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STS544 M. Camachoa et al.
The single-index dynamic factor model stated above can easily be
represented in state-space form and be estimated by maximum likelihood
using the Kalman filter. Additionally, as shown by Camacho and Doménech
(2019), the model can be easily extended in the following dimensions:
1. Dealing with data problems and variables in levels and growth rates
2. Mixed frequencies. Following the approach of treating quarterly series
as monthly series with missing observations, Mariano and Murasawa
(2003) extended the single-index dynamic factor model by including
quarterly GDP data and monthly indicators.
3. Unbalanced data sets and missing data due to different publication
dates, causing the so-called ragged-edge data problem at the end of
the sample.
4. Business-cycle nonlinearities estimated using Markov-switching
dynamic factor models. This allows us to obtain real-time recession
probabilities.
5. Leading indicators, such as the slope of the yield curve or financial
tension indexes.
6. Measurement errors in GDP growth.
We call these extensions MICA models because they are factor Models of
economic and financial Indicators used to monitor the Current development
of the economic Activity.

3. Results
Although BBVA’s DFM are continuously updated in real time, we restrict
this section to the results obtained in the analysis of the models at the time
they were published in academic journals (Camacho and Doménech, 2012,
Camacho and García-Serrador, 2014, Camacho and Martínez-Martín, 2014,
Camacho, dal Bianco, and Martínez-Martín, 2015a).
The implementation of the methodology described in the previous section
requires a selection of the appropriate indicators from a list of potential
business cycle indicators. We simplify this process by choosing them
according to certain properties: timeliness, high statistical correlation and
relevance (high loading factor). A meaningful starting point for selecting
indicators entering a factor model is the approach of Stock and Watson (1991).
Using this baseline model, new indicators are further added when the have
statistically significant loading factors. All monthly series are made stationary
by differencing or log-differencing, if needed, so they appear in quarterly
growth rates (QGR), in monthly growth rates (MGR), in annual growth rates
(AGR) or in levels (L). All variables are standardized by subtracting the mean
and dividing by the standard deviation.
After the selection process, the set of economic indicators with statistically
significant loading factors includes the following variables:

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