Is there a dplyr way to generate an AR(1) time series?

user_2823295 0
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I need to generate an autoregressive timeseries for a simulation study. Ultimately I will need to do this in a nested fashion over many blocks. I thought I could easily achieve this using mutate() and lag() but apparently not:

# Initialise some data
trial.data = tibble(
  trial = rep(1:20, times = 1),
  y = 1
) 

# Replace y values with a new autoregressed value in each row
trial.data %>%
  rowwise() %>%
  mutate(y = lag(y, default = 1)*0.8)

# A tibble: 10 x 2
# Rowwise: 
   trial     y
   <int> <dbl>
 1     1   0.8
 2     2   0.8
 3     3   0.8
 4     4   0.8
 5     5   0.8
 6     6   0.8
 7     7   0.8
 8     8   0.8
 9     9   0.8
10    10   0.8

I get the expected result using a for loop:

for (i in 2:10) {
  trial.data$y[i] <- trial.data$y[i-1]*0.8
}

trial.data

# A tibble: 10 x 2
   trial     y
   <int> <dbl>
 1     1 1    
 2     2 0.8  
 3     3 0.64 
 4     4 0.512
 5     5 0.410
 6     6 0.328
 7     7 0.262
 8     8 0.210
 9     9 0.168
10    10 0.134

Any hints how to do this in a dplyr pipe would be appreciated... One further thought I had was to functionalize my for loop but this doesn't work:

loop_fun <- function(x) {
  for (i in 2:10) {
    x[i] <- x[i-1]*0.8
  }
}

trial.data %>%
  mutate(y2 = loop_fun(y))
rowwise dplyr r
2 Answers

You may use accumulate for such recursive calculation.

library(dplyr)
library(purrr)

trial.data %>% mutate(y = accumulate(y, ~.x * 0.8))

#   trial      y
#   <int>  <dbl>
# 1     1 1     
# 2     2 0.8   
# 3     3 0.64  
# 4     4 0.512 
# 5     5 0.410 
# 6     6 0.328 
# 7     7 0.262 
# 8     8 0.210 
# 9     9 0.168 
#10    10 0.134 
#11    11 0.107 
#12    12 0.0859
#13    13 0.0687
#14    14 0.0550
#15    15 0.0440
#16    16 0.0352
#17    17 0.0281
#18    18 0.0225
#19    19 0.0180
#20    20 0.0144

In base R use Reduce.

trial.data$y <- Reduce(function(x, y) x * 0.8, trial.data$y, accumulate = TRUE)
user_39629140

We can use cumprod in a vectorized way

library(dplyr)
trial.data %>% 
    mutate(y2 = lag(cumprod(y * 0.8), default = 1))

-output

# A tibble: 20 x 3
   trial     y     y2
   <int> <dbl>  <dbl>
 1     1     1 1     
 2     2     1 0.8   
 3     3     1 0.64  
 4     4     1 0.512 
 5     5     1 0.410 
 6     6     1 0.328 
 7     7     1 0.262 
 8     8     1 0.210 
 9     9     1 0.168 
10    10     1 0.134 
11    11     1 0.107 
12    12     1 0.0859
13    13     1 0.0687
14    14     1 0.0550
15    15     1 0.0440
16    16     1 0.0352
17    17     1 0.0281
18    18     1 0.0225
19    19     1 0.0180
20    20     1 0.0144
user_37322710
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