Most of forecasts on sets of large number of time-series are either (1) to predict future values of time-series by, for example, DFM (dynamic factor model) or VAR / VARMA (vector autoregressive / moving-average) models, OR (2) to predict future variance-covariance matrixes by, for example, multivariate GARCH or risk-factor (static factors, either statistical or fundamental) models.

Here, i4cast lists (DFM-based) DFVCM algorithm to make muti-step forecasts of large variance-covariance matrix of large set of time-series.

Advantages of making multivariate volatility forecasts by DFM vs. by multivariate GARCH are presented by Alessi, Barigozzi and Capasso (2007) in “Dynamic factor GARCH: Multivariate volatility forecast for a large number of series”, LEM Working Paper Series, No. 2006/25, Pisa.

Equations for making multi-step forecasts of multivariate volatilities by (DFM-based) DFVCM are detailed by i4cast LLC (2024) in “Introduction to Multi-step Forecast of Multivariate Volatility with Dynamic Factor Model”, https://github.com/i4cast/aws/blob/main/dynamic_factor_variance-covariance_model/publication/ .

In addition to DFVCM (to make volatility forecast), i4cast lists LMVAR model to make multi-step forecasts of values of the same set of time-series.

Both DFVCM and LMVAR models are based on the SAME combination of LMDFM and YWpcAR algorithms by i4cast.

The DFVCM is tuned by metrics evaluating volatility forecasts, while the LMVAR is tuned by metrics evaluating time-series forecasts. Different evaluation metrics can render same algorithm into different models.