Dynamic Factor Models

Description

dfms provides efficient estimation of Dynamic Factor Models via the EM Algorithm — following Doz, Giannone & Reichlin (2011, 2012) and Banbura & Modugno (2014). Contents:

Information Criteria to Determine the Number of Factors

ICr()

• plot(<ICr>)
  

• screeplot(<ICr>)
  

Fit a Dynamic Factor Model

DFM()

• summary(<dfm>)
  

• plot(<dfm>)
  

• as.data.frame(<dfm>)
  

• residuals(<dfm>)
  

• fitted(<dfm>)

Generate Forecasts

predict(<dfm>)

• plot(<dfm_forecast>)
  

• as.data.frame(<dfm_forecast>)
  

Fast Stationary Kalman Filtering and Smoothing

SKF() — Stationary Kalman Filter
FIS() — Fixed Interval Smoother
SKFS() — Stationary Kalman Filter + Smoother

Helper Functions

.VAR() — (Fast) Barebones Vector-Autoregression
ainv() — Armadillo's Inverse Function
apinv() — Armadillo's Pseudo-Inverse Function
tsnarmimp() — Remove and Impute Missing Values in a Multivariate Time Series
em_converged() — Convergence Test for EM-Algorithm

Data

BM14_M — Monthly Series by Banbura and Modugno (2014)
BM14_Q — Quarterly Series by Banbura and Modugno (2014)
BM14_Models — Series Metadata + Small/Medium/Large Model Specifications

References

Doz, C., Giannone, D., & Reichlin, L. (2011). A two-step estimator for large approximate dynamic factor models based on Kalman filtering. Journal of Econometrics, 164(1), 188-205. doi:10.1016/j.jeconom.2011.02.012

Doz, C., Giannone, D., & Reichlin, L. (2012). A quasi-maximum likelihood approach for large, approximate dynamic factor models. Review of Economics and Statistics, 94(4), 1014-1024. doi:10.1162/REST_a_00225

Banbura, M., & Modugno, M. (2014). Maximum likelihood estimation of factor models on datasets with arbitrary pattern of missing data. Journal of Applied Econometrics, 29(1), 133-160. doi:10.1002/jae.2306

(Fast) Barebones Vector-Autoregression

Description

Quickly estimate a VAR(p) model using Armadillo's inverse function.

Usage

.VAR(x, p = 1L)

Arguments

Value

A list containing matrices Y = x[-(1:p), ], X which contains lags 1 - p of x combined column-wise, A which is the np \times n transition matrix, where n is the number of series in x, and the VAR residual matrix res = Y - X %*% A.

A list with the following elements:

See Also

dfms-package

Examples

var = .VAR(diff(EuStockMarkets), 3)
str(var)
var$A
rm(var)

Euro Area Macroeconomic Data from Banbura and Modugno 2014

Description

A data extract from BM 2014 replication files. Some proprietary series (mostly PMI's) are excluded. The dataset BM14_Models provides information about all series and their inclusion in the 'small', 'medium' and 'large' sized dynamic factor models estimated by BM 2014. The actual data is contained in xts format in BM14_M for monthly data and BM14_Q for quarterly data.

Usage

BM14_Models
BM14_M
BM14_Q

Format

BM14_Models is a data frame with 101 obs. (series) and 8 columns:

series

BM14 series code (converted to snake case for R)

label

BM14 series label

code

original series code from data source

freq

series frequency

log_trans

logical indicating whether the series was transformed by the natural log before differencing. Note that all data are provided in untransformed levels, and all data was (log-)differenced by BM14 before estimation.

small

logical indicating series included in the 'small' model of BM14. Proprietary series are excluded.

medium

logical indicating series included in the 'medium' model of BM14. Proprietary series are excluded.

large

logical indicating series included in the 'large' model of BM14. This comprises all series, thus the variable is redundant but included for completeness. Proprietary series are excluded.

Source

Banbura, M., & Modugno, M. (2014). Maximum likelihood estimation of factor models on datasets with arbitrary pattern of missing data. Journal of Applied Econometrics, 29(1), 133-160.

See Also

dfms-package

Examples

library(magrittr)
library(xts)

# Constructing the database for the large model
BM14 = merge(BM14_M, BM14_Q)
BM14[, BM14_Models$log_trans] %<>% log()
BM14[, BM14_Models$freq == "M"] %<>% diff()
BM14[, BM14_Models$freq == "Q"] %<>% diff(3)

# Small Model Database
head(BM14[, BM14_Models$small])

# Medium-Sized Model Database
head(BM14[, BM14_Models$medium])

Estimate a Dynamic Factor Model

Description

Efficient estimation of a Dynamic Factor Model via the EM Algorithm - on stationary data with time-invariant system matrices and classical assumptions, while permitting missing data.

Usage

DFM(
  X,
  r,
  p = 1L,
  ...,
  idio.ar1 = FALSE,
  quarterly.vars = NULL,
  rQ = c("none", "diagonal", "identity"),
  rR = c("diagonal", "identity", "none"),
  em.method = c("auto", "DGR", "BM", "none"),
  min.iter = 25L,
  max.iter = 100L,
  tol = 1e-04,
  pos.corr = TRUE,
  check.increased = FALSE
)

Arguments

Details

This function efficiently estimates a Dynamic Factor Model with the following classical assumptions:

1. Linearity

2. Idiosynchratic measurement (observation) errors (R is diagonal)

3. No direct relationship between series and lagged factors (ceteris paribus contemporaneous factors)

4. No relationship between lagged error terms in the either measurement or transition equation (no serial correlation), unless explicitly modeled as AR(1) processes using idio.ar1 = TRUE.

Factors are allowed to evolve in a VAR(p) process, and data is internally standardized (scaled and centered) before estimation (removing the need of intercept terms). By assumptions 1-4, this translates into the following dynamic form:

\textbf{x}_t = \textbf{C}_0 \textbf{f}_t + \textbf{e}_t \ \sim\ N(\textbf{0}, \textbf{R})

\textbf{f}_t = \sum_{j=1}^p \textbf{A}_j \textbf{f}_{t-j} + \textbf{u}_t \ \sim\ N(\textbf{0}, \textbf{Q}_0)

where the first equation is called the measurement or observation equation and the second equation is called transition, state or process equation, and

This model can be estimated using a classical form of the Kalman Filter and the Expectation Maximization (EM) algorithm, after transforming it to State-Space (stacked, VAR(1)) form:

\textbf{x}_t = \textbf{C} \textbf{F}_t + \textbf{e}_t \ \sim\ N(\textbf{0}, \textbf{R})

\textbf{F}_t = \textbf{A F}_{t-1} + \textbf{u}_t \ \sim\ N(\textbf{0}, \textbf{Q})

where

The filter is initialized with PCA estimates on the imputed dataset—see SKFS for a complete code example.

Value

A list-like object of class 'dfm' with the following elements:

References

Doz, C., Giannone, D., & Reichlin, L. (2011). A two-step estimator for large approximate dynamic factor models based on Kalman filtering. Journal of Econometrics, 164(1), 188-205.

Doz, C., Giannone, D., & Reichlin, L. (2012). A quasi-maximum likelihood approach for large, approximate dynamic factor models. Review of Economics and Statistics, 94(4), 1014-1024.

Banbura, M., & Modugno, M. (2014). Maximum likelihood estimation of factor models on datasets with arbitrary pattern of missing data. Journal of Applied Econometrics, 29(1), 133-160.

Stock, J. H., & Watson, M. W. (2016). Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics. Handbook of Macroeconomics, 2, 415–525. https://doi.org/10.1016/bs.hesmac.2016.04.002

See Also

dfms-package

Examples

library(magrittr)
library(xts)
library(vars)

# BM14 Replication Data. Constructing the database:
BM14 <- merge(BM14_M, BM14_Q)
BM14[, BM14_Models$log_trans] %<>% log()
BM14[, BM14_Models$freq == "M"] %<>% diff()
BM14[, BM14_Models$freq == "Q"] %<>% diff(3)


### Small Model ---------------------------------------

# IC for number of factors
IC_small <- ICr(BM14[, BM14_Models$small], max.r = 5)
plot(IC_small)
screeplot(IC_small)

# I take 2 factors. Now number of lags
VARselect(IC_small$F_pca[, 1:2])

# Estimating the model with 2 factors and 3 lags
dfm_small <- DFM(BM14[, BM14_Models$small], r = 2, p = 3,
    quarterly.vars = BM14_Models %$% series[freq == "Q" & small])

# Inspecting the model
summary(dfm_small)
plot(dfm_small)  # Factors and data
plot(dfm_small, method = "all", type = "individual") # Factor estimates
plot(dfm_small, type = "residual") # Residuals from factor predictions

# 10 periods ahead forecast
plot(predict(dfm_small), xlim = c(300, 370))


### Medium-Sized Model ---------------------------------

# IC for number of factors
IC_medium <- ICr(BM14[, BM14_Models$medium])
plot(IC_medium)
screeplot(IC_medium)

# I take 3 factors. Now number of lags
VARselect(IC_medium$F_pca[, 1:3])

# Estimating the model with 3 factors and 3 lags
dfm_medium <- DFM(BM14[, BM14_Models$medium], r = 3, p = 3,
    quarterly.vars = BM14_Models %$% series[freq == "Q" & medium])

# Inspecting the model
summary(dfm_medium)
plot(dfm_medium)  # Factors and data
plot(dfm_medium, method = "all", type = "individual") # Factor estimates
plot(dfm_medium, type = "residual") # Residuals from factor predictions

# 10 periods ahead forecast
plot(predict(dfm_medium), xlim = c(300, 370))


### Large Model ---------------------------------

# IC for number of factors
IC_large <- ICr(BM14)
plot(IC_large)
screeplot(IC_large)

# I take 6 factors. Now number of lags
VARselect(IC_large$F_pca[, 1:6])

# Estimating the model with 6 factors and 3 lags
dfm_large <- DFM(BM14, r = 6, p = 3,
    quarterly.vars = BM14_Models %$% series[freq == "Q"])

# Inspecting the model
summary(dfm_large)
plot(dfm_large)  # Factors and data
# plot(dfm_large, method = "all", type = "individual") # Factor estimates
plot(dfm_large, type = "residual") # Residuals from factor predictions

# 10 periods ahead forecast
plot(predict(dfm_large), xlim = c(300, 370))

(Fast) Fixed-Interval Smoother (Kalman Smoother)

Description

(Fast) Fixed-Interval Smoother (Kalman Smoother)

Usage

FIS(A, F, F_pred, P, P_pred, F_0 = NULL, P_0 = NULL)

Arguments

Details

The Kalman Smoother is given by:

\textbf{J}_t = \textbf{P}_t \textbf{A} + inv(\textbf{P}^{pred}_{t+1})

\textbf{F}^{smooth}_t = \textbf{F}_t + \textbf{J}_t (\textbf{F}^{smooth}_{t+1} - \textbf{F}^{pred}_{t+1})

\textbf{P}^{smooth}_t = \textbf{P}_t + \textbf{J}_t (\textbf{P}^{smooth}_{t+1} - \textbf{P}^{pred}_{t+1}) \textbf{J}_t'

The initial smoothed values for period t = T are set equal to the filtered values. If F_0 and P_0 are supplied, the smoothed initial conditions (t = 0 values) are also calculated and returned. For further details see any textbook on time series such as Shumway & Stoffer (2017), which provide an analogous R implementation in astsa::Ksmooth0.

Value

Smoothed state and covariance estimates, including initial (t = 0) values.

References

Shumway, R. H., & Stoffer, D. S. (2017). Time Series Analysis and Its Applications: With R Examples. Springer.

Harvey, A. C. (1990). Forecasting, structural time series models and the Kalman filter.

See Also

SKF SKFS dfms-package

Examples

# See ?SKFS

Information Criteria to Determine the Number of Factors (r)

Description

Minimizes 3 information criteria proposed by Bai and Ng (2002) to determine the optimal number of factors r* to be used in an approximate factor model. A Screeplot can also be computed to eyeball the number of factors in the spirit of Onatski (2010).

Usage

ICr(X, max.r = min(20, ncol(X) - 1))

## S3 method for class 'ICr'
print(x, ...)

## S3 method for class 'ICr'
plot(x, ...)

## S3 method for class 'ICr'
screeplot(x, type = "pve", show.grid = TRUE, max.r = 30, ...)

Arguments

Details

Following Bai and Ng (2002) and De Valk et al. (2019), let NSSR(r) be the normalized sum of squared residuals SSR(r) / (n \times T) when r factors are estimated using principal components. Then the information criteria can be written as follows:

IC_{r1} = \ln(NSSR(r)) + r\left(\frac{n + T}{nT}\right) + \ln\left(\frac{nT}{n + T}\right)

IC_{r2} = \ln(NSSR(r)) + r\left(\frac{n + T}{nT}\right) + \ln(\min(n, T))

IC_{r3} = \ln(NSSR(r)) + r\left(\frac{\ln(\min(n, T))}{\min(n, T)}\right)

The optimal number of factors r* corresponds to the minimum IC. The three criteria are are asymptotically equivalent, but may give significantly different results for finite samples. The penalty in IC_{r2} is highest in finite samples.

In the Screeplot a horizontal dashed line is shown signifying an eigenvalue of 1, or a share of variance corresponding to 1 divided by the number of eigenvalues.

Value

A list of 4 elements:

Note

To determine the number of lags (p) in the factor transition equation, use the function vars::VARselect with r* principle components (also returned by ICr).

References

Bai, J., Ng, S. (2002). Determining the Number of Factors in Approximate Factor Models. Econometrica, 70(1), 191-221. https://doi.org/10.1111/1468-0262.00273.

Onatski, A. (2010). Determining the number of factors from empirical distribution of eigenvalues. The Review of Economics and Statistics, 92(4), 1004-1016.

De Valk, S., de Mattos, D., & Ferreira, P. (2019). Nowcasting: An R package for predicting economic variables using dynamic factor models. The R Journal, 11(1), 230-244.

See Also

dfms-package

Examples

library(xts)
library(vars)

ics <- ICr(diff(BM14_M))
print(ics)
plot(ics)
screeplot(ics)

# Optimal lag-order with 6 factors chosen
VARselect(ics$F_pca[, 1:6])

(Fast) Stationary Kalman Filter

Description

A simple and fast C++ implementation of the Kalman Filter for stationary data (or random walks - data should be mean zero and without a trend) with time-invariant system matrices and missing data.

Usage

SKF(X, A, C, Q, R, F_0, P_0, loglik = FALSE)

Arguments

Details

The underlying state space model is:

\textbf{x}_t = \textbf{C} \textbf{F}_t + \textbf{e}_t \sim N(\textbf{0}, \textbf{R})

\textbf{F}_t = \textbf{A F}_{t-1} + \textbf{u}_t \sim N(\textbf{0}, \textbf{Q})

where x_t is X[t, ]. The filter then first performs a time update (prediction)

\textbf{F}_t = \textbf{A F}_{t-1}

\textbf{P}_t = \textbf{A P}_{t-1}\textbf{A}' + \textbf{Q}

where P_t = Cov(F_t). This is followed by the measurement update (filtering)

\textbf{K}_t = \textbf{P}_t \textbf{C}' (\textbf{C P}_t \textbf{C}' + \textbf{R})^{-1}

\textbf{F}_t = \textbf{F}_t + \textbf{K}_t (\textbf{x}_t - \textbf{C F}_t)

\textbf{P}_t = \textbf{P}_t - \textbf{K}_t\textbf{C P}_t

If a row of the data is all missing the measurement update is skipped i.e. the prediction becomes the filtered value. The log-likelihood is computed as

1/2 \sum_t \log(|St|)-e_t'S_te_t-n\log(2\pi)

where S_t = (C P_t C' + R)^{-1} and e_t = x_t - C F_t is the prediction error.

For further details see any textbook on time series such as Shumway & Stoffer (2017), which provide an analogous R implementation in astsa::Kfilter0. For another fast (C-based) implementation that also allows time-varying system matrices and non-stationary data see FKF::fkf.

Value

Predicted and filtered state vectors and covariances.

References

Shumway, R. H., & Stoffer, D. S. (2017). Time Series Analysis and Its Applications: With R Examples. Springer.

Harvey, A. C. (1990). Forecasting, structural time series models and the Kalman filter.

Hamilton, J. D. (1994). Time Series Analysis. Princeton university press.

See Also

FIS SKFS dfms-package

Examples

# See ?SKFS

(Fast) Stationary Kalman Filter and Smoother

Description

(Fast) Stationary Kalman Filter and Smoother

Usage

SKFS(X, A, C, Q, R, F_0, P_0, loglik = FALSE)

Arguments

Value

All results from SKF and FIS, and additionally a rp \times rp \times T matrix PPm_smooth, which is equal to the estimate of Cov(F^{smooth}_t, F^{smooth}_{t-1} | T) and needed for EM iterations. See 'Property 6.3: The Lag-One Covariance Smoother' in Shumway & Stoffer (2017).

References

Shumway, R. H., & Stoffer, D. S. (2017). Time Series Analysis and Its Applications: With R Examples. Springer.

See Also

SKF FIS dfms-package

Examples

library(collapse)

## Two-Step factor estimates from monthly BM (2014) data
X <- fscale(diff(qM(BM14_M))) # Standardizing as KF has no intercept
r <- 5L # 5 Factors
p <- 3L # 3 Lags
n <- ncol(X)

## Initializing the Kalman Filter with PCA results
X_imp <- tsnarmimp(X)                 # Imputing Data
v <- eigen(cov(X_imp))$vectors[, 1:r] # PCA
F_pc <- X_imp %*% v                   # Principal component factor estimates
C <- cbind(v, matrix(0, n, r*p-r))    # Observation matrix
res <- X - tcrossprod(F_pc, v)        # Residuals from static predictions
R <- diag(fvar(res))                  # Observation residual covariance
var <- .VAR(F_pc, p)                  # VAR(p)
A <- rbind(t(var$A), diag(1, r*p-r, r*p))
Q <- matrix(0, r*p, r*p)              # VAR residual matrix
Q[1:r, 1:r] <- cov(var$res)
F_0 <- var$X[1L, ]                    # Initial factor estimate and covariance
P_0 <- ainv(diag((r*p)^2) - kronecker(A,A)) %*% unattrib(Q)
dim(P_0) <- c(r*p, r*p)

## Run standartized data through Kalman Filter and Smoother once
kfs_res <- SKFS(X, A, C, Q, R, F_0, P_0, FALSE)

## Two-step solution is state mean from the Kalman Smoother
F_kal <- kfs_res$F_smooth[, 1:r, drop = FALSE]
colnames(F_kal) <- paste0("f", 1:r)

## See that this is equal to the Two-Step estimate by DFM()
all.equal(F_kal, DFM(X, r, p, em.method = "none", pos.corr = FALSE)$F_2s)

## Same in two steps using SKF() and FIS()
kfs_res2 <- with(SKF(X, A, C, Q, R, F_0, P_0, FALSE), FIS(A, F, F_pred, P, P_pred))
F_kal2 <- kfs_res2$F_smooth[, 1:r, drop = FALSE]
colnames(F_kal2) <- paste0("f", 1:r)
all.equal(F_kal, F_kal2)

rm(X, r, p, n, X_imp, v, F_pc, C, res, R, var, A, Q, F_0, P_0, kfs_res, F_kal, kfs_res2, F_kal2)

Armadillo's Inverse Functions

Description

Matrix inverse and pseudo-inverse by the Armadillo C++ library.

Usage

ainv(x)

apinv(x)

Arguments

Value

The matrix-inverse or pseudo-inverse.

See Also

dfms-package

Examples

ainv(crossprod(diff(EuStockMarkets)))

Extract Factor Estimates in a Data Frame

Description

Extract Factor Estimates in a Data Frame

Usage

## S3 method for class 'dfm'
as.data.frame(
  x,
  ...,
  method = "all",
  pivot = c("long", "wide.factor", "wide.method", "wide", "t.wide"),
  time = seq_row(x$F_pca),
  stringsAsFactors = TRUE
)

Arguments

Value

A data frame of factor estimates.

See Also

dfms-package

Examples

library(xts)
# Fit DFM with 3 factors and 3 lags in the transition equation
mod <- DFM(diff(BM14_M), r = 3, p = 3)

# Taking a single estimate:
print(head(as.data.frame(mod, method = "qml")))
print(head(as.data.frame(mod, method = "qml", pivot = "wide")))

# Adding a proper time variable
time <- index(BM14_M)[-1L]
print(head(as.data.frame(mod, method = "qml", time = time)))

# All estimates: different pivoting methods
for (pv in c("long", "wide.factor", "wide.method", "wide", "t.wide")) {
   cat("\npivot = ", pv, "\n")
   print(head(as.data.frame(mod, pivot = pv, time = time), 3))
}

Convergence Test for EM-Algorithm

Description

Convergence Test for EM-Algorithm

Usage

em_converged(loglik, previous_loglik, tol = 1e-04, check.increased = FALSE)

Arguments

Value

A logical statement indicating whether EM algorithm has converged. if check.increased = TRUE, a vector with 2 elements indicating the convergence status and whether the likelihood has decreased.

See Also

dfms-package

Examples

em_converged(1001, 1000)
em_converged(10001, 10000)
em_converged(10001, 10000, check = TRUE)
em_converged(10000, 10001, check = TRUE)

Plot DFM

Description

Plot DFM

Usage

## S3 method for class 'dfm'
plot(
  x,
  method = switch(x$em.method, none = "2s", "qml"),
  type = c("joint", "individual", "residual"),
  scale.factors = TRUE,
  ...
)

## S3 method for class 'dfm'
screeplot(x, ...)

Arguments

Value

Nothing.

See Also

dfms-package

Examples

# Fit DFM with 3 factors and 3 lags in the transition equation
mod <- DFM(diff(BM14_M), r = 3, p = 3)
plot(mod)
plot(mod, type = "individual", method = "all")
plot(mod, type = "residual")

DFM Forecasts

Description

This function produces h-step ahead forecasts of both the factors and the data, with an option to also forecast autocorrelated residuals with a univariate method and produce a combined forecast.

Usage

## S3 method for class 'dfm'
predict(
  object,
  h = 10L,
  method = switch(object$em.method, none = "2s", "qml"),
  standardized = TRUE,
  resFUN = NULL,
  resAC = 0.1,
  ...
)

## S3 method for class 'dfm_forecast'
print(x, digits = 4L, ...)

## S3 method for class 'dfm_forecast'
plot(
  x,
  main = paste(x$h, "Period Ahead DFM Forecast"),
  xlab = "Time",
  ylab = "Standardized Data",
  factors = seq_len(ncol(x$F)),
  scale.factors = TRUE,
  factor.col = rainbow(length(factors)),
  factor.lwd = 1.5,
  fcst.lty = "dashed",
  data.col = c("grey85", "grey65"),
  legend = TRUE,
  legend.items = paste0("f", factors),
  grid = FALSE,
  vline = TRUE,
  vline.lty = "dotted",
  vline.col = "black",
  ...
)

## S3 method for class 'dfm_forecast'
as.data.frame(
  x,
  ...,
  use = c("factors", "data", "both"),
  pivot = c("long", "wide"),
  time = seq_len(nrow(x$F) + x$h),
  stringsAsFactors = TRUE
)

Arguments

Value

A list-like object of class 'dfm_forecast' with the following elements:

See Also

dfms-package

Examples

library(xts)
library(collapse)

# Fit DFM with 3 factors and 3 lags in the transition equation
mod <- DFM(diff(BM14_M), r = 3, p = 3)

# 15 period ahead forecast
fc <- predict(mod, h = 15)
print(fc)
plot(fc, xlim = c(300, 370))

# Also forecasting autocorrelated residuals with an AR(1)
fcfun <- function(x, h) predict(ar(na_rm(x)), n.ahead = h)$pred
fcar <- predict(mod, resFUN = fcfun, h = 15)
plot(fcar, xlim = c(300, 370))

# Retrieving a data frame of the forecasts
head(as.data.frame(fcar, pivot = "wide")) # Factors
head(as.data.frame(fcar, use = "data"))   # Data
head(as.data.frame(fcar, use = "both"))   # Both

DFM Residuals and Fitted Values

Description

The residuals \textbf{e}_t = \textbf{x}_t - \textbf{C} \textbf{F}_t or fitted values \textbf{C} \textbf{F}_t of the DFM observation equation.

Usage

## S3 method for class 'dfm'
residuals(
  object,
  method = switch(object$em.method, none = "2s", "qml"),
  orig.format = FALSE,
  standardized = FALSE,
  na.keep = TRUE,
  ...
)

## S3 method for class 'dfm'
fitted(
  object,
  method = switch(object$em.method, none = "2s", "qml"),
  orig.format = FALSE,
  standardized = FALSE,
  na.keep = TRUE,
  ...
)

Arguments

Value

A matrix of DFM residuals or fitted values. If orig.format = TRUE the format may be different, e.g. a data frame.

See Also

dfms-package

Examples

library(xts)
# Fit DFM with 3 factors and 3 lags in the transition equation
mod <- DFM(diff(BM14_M), r = 3, p = 3)

# Residuals
head(resid(mod))
plot(resid(mod, orig.format = TRUE)) # this is an xts object

# Fitted values
head(fitted(mod))
head(fitted(mod, orig.format = TRUE)) # this is an xts object

DFM Summary Methods

Description

Summary and print methods for class 'dfm'. print.dfm just prints basic model information and the factor transition matrix \textbf{A}, coef.dfm returns \textbf{A} and \textbf{C} in a plain list, whereas summary.dfm returns all system matrices and additional residual and goodness of fit statistics—with a print method allowing full or compact printout.

Usage

## S3 method for class 'dfm'
print(x, digits = 4L, ...)

## S3 method for class 'dfm'
coef(object, ...)

## S3 method for class 'dfm'
logLik(object, ...)

## S3 method for class 'dfm'
summary(object, method = switch(object$em.method, none = "2s", "qml"), ...)

## S3 method for class 'dfm_summary'
print(x, digits = 4L, compact = sum(x$info["n"] > 15, x$info["n"] > 40), ...)

Arguments

Value

Summary information following a dynamic factor model estimation. coef() returns \textbf{A} and \textbf{C}.

See Also

dfms-package

Examples

mod <- DFM(diff(BM14_Q), 2, 3)
print(mod)
summary(mod)

Remove and Impute Missing Values in a Multivariate Time Series

Description

This function imputes missing values in a stationary multivariate time series using various methods, and removes cases with too many missing values.

Usage

tsnarmimp(
  X,
  max.missing = 0.8,
  na.rm.method = c("LE", "all"),
  na.impute = c("median.ma.spline", "median.ma", "median", "rnorm"),
  ma.terms = 3L
)

Arguments

Value

The imputed matrix X_imp, with attributes:

See Also

dfms-package

Examples

library(xts)
str(tsnarmimp(BM14_M))