrig(om = 2 * pi / 6.3, q = 2)
all.equal(unlist(m1), unlist(m2))
|
$FF
[,1] [,2]
[1,] 1 0
$V
[,1]
[1,] 1
$GG
[,1] [,2]
[1,] -0.5000000 0.8660254
[2,] -0.8660254 -0.5000000
$W
[,1] [,2]
[1,] 0 0
[2,] 0 0
$m0
[1] 0 0
$C0
[,1] [,2]
[1,] 1e+07 0e+00
[2,] 0e+00 1e+07
$FF
[,1] [,2]
[1,] 1 0
$V
[,1]
[1,] 1
$GG
[,1] [,2]
[1,] -0.5000000 0.8660254
[2,] -0.8660254 -0.5000000
$W
[,1] [,2]
[1,] 0 0
[2,] 0 0
$m0
[1] 0 0
$C0
[,1] [,2]
[1,] 1e+07 0e+00
[2,] 0e+00 1e+07
$FF
[,1] [,2] [,3]
[1,] 1 0 1
$V
[,1]
[1,] 1
$GG
[,1] [,2] [,3]
[1,] 6.123234e-17 1.000000e+00 0
[2,] -1.000000e+00 6.123234e-17 0
[3,] 0.000000e+00 0.000000e+00 -1
$W
[,1] [,2] [,3]
[1,] 0 0 0
[2,] 0 0 0
[3,] 0 0 0
$m0
[1] 0 0 0
$C0
[,1] [,2] [,3]
[1,] 1e+07 0e+00 0e+00
[2,] 0e+00 1e+07 0e+00
[3,] 0e+00 0e+00 1e+07
$FF
[,1] [,2]
[1,] 1 0
$V
[,1]
[1,] 1
$GG
[,1] [,2]
[1,] 6.123234e-17 1.000000e+00
[2,] -1.000000e+00 6.123234e-17
$W
[,1] [,2]
[1,] 0 0
[2,] 0 0
$m0
[1] 0 0
$C0
[,1] [,2]
[1,] 1e+07 0e+00
[2,] 0e+00 1e+07
$FF
[,1] [,2] [,3] [,4]
[1,] 1 0 1 0
$V
[,1]
[1,] 1
$GG
[,1] [,2] [,3] [,4]
[1,] 6.123234e-17 1.000000e+00 0.000000e+00 0.000000e+00
[2,] -1.000000e+00 6.123234e-17 0.000000e+00 0.000000e+00
[3,] 0.000000e+00 0.000000e+00 -1.000000e+00 1.224647e-16
[4,] 0.000000e+00 0.000000e+00 -1.224647e-16 -1.000000e+00
$W
[,1] [,2] [,3] [,4]
[1,] 0 0 0 0
[2,] 0 0 0 0
[3,] 0 0 0 0
[4,] 0 0 0 0
$m0
[1] 0 0 0 0
$C0
[,1] [,2] [,3] [,4]
[1,] 1e+07 0e+00 0e+00 0e+00
[2,] 0e+00 1e+07 0e+00 0e+00
[3,] 0e+00 0e+00 1e+07 0e+00
[4,] 0e+00 0e+00 0e+00 1e+07
$FF
[,1] [,2] [,3] [,4]
[1,] 1 0 1 0
$V
[,1]
[1,] 1
$GG
[,1] [,2] [,3] [,4]
[1,] 0.5425463 0.8400259 0.0000000 0.0000000
[2,] -0.8400259 0.5425463 0.0000000 0.0000000
[3,] 0.0000000 0.0000000 -0.4112871 0.9115059
[4,] 0.0000000 0.0000000 -0.9115059 -0.4112871
$W
[,1] [,2] [,3] [,4]
[1,] 0 0 0 0
[2,] 0 0 0 0
[3,] 0 0 0 0
[4,] 0 0 0 0
$m0
[1] 0 0 0 0
$C0
[,1] [,2] [,3] [,4]
[1,] 1e+07 0e+00 0e+00 0e+00
[2,] 0e+00 1e+07 0e+00 0e+00
[3,] 0e+00 0e+00 1e+07 0e+00
[4,] 0e+00 0e+00 0e+00 1e+07
[1] TRUE
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