Estimate a Dynamic Factor Model Using the Expectations-Maximization Algorithm

Estimate the model parameters using the Expectations-Maximization (EM) algorithm, with PCA-based initialization by default. The function includes optional arguments to tune the estimation process.

Usage

estimate_em(
  dfm,
  data,
  standardized = FALSE,
  input_standardization = NULL,
  pca_init = TRUE,
  max_iter = 100,
  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 the EM algorithm. The default is TRUE.

max_iter

Integer. Specifies the maximum number of iterations in the EM algorithm. The default is 100.

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.

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;

• a couple of other elements not relevant for the EM estimates;

• has_converged [[8]] a boolean indicating whether the EM algorithm has converged.

See also

create_model() to define a new model,

estimate_pca() for estimation using principal components analysis,

estimate_ml() for estimation using maximum likelihood,

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 using EM algorithm
est_em_a <- estimate_em(dfm, data)

# results and forecasts
rslts_a <- get_results(est_em_a)
fcsts_a <- get_forecasts(est_em_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_em_b <- estimate_em(est_em_a$dfm,
                        data_new,
                        input_standardization = rslts_a$preprocessing$sample_mean_stdev,
                        re_estimate = FALSE)
}