simFM: Simulate Dynamic Factor Models.
In TwoStepSDFM: Estimate a Sparse Mixed Frequency Gaussian Factor Model Using a Two-Step Procedure
simFM R Documentation
Simulate Dynamic Factor Models.
Description
Simulate data from a linear Gaussian state-space model (latent factor model),
with measurement equation
\bm{x}_t = \bm{\Lambda} \bm{f}_{t} + \bm{\xi}_t,\quad \bm{\xi}_t \sim \mathcal{N}(\bm{\mu}, \bm{\Sigma}_{\xi}),
and transition equation
\bm{f}_t = \sum_{p=1}^P\bm{\Phi}_p \bm{f}_{t-p} + \bm{\epsilon}_t,\quad \bm{\epsilon}_t \sim \mathcal{N}(\bm{0}, \bm{\Sigma}_{f}).
for t = 1, ..., T, as is used in, among others,
\insertReffranjic2024nowcastingTwoStepSDFM.
Usage
simFM(
no_of_obs,
no_of_vars,
no_of_factors,
loading_matrix,
meas_error_mean,
meas_error_var_cov,
trans_error_var_cov,
trans_var_coeff,
factor_lag_order,
delay = NULL,
quarterfy = FALSE,
quarterly_variable_ratio = 0,
corr = FALSE,
beta_param = Inf,
seed = 20022024,
burn_in = 1000,
rescale = TRUE,
starting_date = NULL,
check_stationarity = FALSE,
stationarity_check_threshold = 1e-05,
parallel = FALSE
)
Arguments
no_of_obs
Integer number of observations.
no_of_vars
Integer number of Variables.
no_of_factors
Integer number of factors.
loading_matrix
Numeric (no_of_vars \times no_of_factors)
loading matrix.
meas_error_mean
Numeric vector of the means of the measurement errors.
meas_error_var_cov
Numeric (no_of_vars \times
no_of_vars) variance-covariance matrix of the measurement errors.
trans_error_var_cov
Numeric (no_of_factors \times
no_of_factors) variance-covariance matrix of the transition errors.
trans_var_coeff
Either a list of length max_factor_lag_order with
each entry a numeric (no_of_factors \times no_of_factors) VAR
coefficient matrix or a matrix of dimensions (no_of_factors \times
(no_of_factors * max_factor_lag_order)) holding the VAR coefficients of the
factor VAR process in each (no_of_factors \times no_of_factors)
block.
factor_lag_order
Integer order of the VAR process in the transition
equation.
delay
Integer vector of delays imposed onto the end of the data
(ragged edges).
quarterfy
Logical, whether or not some of the data should be
aggregated to quarterly representations.
quarterly_variable_ratio
Ratio of variables ought to be quarterfied.
corr
Logical, whether or not the measurement error should be randomly
correlated inside the function using a random correlation matrix with
off-diagonal elements governed by a beta-distribution.
beta_param
Parameter of the beta-distribution governing the
off-diagonal elements of the variance-covariance matrix of the measurement
error.
seed
32-bit unsigned integer seed for all random processes inside the
function.
burn_in
Integer burn-in period of the simulated data ought to be
discarded at the beginning of the sample.
rescale
Logical, whether or not the variance of the measurement error
should be rescaled by the common component to equalise the
signal-to-noise ratio.
starting_date
A date type object indicating the start of the dataset.
If NULL (default), the function returns matrices with observations along the
second dimension (i.e., time in columns). If specified, the function treats
the data as a time series and returns a zoo object.
check_stationarity
Logical, whether or not the stationarity properties
of the factor VAR process should be checked.
stationarity_check_threshold
Threshold of the stationarity check for
when to deem an eigenvalue numerically negative.
parallel
Logical, make use of Eigen internal parallel matrix
operations.
Details
The delay vector indicates the number of observations at the end of the
sample that will be set to NA for each variable. Here, delay refers to
the number of months for monthly data and the number of quarters for
quarterly data. For example, consider delay <- c(1, 1) and assume the
variable with index 1 will be quarterfied. In that case, the variable with
index 1 will be delayed by 1 quarter, i.e., it will be missing 3
observations at the end of the panel. The variable with index 2 will be
delayed by 1 month, i.e., it will be missing 1 observation at the end of the
panel. This convention differs from the delay object of the SimulData
class this function returns. There, delay represents the number of months
since the most recent publication. For monthly variables, these values
coincide, but for quarterly variables they are inherently different.
If quarterfy = TRUE, floor(quarterly_variable_ratio * no_of_vars)
variables will be aggregated to a quarterly representation using the
geometric mean according to
\insertRefMariano2003new_coincidentTwoStepSDFM.
If corr = TRUE, the matrix meas_error_var_cov is internally replaced by a
random variance-covariance matrix:
\tilde{\bm{\Sigma}}:=\bm{S}\bm{R}\bm{S},
where \bm{S} is a diagonal matrix with entries
equal to sqrt(diag(meas_error_var_cov)) and \bm{R} is a
random correlation matrix. \bm{R} is drawn according to
\insertReflewandowski2009generatingTwoStepSDFM (see also
https://stats.stackexchange.com/questions/2746/how-to-efficiently-generate-random-positive-semidefinite-correlation-matrices).
The parameter beta_param governs the degree of cross-correlation of the
off-diagonal elements. For more information see the literature cited above.
The random draws of the fundamental error terms are drawn within the C++
backend. Therefore, seed must be provided and set.seed() will not
guarantee reproduceability.
Value
Returns a SimulData containing the following elements:
- data
If starting_date is provided, a zoo object, else,
a (no_of_vars \times no_of_obs) numeric matrix holding the
simulated data.
- factors
If starting_date is provided, a zoo object, else a
(no_of_factors \times no_of_obs) numeric matrix holding the
simulated latent factors.
- trans_var_coeff
Numeric (no_of_factors \times
(no_of_factors * factor_lag_order)) factor VAR coefficient matrix.
- loading_matrix
Numeric factor loading matrix.
- meas_error
If starting_date is provided, a zoo object, else
a (no_of_vars \times no_of_obs) numeric matrix holding the
fundamental measurement errors.
- meas_error_var_cov
Numeric measurement error
variance-covariance matrix.
- trans_error_var_cov
Numeric transition error
variance-covariance matrix.
- frequency
Integer vector of variable frequencies.
- delay
Integer vector of variable delays, measured as the number of
months since the latest available observation.
Author(s)
Domenic Franjic
References
\insertRefMariano2003new_coincidentTwoStepSDFM
\insertReflewandowski2009generatingTwoStepSDFM
\insertReffranjic2024nowcastingTwoStepSDFM
Examples
seed <- 02102025
set.seed(seed)
no_of_obs <- 100
no_of_vars <- 50
no_of_factors <- 3
trans_error_var_cov <- diag(1, no_of_factors)
loading_matrix <- matrix(round(rnorm(no_of_vars * no_of_factors)), no_of_vars, no_of_factors)
meas_error_mean <- rep(0, no_of_vars)
meas_error_var_cov <- diag(1, no_of_vars)
trans_var_coeff <- cbind(diag(0.5, no_of_factors), -diag(0.25, no_of_factors))
factor_lag_order <- 2
delay <- c(floor(rexp(no_of_vars, 1)))
quarterfy <- FALSE
quarterly_variable_ratio <- 0
corr <- TRUE
beta_param <- 2
burn_in <- 999
starting_date <- "1970-01-01"
rescale <- TRUE
check_stationarity <- TRUE
stationarity_check_threshold <- 1e-10
factor_model <- simFM(no_of_obs = no_of_obs, no_of_vars = no_of_vars,
no_of_factors = no_of_factors, loading_matrix = loading_matrix,
meas_error_mean = meas_error_mean,
meas_error_var_cov = meas_error_var_cov,
trans_error_var_cov = trans_error_var_cov,
trans_var_coeff = trans_var_coeff,
factor_lag_order = factor_lag_order, delay = delay,
quarterfy = quarterfy,
quarterly_variable_ratio = quarterly_variable_ratio, corr = corr,
beta_param = beta_param, seed = seed, burn_in = burn_in,
starting_date = starting_date, rescale = rescale,
check_stationarity = check_stationarity,
stationarity_check_threshold = stationarity_check_threshold)
print(factor_model)
spca_plots <- plot(factor_model)
spca_plots$`Factor Time Series Plots`
spca_plots$`Loading Matrix Heatmap`
spca_plots$`Meas. Error Var.-Cov. Matrix Heatmap`
spca_plots$`Meas. Error Var.-Cov. Eigenvalue Plot`
spca_plots$`Data Var.-Cov. Matrix Heatmap`
spca_plots$`Data Var.-Cov. Eigenvalue Plot`
TwoStepSDFM documentation built on May 19, 2026, 9:07 a.m.
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| simFM | R Documentation |
Simulate Dynamic Factor Models.
Description
Simulate data from a linear Gaussian state-space model (latent factor model), with measurement equation
\bm{x}_t = \bm{\Lambda} \bm{f}_{t} + \bm{\xi}_t,\quad \bm{\xi}_t \sim \mathcal{N}(\bm{\mu}, \bm{\Sigma}_{\xi}),
and transition equation
\bm{f}_t = \sum_{p=1}^P\bm{\Phi}_p \bm{f}_{t-p} + \bm{\epsilon}_t,\quad \bm{\epsilon}_t \sim \mathcal{N}(\bm{0}, \bm{\Sigma}_{f}).
for t = 1, ..., T, as is used in, among others, \insertReffranjic2024nowcastingTwoStepSDFM.
Usage
simFM(
no_of_obs,
no_of_vars,
no_of_factors,
loading_matrix,
meas_error_mean,
meas_error_var_cov,
trans_error_var_cov,
trans_var_coeff,
factor_lag_order,
delay = NULL,
quarterfy = FALSE,
quarterly_variable_ratio = 0,
corr = FALSE,
beta_param = Inf,
seed = 20022024,
burn_in = 1000,
rescale = TRUE,
starting_date = NULL,
check_stationarity = FALSE,
stationarity_check_threshold = 1e-05,
parallel = FALSE
)
Arguments
no_of_obs |
Integer number of observations. |
no_of_vars |
Integer number of Variables. |
no_of_factors |
Integer number of factors. |
loading_matrix |
Numeric ( |
meas_error_mean |
Numeric vector of the means of the measurement errors. |
meas_error_var_cov |
Numeric ( |
trans_error_var_cov |
Numeric ( |
trans_var_coeff |
Either a list of length |
factor_lag_order |
Integer order of the VAR process in the transition equation. |
delay |
Integer vector of delays imposed onto the end of the data (ragged edges). |
quarterfy |
Logical, whether or not some of the data should be aggregated to quarterly representations. |
quarterly_variable_ratio |
Ratio of variables ought to be quarterfied. |
corr |
Logical, whether or not the measurement error should be randomly correlated inside the function using a random correlation matrix with off-diagonal elements governed by a beta-distribution. |
beta_param |
Parameter of the beta-distribution governing the off-diagonal elements of the variance-covariance matrix of the measurement error. |
seed |
32-bit unsigned integer seed for all random processes inside the function. |
burn_in |
Integer burn-in period of the simulated data ought to be discarded at the beginning of the sample. |
rescale |
Logical, whether or not the variance of the measurement error should be rescaled by the common component to equalise the signal-to-noise ratio. |
starting_date |
A date type object indicating the start of the dataset.
If NULL (default), the function returns matrices with observations along the
second dimension (i.e., time in columns). If specified, the function treats
the data as a time series and returns a |
check_stationarity |
Logical, whether or not the stationarity properties of the factor VAR process should be checked. |
stationarity_check_threshold |
Threshold of the stationarity check for when to deem an eigenvalue numerically negative. |
parallel |
Logical, make use of Eigen internal parallel matrix operations. |
Details
The delay vector indicates the number of observations at the end of the
sample that will be set to NA for each variable. Here, delay refers to
the number of months for monthly data and the number of quarters for
quarterly data. For example, consider delay <- c(1, 1) and assume the
variable with index 1 will be quarterfied. In that case, the variable with
index 1 will be delayed by 1 quarter, i.e., it will be missing 3
observations at the end of the panel. The variable with index 2 will be
delayed by 1 month, i.e., it will be missing 1 observation at the end of the
panel. This convention differs from the delay object of the SimulData
class this function returns. There, delay represents the number of months
since the most recent publication. For monthly variables, these values
coincide, but for quarterly variables they are inherently different.
If quarterfy = TRUE, floor(quarterly_variable_ratio * no_of_vars)
variables will be aggregated to a quarterly representation using the
geometric mean according to
\insertRefMariano2003new_coincidentTwoStepSDFM.
If corr = TRUE, the matrix meas_error_var_cov is internally replaced by a
random variance-covariance matrix:
\tilde{\bm{\Sigma}}:=\bm{S}\bm{R}\bm{S},
where \bm{S} is a diagonal matrix with entries
equal to sqrt(diag(meas_error_var_cov)) and \bm{R} is a
random correlation matrix. \bm{R} is drawn according to
\insertReflewandowski2009generatingTwoStepSDFM (see also
https://stats.stackexchange.com/questions/2746/how-to-efficiently-generate-random-positive-semidefinite-correlation-matrices).
The parameter beta_param governs the degree of cross-correlation of the
off-diagonal elements. For more information see the literature cited above.
The random draws of the fundamental error terms are drawn within the C++
backend. Therefore, seed must be provided and set.seed() will not
guarantee reproduceability.
Value
Returns a SimulData containing the following elements:
- data
If
starting_dateis provided, azooobject, else, a (no_of_vars\timesno_of_obs) numeric matrix holding the simulated data.- factors
If
starting_dateis provided, azooobject, else a (no_of_factors\timesno_of_obs) numeric matrix holding the simulated latent factors.- trans_var_coeff
Numeric (
no_of_factors\times(no_of_factors*factor_lag_order)) factor VAR coefficient matrix.- loading_matrix
Numeric factor loading matrix.
- meas_error
If
starting_dateis provided, azooobject, else a (no_of_vars\timesno_of_obs) numeric matrix holding the fundamental measurement errors.- meas_error_var_cov
Numeric measurement error variance-covariance matrix.
- trans_error_var_cov
Numeric transition error variance-covariance matrix.
- frequency
Integer vector of variable frequencies.
- delay
Integer vector of variable delays, measured as the number of months since the latest available observation.
Author(s)
Domenic Franjic
References
\insertRefMariano2003new_coincidentTwoStepSDFM
\insertReflewandowski2009generatingTwoStepSDFM
\insertReffranjic2024nowcastingTwoStepSDFM
Examples
seed <- 02102025
set.seed(seed)
no_of_obs <- 100
no_of_vars <- 50
no_of_factors <- 3
trans_error_var_cov <- diag(1, no_of_factors)
loading_matrix <- matrix(round(rnorm(no_of_vars * no_of_factors)), no_of_vars, no_of_factors)
meas_error_mean <- rep(0, no_of_vars)
meas_error_var_cov <- diag(1, no_of_vars)
trans_var_coeff <- cbind(diag(0.5, no_of_factors), -diag(0.25, no_of_factors))
factor_lag_order <- 2
delay <- c(floor(rexp(no_of_vars, 1)))
quarterfy <- FALSE
quarterly_variable_ratio <- 0
corr <- TRUE
beta_param <- 2
burn_in <- 999
starting_date <- "1970-01-01"
rescale <- TRUE
check_stationarity <- TRUE
stationarity_check_threshold <- 1e-10
factor_model <- simFM(no_of_obs = no_of_obs, no_of_vars = no_of_vars,
no_of_factors = no_of_factors, loading_matrix = loading_matrix,
meas_error_mean = meas_error_mean,
meas_error_var_cov = meas_error_var_cov,
trans_error_var_cov = trans_error_var_cov,
trans_var_coeff = trans_var_coeff,
factor_lag_order = factor_lag_order, delay = delay,
quarterfy = quarterfy,
quarterly_variable_ratio = quarterly_variable_ratio, corr = corr,
beta_param = beta_param, seed = seed, burn_in = burn_in,
starting_date = starting_date, rescale = rescale,
check_stationarity = check_stationarity,
stationarity_check_threshold = stationarity_check_threshold)
print(factor_model)
spca_plots <- plot(factor_model)
spca_plots$`Factor Time Series Plots`
spca_plots$`Loading Matrix Heatmap`
spca_plots$`Meas. Error Var.-Cov. Matrix Heatmap`
spca_plots$`Meas. Error Var.-Cov. Eigenvalue Plot`
spca_plots$`Data Var.-Cov. Matrix Heatmap`
spca_plots$`Data Var.-Cov. Eigenvalue Plot`
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