Smooth and Abrupt Dynamics in Financial Volatility: The MS‐MEM‐MIDAS*
| Published date | 01 February 2024 |
| Author | Luca Scaffidi Domianello,Giampiero M. Gallo,Edoardo Otranto |
| Date | 01 February 2024 |
| DOI | http://doi.org/10.1111/obes.12576 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 86, 1 (2024) 0305-9049
doi: 10.1111/obes.12576
Smooth and Abrupt Dynamics in Financial Volatility:
The MS-MEM-MIDAS*
LUCA SCAFFIDI DOMIANELLO,† GIAMPIERO M. GALLO‡,§
and EDOARDO OTRANTO§,¶
†Department of Statistics, Computer Science Applications, University of Florence, Florence, Italy
e-mail: luca.scaffididomianello@unifi.it
‡New York University in Florence, Florence, Italy e-mail: giampiero.gallo@nyu.edu
§CRENoS, Cagliari, Italy e-mail: eotranto@unime.it
¶Department of Economics, University of Messina, Messina, Italy
Abstract
In this paper, we maintain that the evolution of the realized volatility is characterized
by a combination of high-frequency dynamics and smoother, yet persistent, dynamics
evolving at a lower frequency. We suggest a new Multiplicative Error Model which
combines the mixed frequency features of a MIDAS at the monthly level with Markovian
dynamics at the daily level. When estimated in-sample on the realized kernel volatility
of the S&P500 index, this model dominates other simpler specifications, especially when
monthly aggregated realized volatility is used. The same pattern is confirmed in the
out-of-sample forecasting performance which suggests that adding an abrupt change in
the average level of volatility better helps in tracking quick bursts of volatility and a
relatively rapid absorption of the shocks.
I. Introduction
Recurrent global economic and financial crises have prompted an interest in studying
the interdependence between the real economy and financial market volatility. Starting
from Officer (1973) and Schwert (1989), several authors document the economic sources
of volatility and, in particular, its increase during a recession while reverting to more
physiological states during expansion phases (the so-called countercyclical pattern of
stock market volatility). In an attempt to bring together economic factors (typically
measured at a low frequency) within a financial framework (whose status is observable
at a much higher frequency), Engle, Ghysels, and Sohn (2013) provided a pathbreaking
perspective within the strand of literature about volatility modeling by introducing the
JEL Classification numbers: C22, C24, C38, C58.
*We are grateful to Giovanni De Luca for including a preliminary version of this paper within the solicited
session: Statistics for finance: new models, new data at the 51st Scientific Meeting of the Italian Statistical Society
(June 2022). Edoardo Otranto acknowledges financial support from the Italian PRIN 2022 grant ‘Methodological
and computational issues in large-scale time series models for economics and finance’ (20223725WE).
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©2023 Oxford University and John Wiley & Sons Ltd.
22 Bulletin
GARCH-MIDAS model, a multiplicative component model in which the conditional
variance is decomposed into short- and long-run components. Component models,
introduced by Engle and Lee (1999), can capture the volatility dynamics putting together
a parsimonious structure containing a slow-moving, more persistent component and
a shorter-lived one. In the case of the GARCH-MIDAS, the short-run component
follows a GARCH-type dynamics aimed at capturing volatility clustering and daily
fluctuations, while the long-run one represents a time-varying average level of volatility,
driven by macroeconomic and/or financial variables. A distinctive merit of this class
of models is the ability to mix different frequencies of observability within the same
analysis.
Volatility modelling within the GARCH framework is based on the daily squared
returns, a noisy, albeit unbiased, measure of conditional variance. A big boost to studying
the dynamics of volatility is provided by the availability of ultra-high frequency data,
which allows for more precise volatility measures in the wide class of Realized Volatility
(RV) Andersen et al. (2003): from the plain vanilla version of RV, as the sum of squared
high-frequency returns (sampled at, e.g. 5 minutes), more refined versions taking into
consideration autocorrelation of intradaily returns or microstructure noise, such as the
Realized kernel volatility of Barndorff-Nielsen et al. (2008), are available as more robust
estimators of volatility. Following Andersen and Bollerslev (1998), it is now customary to
use such a variable as the suitable target to evaluate the forecast performance of volatility
models.
Apart from being a consistent measure of ex-post daily volatility, RV lends itself
to being modelled for forecasting purposes, given its empirical features of long-run
dependence and volatility clustering: being a positive-valued process, new models such as
the Multiplicative Error Model (MEM, Engle, 2002; Engle and Gallo, 2006) have proved
useful to reproduce its dynamics. Some component extension of the MEM are present in
the literature (see, e.g. the Composite MEM of Brownlees, Cipollini, and Gallo, 2012),
while Amendola et al. (2021) proposed the MEM-MIDAS to exploit the relationship
between economics and financial volatility by focusing on the RV as the variable of
interest, in lieu of the squared returns as in the GARCH-MIDAS.
While the modelling effort provides some interesting insights on the interpretability
of the low-frequency component of volatility responding to economic factors, the MEM-
MIDAS model is not able to capture abrupt shifts in the average level of volatility, which
are typical of sudden crises and panic behaviour in the financial markets, accompanying
a change in the high-frequency dynamics (i.e. more sensitivity to recent news). To this
end, in this paper, we add a Markov Switching (MS) pattern in the high-frequency
dynamics: the resulting model is the MS-MEM-MIDAS1. The MS models can be seen
as an alternative approach to capture a changing level of average volatility (the high-
frequency component reacts across regimes with a step function and then remains constant
within each regime); our model provides some insights about which among the features
component provides a better fit to the observed slow-moving behaviour of volatility,
whether it is the contribution of economic variables observed at a lower frequency,
or the Markov switching component (with its sudden adjustment of the average level
1The model by Pan et al. (2017) adopts a simplified MS setup for the constant term in a GARCH-MIDAS framework.
©2023 Oxford University and John Wiley & Sons Ltd.
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