dfms: Dynamic Factor Models for R

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dfms provides efficient estimation of Dynamic Factor Models via the EM Algorithm. Factors are assumed to follow a stationary VAR process of order p. Estimation can be done in 3 different ways following:

• 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

The default is em.method = "auto", which chooses "BM" following Banbura & Modugno (2014) with missing data or mixed frequency, and "DGR" following Doz, Giannone & Reichlin (2012) otherwise. Using em.method = "none" generates Two-Step estimates following Doz, Giannone & Reichlin (2011). This is extremely efficient on bigger datasets. PCA and Two-Step estimates are also reported in EM-estimation. All methods support missing data, but em.method = "DGR" does not model them in EM iterations.

The package is currently stable, but functionality may expand in the future. In particular, mixed-frequency estimation with autoregressive errors is planned for the near future, and generation of the 'news' may be added in the further future.

Comparison with Other R Packages

dfms is intended to provide a simple, numerically robust, and computationally efficient baseline implementation of (linear Gaussian) Dynamic Factor Models for R, allowing straightforward application to various contexts such as time series dimensionality reduction and forecasting. The implementation is based on efficient C++ code, making dfms orders of magnitude faster than packages that can be used to fit dynamic factor models such as MARSS, or nowcasting and nowcastDFM geared to mixed-frequency nowcasting applications - supporting blocking of variables into different groups for which factors are to be estimated and evaluation of news content. For large-scale nowcasting models the DynamicFactorMQ class in the statsmodels Python library is probably the most robust implementation - see the example by Chad Fulton. <!-- , and EM adjustments for variables at different frequencies. dfms with em.method = "BM" does allow mixed-frequency data but performs no specific adjustments for the frequency of the data^[All series are weighted equally, and the prevalence of missing values in lower-frequency series downweights them. To remedy this lower frequency series could be included multiple times in the dataset e.g. include a quarterly series 3 times in a monthly dataset.]. dfms currently also does not allow residual autocorrelation in the estimation (i.e. it cannot estimate approximate factor models), but the addition of this feature is planned. --> The dfms package is not intended to fit more general forms of the state space model like MARSS.

Installation

```r

CRAN

install.packages("dfms")

Development Version

install.packages('dfms', repos = c('https://sebkrantz.r-universe.dev', 'https://cloud.r-project.org'))

```

Usage Example

```r library(dfms)

Fit DFM with 6 factors and 3 lags in the transition equation

mod <- DFM(diff(BM14_M), r = 6, p = 3) ```

```

Converged after 32 iterations.

```

```r

'dfm' methods

summary(mod) ```

```

Dynamic Factor Model: n = 92, T = 356, r = 6, p = 3, %NA = 25.8366

Call: DFM(X = diff(BM14_M), r = 6, p = 3)

Summary Statistics of Factors [F]

N Mean Median SD Min Max

f1 356 -0.1189 0.4409 4.0228 -22.9164 7.8513

f2 356 -0.4615 -0.3476 2.9201 -9.0973 10.7003

f3 356 -0.0173 0.0377 2.2719 -8.5067 7.3009

f4 356 -0.007 -0.1338 1.9378 -9.5052 9.3673

f5 356 0.237 0.1091 2.0857 -8.7252 9.6715

f6 356 -0.8361 -0.304 3.1406 -11.6611 15.4897

Factor Transition Matrix [A]

L1.f1 L1.f2 L1.f3 L1.f4 L1.f5 L1.f6 L2.f1 L2.f2 L2.f3

f1 0.53029 -0.53009 0.367302 0.04607 -0.06351 0.10310 0.02457 0.11673 -0.12638

f2 -0.28380 0.07421 -0.032292 0.29741 -0.10094 0.21989 0.09958 -0.09149 0.06708

f3 0.17607 0.12979 0.378798 -0.06662 -0.12236 0.06685 -0.08068 0.09101 -0.22232

f4 0.02711 0.08936 0.004643 0.37159 0.12100 -0.02763 0.01234 -0.05147 0.02195

f5 -0.26227 -0.03469 -0.046294 0.12712 0.26847 0.03141 0.06400 0.01971 0.04806

f6 0.08251 0.17619 -0.013374 -0.08731 -0.03875 0.27812 -0.01662 0.04877 0.02279

L2.f4 L2.f5 L2.f6 L3.f1 L3.f2 L3.f3 L3.f4 L3.f5 L3.f6

f1 0.23135 0.117184 0.21941 0.18478 0.02259 -0.03719 -0.07236 -0.03026 -0.12606

f2 -0.09768 -0.043057 0.08489 0.21107 0.16261 0.03057 0.04835 0.12249 0.13357

f3 0.09799 -0.060666 -0.18028 -0.02773 0.01798 0.10143 -0.12420 0.04207 -0.07011

f4 0.01266 0.050912 0.05144 -0.05601 0.04665 0.05710 -0.11412 -0.05680 -0.01609

f5 -0.03965 -0.009952 -0.18471 0.08332 -0.04640 -0.02047 0.02458 0.16397 0.07820

f6 0.01163 -0.100859 0.07152 0.00792 0.06071 0.11381 0.02520 -0.17897 0.30328

Factor Covariance Matrix [cov(F)]

f1 f2 f3 f4 f5 f6

f1 16.1832 -0.4329 0.2483 -0.8224* -1.7708* 0.7702

f2 -0.4329 8.5272 0.0051 0.2954 -0.2114 4.2080*

f3 0.2483 0.0051 5.1614 -0.1851 -0.3979 0.2979

f4 -0.8224* 0.2954 -0.1851 3.7550 0.4344* 0.2211

f5 -1.7708* -0.2114 -0.3979 0.4344* 4.3503 -1.9785*

f6 0.7702 4.2080* 0.2979 0.2211 -1.9785* 9.8634

Factor Transition Error Covariance Matrix [Q]

u1 u2 u3 u4 u5 u6

u1 7.2142 0.1151 -0.8208 -0.4379 0.4110 -0.1206

u2 0.1151 4.8724 0.1076 -0.1438 0.1418 0.1759

u3 -0.8208 0.1076 4.0584 -0.0788 0.0163 0.0038

u4 -0.4379 -0.1438 -0.0788 3.0003 0.2562 0.0243

u5 0.4110 0.1418 0.0163 0.2562 2.8410 -0.1031

u6 -0.1206 0.1759 0.0038 0.0243 -0.1031 2.9284

Summary of Residual AR(1) Serial Correlations

N Mean Median SD Min Max

92 -0.0644 -0.1024 0.2702 -0.5113 0.6674

Summary of Individual R-Squared's

N Mean Median SD Min Max

92 0.4556 0.4069 0.3041 0.0112 0.9989

```

r plot(mod)

r as.data.frame(mod) |> head()

```

Method Factor Time Value

1 PCA f1 1 0.8445713

2 PCA f1 2 0.5259228

3 PCA f1 3 -1.2107116

4 PCA f1 4 -1.5399532

5 PCA f1 5 -0.4631786

6 PCA f1 6 0.2399304

```

```r

Forecasting 12 periods ahead

fc <- predict(mod, h = 12)

'dfm_forecast' methods

plot(fc, xlim = c(320, 370)) ```

r as.data.frame(fc) |> head()

```

Variable Time Forecast Value

1 f1 1 FALSE 4.179331

2 f1 2 FALSE -1.368577

3 f1 3 FALSE -12.845157

4 f1 4 FALSE -14.562265

5 f1 5 FALSE -7.791254

6 f1 6 FALSE -1.254970

```