Brownian Motion

Create a Brownian Motion Tibble

Usage

ts_brownian_motion_augment(
  .data,
  .date_col,
  .value_col,
  .time = 100,
  .num_sims = 10,
  .delta_time = NULL
)

Arguments

.data

The data.frame/tibble being augmented.

.date_col

The column that holds the date.

.value_col

The value that is going to get augmented. The last value of this column becomes the initial value internally.

.time

How many time steps ahead.

.num_sims

How many simulations should be run.

.delta_time

Time step size.

Value

A tibble/matrix

Details

Brownian Motion, also known as the Wiener process, is a continuous-time random process that describes the random movement of particles suspended in a fluid. It is named after the physicist Robert Brown, who first described the phenomenon in 1827.

The equation for Brownian Motion can be represented as:

W(t) = W(0) + sqrt(t) * Z

Where W(t) is the Brownian motion at time t, W(0) is the initial value of the Brownian motion, sqrt(t) is the square root of time, and Z is a standard normal random variable.

Brownian Motion has numerous applications, including modeling stock prices in financial markets, modeling particle movement in fluids, and modeling random walk processes in general. It is a useful tool in probability theory and statistical analysis.

See also

Other Data Generator: tidy_fft(), ts_brownian_motion(), ts_geometric_brownian_motion(), ts_geometric_brownian_motion_augment(), ts_random_walk()

Author

Steven P. Sanderson II, MPH

Examples

rn <- rnorm(31)
df <- data.frame(
 date_col = seq.Date(from = as.Date("2022-01-01"),
                      to = as.Date("2022-01-31"),
                      by = "day"),
 value = rn
)

ts_brownian_motion_augment(
  .data = df,
  .date_col = date_col,
  .value_col = value
)
#> # A tibble: 1,041 × 3
#>    sim_number  date_col     value
#>    <fct>       <date>       <dbl>
#>  1 actual_data 2022-01-01  0.900 
#>  2 actual_data 2022-01-02  0.0962
#>  3 actual_data 2022-01-03 -0.477 
#>  4 actual_data 2022-01-04  0.673 
#>  5 actual_data 2022-01-05 -0.239 
#>  6 actual_data 2022-01-06 -0.240 
#>  7 actual_data 2022-01-07  0.416 
#>  8 actual_data 2022-01-08  0.159 
#>  9 actual_data 2022-01-09  0.883 
#> 10 actual_data 2022-01-10  0.990 
#> # ℹ 1,031 more rows