| trigBasisExp {LaMa} | R Documentation |
Trigonometric Basis Expansion
Description
Given a periodically varying variable such as time of day or day of year and the associated cycle length, this function performs a basis expansion to efficiently calculate a linear predictor of the form
\eta^{(t)} = \beta_0 + \sum_{k=1}^K \bigl( \beta_{1k} \sin(\frac{2 \pi k t}{L}) + \beta_{2k} \cos(\frac{2 \pi k t}{L}) \bigr).
This is relevant for modeling e.g. diurnal variation and the flexibility can be increased by adding smaller frequencies (i.e. increasing K).
Usage
trigBasisExp(tod, L = 24, degree = 1)
Arguments
tod |
Time variable, describing the time point in a cycle. Could for example be time of day (between 0 and 24) or day of year. |
L |
Length of one cycle on the scale of the time variable. For time of day, this would be 24. |
degree |
Degree K of the trigonometric link above. Increasing K increases the flexibility. |
Value
A design matrix (without intercept column of ones), ordered as sin1, cos1, sin2, cos2, ...
Examples
## hourly data
tod = rep(1:24, 10)
Z = trigBasisExp(tod, L = 24, degree = 2)
## half-hourly data
tod = rep(1:48/2, 10) # in [0,24] -> L = 24
Z1 = trigBasisExp(tod, L = 24, degree = 3)
tod = rep(1:48, 10) # in [1,48] -> L = 48
Z2 = trigBasisExp(tod, L = 48, degree = 3)
Z1 - Z2
# The latter two are equivalent specifications!