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Discrete Sampled Walk

Source: R/gen-discrete-walk.R
discrete_walk.Rd

The discrete_walk function generates multiple random walks over discrete time periods. Each step in the walk is determined by a probabilistic sample from specified upper and lower bounds. This function is useful for simulating stochastic processes, such as stock price movements or other scenarios where outcomes are determined by a random process.

Usage

discrete_walk(
  .num_walks = 25,
  .n = 100,
  .upper_bound = 1,
  .lower_bound = -1,
  .upper_probability = 0.5,
  .initial_value = 100,
  .dimensions = 1
)

Arguments

.num_walks

Total number of simulations.

.n

Total time of the simulation.

.upper_bound

The upper bound of the random walk.

.lower_bound

The lower bound of the random walk.

.upper_probability

The probability of the upper bound. Default is 0.5. The lower bound is calculated as 1 - .upper_probability.

.initial_value

The initial value of the random walk. Default is 100.

.dimensions

The default is 1. Allowable values are 1, 2 and 3.

Value

A tibble containing the generated random walks with columns depending on the number of dimensions:

  • walk_number: Factor representing the walk number.

  • step_number: Step index.

  • y: If .dimensions = 1, the value of the walk at each step.

  • x, y: If .dimensions = 2, the values of the walk in two dimensions.

  • x, y, z: If .dimensions = 3, the values of the walk in three dimensions.

The following are also returned based upon how many dimensions there are and could be any of x, y and or z:

  • cum_sum: Cumulative sum of dplyr::all_of(.dimensions).

  • cum_prod: Cumulative product of dplyr::all_of(.dimensions).

  • cum_min: Cumulative minimum of dplyr::all_of(.dimensions).

  • cum_max: Cumulative maximum of dplyr::all_of(.dimensions).

  • cum_mean: Cumulative mean of dplyr::all_of(.dimensions).

Details

The function discrete_walk simulates random walks for a specified number of simulations (.num_walks) over a given total time (.n). Each step in the walk is either the upper bound or the lower bound, determined by a probability (.upper_probability). The initial value of the walk is set by the user (.initial_value), and the cumulative sum, product, minimum, and maximum of the steps are calculated for each walk. The results are returned in a tibble with detailed attributes, including the parameters used for the simulation.

See also

Other Generator Functions: brownian_motion(), geometric_brownian_motion(), random_normal_drift_walk(), random_normal_walk()

Author

Steven P. Sanderson II, MPH

Examples

set.seed(123)
discrete_walk()
#> # A tibble: 2,500 × 8
#>    walk_number step_number     y cum_sum_y cum_prod_y cum_min_y cum_max_y
#>    <fct>             <int> <dbl>     <dbl>      <dbl>     <dbl>     <dbl>
#>  1 1                     1    -1        99          0        99        99
#>  2 1                     2     1       100          0        99       101
#>  3 1                     3    -1        99          0        99       101
#>  4 1                     4     1       100          0        99       101
#>  5 1                     5     1       101          0        99       101
#>  6 1                     6    -1       100          0        99       101
#>  7 1                     7     1       101          0        99       101
#>  8 1                     8     1       102          0        99       101
#>  9 1                     9     1       103          0        99       101
#> 10 1                    10    -1       102          0        99       101
#> # ℹ 2,490 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>

set.seed(123)
discrete_walk(.dimensions = 3) |>
  head() |>
  t()
#>             [,1]        [,2]        [,3]        [,4]        [,5]       
#> walk_number "1"         "1"         "1"         "1"         "1"        
#> step_number "1"         "2"         "3"         "4"         "5"        
#> x           "-1"        " 1"        "-1"        " 1"        " 1"       
#> y           " 1"        "-1"        "-1"        " 1"        "-1"       
#> z           "-1"        " 1"        " 1"        " 1"        "-1"       
#> cum_sum_x   " 99"       "100"       " 99"       "100"       "101"      
#> cum_sum_y   "101"       "100"       " 99"       "100"       " 99"      
#> cum_sum_z   " 99"       "100"       "101"       "102"       "101"      
#> cum_prod_x  "0"         "0"         "0"         "0"         "0"        
#> cum_prod_y  "200"       "  0"       "  0"       "  0"       "  0"      
#> cum_prod_z  "0"         "0"         "0"         "0"         "0"        
#> cum_min_x   "99"        "99"        "99"        "99"        "99"       
#> cum_min_y   "101"       " 99"       " 99"       " 99"       " 99"      
#> cum_min_z   "99"        "99"        "99"        "99"        "99"       
#> cum_max_x   " 99"       "101"       "101"       "101"       "101"      
#> cum_max_y   "101"       "101"       "101"       "101"       "101"      
#> cum_max_z   " 99"       "101"       "101"       "101"       "101"      
#> cum_mean_x  " 99.00000" "100.00000" " 99.66667" "100.00000" "100.20000"
#> cum_mean_y  "101.00000" "100.00000" " 99.66667" "100.00000" " 99.80000"
#> cum_mean_z  " 99.0000"  "100.0000"  "100.3333"  "100.5000"  "100.2000" 
#>             [,6]       
#> walk_number "1"        
#> step_number "6"        
#> x           "-1"       
#> y           " 1"       
#> z           " 1"       
#> cum_sum_x   "100"      
#> cum_sum_y   "100"      
#> cum_sum_z   "102"      
#> cum_prod_x  "0"        
#> cum_prod_y  "  0"      
#> cum_prod_z  "0"        
#> cum_min_x   "99"       
#> cum_min_y   " 99"      
#> cum_min_z   "99"       
#> cum_max_x   "101"      
#> cum_max_y   "101"      
#> cum_max_z   "101"      
#> cum_mean_x  "100.00000"
#> cum_mean_y  "100.00000"
#> cum_mean_z  "100.3333"