Introduction

Sometimes in modeling you may want to get a discrete 1/0 vector of a fourier transform of some input vector. With {healthyR.ai} we can do this easily.

Function

Here is the full function call:

hai_fourier_discrete_vec(
  .x,
  .period,
  .order,
  .scale_type = c("sin", "cos", "sincos")
)

Here are the parameters to the function and what they expect:

.x - A numeric vector
.period - The number of observations that complete a cycle
.order - The fourier term order
.scale_type - A character of one of the following: sin,cos,sincos

The internal caluclation is straightforward:

sin = sin(2 * pi * h * x), where h = .order/.period
cos = cos(2 * pi * h * x), where h = .order/.period
sincos = sin(2 * pi * h * x) * cos(2 * pi * h * x) where h = .order/.period

Example

Let’s work throught a quick and simple example.

library(dplyr)
library(ggplot2)
library(healthyR.ai)
library(tidyr)

len_out <- 24
by_unit <- "month"
start_date <- as.Date("2021-01-01")

data_tbl <- tibble(
  date_col = seq.Date(
    from = start_date, 
    length.out = len_out, 
    by = by_unit
  ),
  a = rnorm(len_out, sd = 2),
  fv_sin = hai_fourier_discrete_vec(a, 12, 1, "sin"),
  fv_cos = hai_fourier_discrete_vec(a, 12, 1, "cos"),
  fv_sc  = hai_fourier_discrete_vec(a, 12, 1, "sincos")
)

data_tbl

# A tibble: 24 × 5
   date_col         a fv_sin fv_cos fv_sc
   <date>       <dbl>  <dbl>  <dbl> <dbl>
 1 2021-01-01 -0.486       0      1     0
 2 2021-02-01 -0.708       0      1     0
 3 2021-03-01 -0.119       0      1     0
 4 2021-04-01  0.0405      1      1     1
 5 2021-05-01  1.19        1      1     1
 6 2021-06-01  1.88        1      1     1
 7 2021-07-01 -1.32        0      1     0
 8 2021-08-01 -0.0214      0      1     0
 9 2021-09-01  2.80        1      1     1
10 2021-10-01  1.67        1      1     1
# … with 14 more rows

Visual

Let’s visualize.

data_tbl %>% 
  pivot_longer(cols = -date_col) %>% 
  ggplot(aes(x = date_col, y = value, color = name)) + 
  geom_line() + 
  facet_wrap(~ name, scales = "free") +
  theme_minimal() +
  labs(color = "")

Voila!