Luca Mattia Rolla | Searcharxiv

arXiv2023

Testing the martingale difference hypothesis using martingale difference divergence function

This article proposes a novel test for the martingale difference hypothesis based on the martingale difference divergence function, a recently developed dependence measure suitable for measuring the degree of conditional mean dependence of a random variable with respect to another. First, we discuss the use of martingale difference divergence in a time series framework as an alternative to the autocovariance function for detecting the existence of forms of nonlinear serial dependence. In particular, the measure equals zero if and only if the considered time-series components are conditionally mean-independent. This characteristic makes it suitable for studying the behavior of white noise processes characterized by non-null mean conditional on the past. We discuss the asymptotic properties of sample martingale difference divergence in a univariate time series framework, refining some of the results existing in the literature. Doing this allows us to build a Ljung-Box-type test statistic by summing the sample martingale difference divergence function over a finite number of lags. Under suitable conditions, the asymptotic null distribution of our test statistic is also established. The finite sample performance is discussed via a Monte Carlo study as we demonstrate its consistency against uncorrelated non-martingale processes. Finally, we show an empirical application for our methodology in analyzing the properties of the Standard and Poor's 500 stock index.

stat.AP↗

arXiv2023

The Forecasting performance of the Factor model with Martingale Difference errors

This paper analyses the forecasting performance of a new class of factor models with martingale difference errors (FMMDE) recently introduced by Lee and Shao (2018). The FMMDE makes it possible to retrieve a transformation of the original series so that the resulting variables can be partitioned according to whether they are conditionally mean-independent with respect to past information. We contribute to the literature in two respects. First, we propose a novel methodology for selecting the number of factors in FMMDE. Through simulation experiments, we show the good performance of our approach for finite samples for various panel data specifications. Second, we compare the forecasting performance of FMMDE with alternative factor model specifications by conducting an extensive forecasting exercise using FRED-MD, a comprehensive monthly macroeconomic database for the US economy. Our empirical findings indicate that FMMDE provides an advantage in predicting the evolution of the real sector of the economy when the novel methodology for factor selection is adopted. These results are confirmed for key aggregates such as Production and Income, the Labor Market, and Consumption.

econ.EM↗