Ar() + fitted()

Interfaces brms
1
  • Operating System: Mac
  • brms Version: 2.14.4

I’d like to use fitted() following a model with an autoregressive structure. However, the current results seem off. Here’s the example from the brms UG:

library(brms)
library(tidyverse)

data("LakeHuron")
LakeHuron <- as.data.frame(LakeHuron)

fit <- brm(x ~ ar(p = 2), data = LakeHuron)
summary(fit)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: x ~ ar(p = 2) 
   Data: LakeHuron (Number of observations: 98) 
Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup samples = 4000

Correlation Structures:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
ar[1]     1.07      0.10     0.88     1.26 1.00     1739     2187
ar[2]    -0.25      0.10    -0.45    -0.06 1.00     1717     2018

Population-Level Effects: 
          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept   579.24      0.40   578.52   580.17 1.00     2796     1625

Family Specific Parameters: 
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.72      0.05     0.63     0.83 1.00     2546     2209

Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

That part seems to work fine. Things look off, here.

fitted(fit) %>% 
  data.frame() %>% 
  bind_cols(LakeHuron) %>% 
  mutate(time = 1:n()) %>% 
  
  ggplot(aes(time, ymin = Q2.5, ymax = Q97.5)) +
  geom_ribbon(alpha = 1/2) +
  geom_line(aes(y = Estimate), color = "blue") +
  geom_point(aes(y = x))

fitted
fitted1984×1226 276 KB

Seems like the fitted line should be shifted to the left. What am I missing?

2

This is expected behavior of AR and surprised me as well when I first encountered it. I found a math explanation of stack exchange somewhere back then but cannot seem to find it right now.

1 Like
3

Huh. Thanks for the heads up.

4

Maybe you are looking for this one?: https://stats.stackexchange.com/questions/404650/why-is-arima-in-r-one-time-step-off

2 Likes
5

Thanks for the link, @hhau. This was helpful.