Estimate a Dynamic Factor Model by Maximum Likelihood

Estimate the model parameters by Maximum Likelihood (ML), with initial values obtained from the Expectations-Maximization (EM) algorithm by default. The function includes optional arguments to tune the estimation process.

Usage

estimate_ml(
  dfm,
  data,
  standardized = FALSE,
  input_standardization = NULL,
  pca_init = TRUE,
  em_init = TRUE,
  em_max_iter = 100,
  em_eps = 1e-09,
  max_iter = 1000,
  max_block_iter = 5,
  simpl_model_iter = 15,
  independent_var_shocks = FALSE,
  mixedEstimation = TRUE,
  eps = 1e-09,
  re_estimate = TRUE
)

Arguments

dfm

An object of class "JD3_DFMMODEL", typically generated using the create_model() function.

data

A "mts" object containing the (transformed) input data.

standardized

Boolean. Indicates whether the input data are already standardized. The default is FALSE, in which case standardization is applied as a preprocessing step.

input_standardization

A matrix specifying the mean and standard deviation of the series to be used during standardization. The default is NULL, meaning that these quantities are computed from the data. This argument can be set using the output of get_results()$preprocessing$sample_mean_stdev from a previous model estimation. If provided manually, it must be a two-column matrix with the means in the first column and the standard deviations in the second column. The ordering of the rows must match the series in data. This argument must be provided if re_estimate = FALSE, and is ignored if standardized = TRUE.

pca_init

Boolean. Indicates whether a Principal Components Analysis (PCA) is performed beforehand and used to initialize either the EM algorithm (if em_init = TRUE) or directly the ML estimation. The default is TRUE.

em_init

Boolean. Indicates whether the EM algorithm is run prior to ML estimation and used to provide initial values. The default is TRUE.

em_max_iter

Integer. Specifies the maximum number of iterations for the EM algorithm. Ignored if em_init = FALSE. The default is 100.

em_eps

Numeric. The EM algorithm runs until the increase of the percentage likelihood falls below the eps value (default is 1e-9), or when the maximum number of iterations is reached. Ignored if em_init = FALSE.

max_iter

Integer. Specifies the maximum number of iterations for the ML estimation. The default is 1000.

max_block_iter

Integer. Specifies the maximum number of iterations per block in the optimization process. Model parameters are divided into two blocks: one for measurement equation and one for VAR equations. Unlike the EM algorithm (one iteration per block), numerical optimization allows multiple iterations per block. The default is 5.

simpl_model_iter

Integer. Specifies the number of iterations allowed for the simplified model. The default is 15.

independent_var_shocks

Boolean. Indicates whether shocks in the VAR block are assumed to be independent. The default is FALSE.

mixedEstimation

Boolean. Indicates whether to alternate between iterations on the VAR block alone and simultaneous iterations on the two blocks. The default is TRUE.

eps

Numeric. The ML estimation runs until the increase of the percentage likelihood falls below the eps value (default is 1e-9), or when the maximum number of iterations is reached.

re_estimate

Boolean. Indicates whether the model parameters should be re-estimated. The default is TRUE. It can be set to FALSE to keep the model frozen for some period of time, although prolonged use of a frozen model is not recommended.

Value

An object of class "JD3_DFMESTIMATES" is returned. The following are returned invisibly as a list:

• dfm [[1]] an object of class "JD3_DFMMODEL" containing the estimated model parameters;

• data [[2]] the value of the data argument;

• is_standardized [[3]] the value of the standardized argument;

• input_standardization [[4]] the value of the input_standardization argument;

• log_likelihood [[5]] the estimated log-likelihood;

• gradient [[6]] the estimated gradient at the solution;

• hessian [[7]] the estimated hessian matrix at the solution;

• has_converged [[8]] a boolean indicating whether the ML estimation process has converged.

See also

create_model() to define a new model,

estimate_pca() for estimation using principal components analysis,

estimate_em() for estimation using EM algorithm,

get_results() to access estimation results,

get_forecasts() to obtain forecasts.

For more information, see the vignette:

utils::browseVignettes(), e.g. browseVignettes(package = "rjd3nowcasting")

Examples

if (FALSE) { # rjd3toolkit::get_java_version() >= rjd3toolkit::minimal_java_version
# input data
set.seed(100)
data <- ts(matrix(rnorm(500), 100, 5),
           frequency = 12,
           start = c(2010, 1))
data[100, 1] <- data[99:100, 2] <- data[(1:100)[-seq(3, 100, 3)], 5] <- NA

# define a new model
dfm <- create_model(
    nfactors = 2,
    nlags = 2,
    factors_type = c("M", "M", "YoY", "M", "Q"),
    factors_loading = matrix(data = TRUE, 5, 2),
    var_init = "Unconditional"
)

# estimate by maximum likelihood
est_ml_a <- estimate_ml(dfm, data)

# results and forecasts
rslts_a <- get_results(est_ml_a)
fcsts_a <- get_forecasts(est_ml_a)

# no re-estimation of a previous model while integrating updated data in the output object
data_new <- data
data_new[99, 2] <- 1
est_ml_b <- estimate_ml(est_ml_a$dfm,
                        data_new,
                        input_standardization = rslts_a$preprocessing$sample_mean_stdev,
                        re_estimate = FALSE)
}