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Philipp Gersing

Publications and source records attributed to Philipp Gersing.

5 recordsLinked to original sources
arXiv2024

A Distributed Lag Approach to the Generalised Dynamic Factor Model

We propose a simple estimator for the dynamic decomposition of the Generalized Dynamic Factor Model that avoids frequency-domain methods. First, we show that it is a reasonable approximation to assume that the dynamic common component of the Generalized Dynamic Factor Model admits a representation in terms of current and lagged statically pervasive factors. Then, assuming finite lag order, this simplification reduces estimation to a regression of the observed variables on estimated factors and their lags, where the factors are extracted via static principal components. The proposed approach naturally accommodates weak, non-pervasive factors within the dynamic common space. We establish consistency and asymptotic normality for both the dynamic and weak common components under a new asymptotic framework that allows for such weak factors. In an application to three high-dimensional time series panels of European macroeconomic data we detect a sizeable weak common component share in several key macroeconomic indicators.

econ.EM↗
arXiv2024

Actually, There is No Rotational Indeterminacy in the Approximate Factor Model

We show that in the approximate factor model the population normalised principal components converge in mean square (up to sign) under the standard assumptions for $n\to \infty$. Consequently, we have a generic interpretation of what the principal components estimator is actually identifying and existing results on factor identification are reinforced and refined. Based on this result, we provide a new asymptotic theory for the approximate factor model entirely without rotation matrices. We show that the factors space is consistently estimated with finite $T$ for $n\to \infty$ while consistency of the factors a.k.a the $L^2$ limit of the normalised principal components requires that both $(n, T)\to \infty$.

econ.EM↗
arXiv2023

The Canonical Decomposition of Factor Models: Weak Factors are Everywhere

We derive a novel canonical decomposition of factor models encompassing both the static factor model - where factors are loaded only contemporaneously - and the Generalised Dynamic Factor Model - where factors are loaded with lags. This decomposition features a new term: the weak common component, defined as the difference between the dynamic and static common components. It is driven by (possibly infinitely many) non-pervasive weak factors which belong to the dynamically common space. Through theoretical and empirical examples - both on U.S. macroeconomic indicators and global financial volatilities - we show that, in general, the weak common component shall not be neglected. Furthermore, we show that, by accounting for the presence of weak common components, we are likely to obtain Impulse Response Functions with more plausible shapes than those obtained from purely static approaches. In addition, we provide consistent estimators for all terms of the canonical decomposition and for the weak factors.

econ.EM↗
arXiv2023

Retrieval from Mixed Sampling Frequency: Generic Identifiability in the Unit Root VAR

The "REtrieval from MIxed Sampling" (REMIS) approach based on blocking developed in Anderson et al. (2016a) is concerned with retrieving an underlying high frequency model from mixed frequency observations. In this paper we investigate parameter-identifiability in the Johansen (1995) vector error correction model for mixed frequency data. We prove that from the second moments of the blocked process after taking differences at lag N (N is the slow sampling rate), the parameters of the high frequency system are generically identified. We treat the stock and the flow case as well as deterministic terms.

econ.EM↗