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.

## 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:

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_augment()`

,
`ts_geometric_brownian_motion()`

,
`ts_random_walk()`

## 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 0.497
#> 2 actual_data 2022-01-02 -1.43
#> 3 actual_data 2022-01-03 0.643
#> 4 actual_data 2022-01-04 2.00
#> 5 actual_data 2022-01-05 0.0101
#> 6 actual_data 2022-01-06 1.93
#> 7 actual_data 2022-01-07 0.103
#> 8 actual_data 2022-01-08 0.689
#> 9 actual_data 2022-01-09 0.360
#> 10 actual_data 2022-01-10 0.910
#> # ℹ 1,031 more rows
```