emDFM

The goal of emDFM is to provide an easy tool for estimation of the dynamic factor model:

$$ \begin{aligned} x_t &= \Lambda f_t + \xi_t \\ f_t &= A_1 f_{t-1} + \dots + A_p f_{t-p} + \eta_t, \end{aligned} $$

where $x_t$ is time $t$ observation of the $N$ series and $f_t$ is a $r$-dimensional factor with $r<<p$.

The package allows to estimate the model using PCA, the Kalman filter or the Expectation Maximization algorithm. Moreover, it provides useful functions for forecast evaluation and visualization.

Installation

You can install the development version of emDFM from GitHub with:

# install.packages("devtools")
devtools::install_github("aciancetta/emDFM")

Example

The dataset must be a tibble of time series, with the first column named date containing the observation dates. The emDFM package provides the download_clean_data function, which takes as input the ISO code of a European country and automatically retrieves its updated macroeconomic series from Eurostat. Also, it downloads the daily Google Mobility Indexes referred to that country. The output of the function is a list of two tibbles, the first containing both the official statistics from Eurostat and the GMI from Google, the second containing only the official macroeconomic series. All the series are are made stationary.

library(emDFM)
## Download Italian time series from Eurostat and Google
data <- download_clean_data("IT")
d <- data$data_high_freq

First, we have to scale the data in order to get stable result and make the results of the estimation scale-independent.

## Scale the data
scale_fit <- scale_tibble(d)
d_scaled <- scale_fit$scaled_tibble

Now, we can move to estimation. The functions pca_estimator, kalman_filter, kalman_smoother and em_algorithm are useful to comapre the dynamic factors and loadings as estimated by the four different algorithms. At this stage, we have to choose how many factors we want to estimate (r) and how many lags do we want to use in the state equation (p).

## PCA
d_scaled_imputed <- scale_impute(d)
pc_fit <- pca_estimator(d_scaled_imputed, r = 4, p = 1)

## Kalman filter
param_list <- initialize_filter(pc_fit)
kf_fit <- kalman_filter(d_scaled, param_list)

## Kalman smoother
ks_fit <- kalman_smoother(kf_fit)
em_fit <- em_algorithm(d_scaled, r = 4, p = 1)

The forecast_pipeline function allows to easily get the forecasts of the model estimated using the preferred algorithm and to plot the results relative to a chosen variable.

# Plot forecasts
forecast_input <- list(
            estimator = "EM",
            variable = "indpro_SCA",
            horizon = 6,
            r = 4,
            p = 1,
            thresh = 1,
            thresh_imputation = 0.05)

forecast_plot <- forecast_pipeline(d, forecast_input)

Finally, the forecast_evaluation function allows to evaluate the forecasting performances of the model using a sliding-window approach.

# Forecast evaluation
evaluation_input <- list(d = d,
                         horizon = 1,
                         window_size = 376,
                         r = 4,
                         p = 1,
                         thresh_imputation = 0.05,
                         thresh = 0.01
)

param_list <- initialize_filter(pc_fit)
em_eval <- forecast_evaluation(type = "EM", evaluation_input)
plot_forecast_evaluation(em_eval)

Credits

This package has been developed during my internship at IRPET (Regional Institute for Economic Planning of Tuscany).