Set up an autoregressive moving average (ARMA) term of order (p, q) in brms. The function does not evaluate its arguments – it exists purely to help set up a model with ARMA terms.
Arguments
- time
An optional time variable specifying the time ordering of the observations. By default, the existing order of the observations in the data is used.
- gr
An optional grouping variable. If specified, the correlation structure is assumed to apply only to observations within the same grouping level.
- p
A non-negative integer specifying the autoregressive (AR) order of the ARMA structure. Default is
1.- q
A non-negative integer specifying the moving average (MA) order of the ARMA structure. Default is
1.- cov
A flag indicating whether ARMA effects should be estimated by means of residual covariance matrices. This is currently only possible for stationary ARMA effects of order 1. If the model family does not have natural residuals, latent residuals are added automatically. If
FALSE(the default), a regression formulation is used that is considerably faster and allows for ARMA effects of order higher than 1 but is only available forgaussianmodels and some of its generalizations.
Value
An object of class 'arma_term', which is a list
of arguments to be interpreted by the formula
parsing functions of brms.
See also
autocor-terms, ar, ma,
Examples
# \dontrun{
data("LakeHuron")
LakeHuron <- as.data.frame(LakeHuron)
fit <- brm(x ~ arma(p = 2, q = 1), data = LakeHuron)
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 5.5e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.55 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
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#> Chain 1:
#> Chain 1: Elapsed Time: 6.565 seconds (Warm-up)
#> Chain 1: 0.753 seconds (Sampling)
#> Chain 1: 7.318 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 3e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.3 seconds.
#> Chain 2: Adjust your expectations accordingly!
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#> Chain 2:
#> Chain 2: Elapsed Time: 27.259 seconds (Warm-up)
#> Chain 2: 29.823 seconds (Sampling)
#> Chain 2: 57.082 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 3.1e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.31 seconds.
#> Chain 3: Adjust your expectations accordingly!
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#> Chain 3:
#> Chain 3: Elapsed Time: 2.479 seconds (Warm-up)
#> Chain 3: 5.194 seconds (Sampling)
#> Chain 3: 7.673 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 3.1e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.31 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4:
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#> Chain 4:
#> Chain 4: Elapsed Time: 2.804 seconds (Warm-up)
#> Chain 4: 0.578 seconds (Sampling)
#> Chain 4: 3.382 seconds (Total)
#> Chain 4:
#> Warning: There were 51 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: There were 1000 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
#> https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: The largest R-hat is 1.53, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
summary(fit)
#> Warning: Inference for the model posterior has not converged (some Rhats are > 1.05). Be careful when analysing the results! We recommend running more iterations or setting stronger priors.
#> Warning: There were 51 divergent transitions after warmup. Increasing adapt_delta above 0.8 may help. See http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> Family: gaussian
#> Links: mu = identity
#> Formula: x ~ arma(p = 2, q = 1)
#> Data: LakeHuron (Number of observations: 98)
#> Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#> total post-warmup draws = 4000
#>
#> Correlation Structures:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> ar[1] 1.02 0.62 0.11 1.98 1.53 7 NA
#> ar[2] -0.17 0.47 -0.86 0.58 1.53 7 4
#> ma[1] -0.05 0.78 -1.33 0.87 1.53 7 4
#>
#> Regression Coefficients:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept 434.75 250.29 1.29 580.08 1.53 7 4
#>
#> Further Distributional Parameters:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sigma 1.46 1.29 0.62 3.70 1.53 7 NA
#>
#> Draws were sampled 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).
# }