
on Econometric Time Series 
By:  Alessandra Canepa,; Karanasos, Menelaos; Paraskevopoulos, Athanasios; Chini, Emilio Zanetti (University of Turin) 
Abstract:  In this paper we employ an autoregressive GARCHinmeanlevel process with variable coe¢ cients to forecast in?ation and investigate the behavior of its persistence in the United States. We propose new measures of time varying persistence, which not only distinguish between changes in the dynamics of in?ation and its volatility, but are also allow for feedback between the two variables. Since it is clear from our analysis that predictability is closely interlinked with (?rstorder) persistence we coin the term persistapredictability. Our empirical results suggest that the proposed model has good forecasting properties. 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:uto:dipeco:202212&r=ets 
By:  Matteo Barigozzi 
Abstract:  This paper revisits and provides an alternative derivation of the asymptotic results for the Principal Components estimator of a large approximate factor model as considered in Stock and Watson (2002), Bai (2003), and Forni et al. (2009). Results are derived under a minimal set of assumptions with a special focus on the time series setting, which is usually considered in almost all recent empirical applications. Hence, $n$ and $T$ are not treated symmetrically, the former being the dimension of the considered vector of time series, while the latter being the sample size and, therefore, being relevant only for estimation purposes, but not when it comes to just studying the properties of the model at a population level. As a consequence, following Stock and Watson (2002) and Forni et al. (2009), estimation is based on the classical $n \times n$ sample covariance matrix. As expected, all asymptotic results we derive are equivalent to those stated in Bai (2003), where, however, a $T\times T$ covariance matrix is considered as a starting point. A series of useful complementary results is also given. In particular, we give some alternative sets of primitive conditions for meansquared consistency of the sample covariance matrix of the factors, of the idiosyncratic components, and of the observed time series. We also give more intuitive asymptotic expansions for the estimators showing that PCA is equivalent to OLS as long as $\sqrt{T}/n\to 0$ and $\sqrt{n}/T\to 0$, that is loadings are estimated in a time series regression as if the factors were known, while factors are estimated in a crosssectional regression as if the loadings were known. The issue of testing multiple restrictions on the loadings as well as building joint confidence intervals for the factors is discussed. 
Date:  2022–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2211.01921&r=ets 
By:  Rub\'en LoaizaMaya; Didier Nibbering 
Abstract:  Variational Bayes methods are a scalable estimation approach for many complex state space models. However, existing methods exhibit a tradeoff between accurate estimation and computational efficiency. This paper proposes a variational approximation that mitigates this tradeoff. This approximation is based on importance densities that have been proposed in the context of efficient importance sampling. By directly conditioning on the observed data, the proposed method produces an accurate approximation to the exact posterior distribution. Because the steps required for its calibration are computationally efficient, the approach is faster than existing variational Bayes methods. The proposed method can be applied to any state space model that has a closedform measurement density function and a state transition distribution that belongs to the exponential family of distributions. We illustrate the method in numerical experiments with stochastic volatility models and a macroeconomic empirical application using a highdimensional state space model. 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2210.11010&r=ets 
By:  Daniel Borup; Philippe Goulet Coulombe; Erik Christian Montes Schütte; David E. Rapach; Sander SchwenkNebbe 
Abstract:  We develop metrics based on Shapley values for interpreting timeseries forecasting models, including “blackbox” models from machine learning. Our metrics are model agnostic, so that they are applicable to any model (linear or nonlinear, parametric or nonparametric). Two of the metrics, iShapleyVI and oShapleyVI, measure the importance of individual predictors in fitted models for explaining the insample and outofsample predicted target values, respectively. The third metric is the performancebased Shapley value (PBSV), our main methodological contribution. PBSV measures the contributions of individual predictors in fitted models to the outofsample loss and thereby anatomizes outofsample forecasting accuracy. In an empirical application forecasting US inflation, we find important discrepancies between individual predictor relevance according to the insample iShapleyVI and outofsample PBSV. We use simulations to analyze potential sources of the discrepancies, including overfitting, structural breaks, and evolving predictor volatilities. 
Keywords:  variable importance; outofsample performance; Shapley value; loss function; machine learning; inflation 
JEL:  C22 C45 C53 E37 G17 
Date:  2022–11–07 
URL:  http://d.repec.org/n?u=RePEc:fip:fedawp:94993&r=ets 
By:  Giovanni Ballarin; Petros Dellaportas; Lyudmila Grigoryeva; Marcel Hirt; Sophie van Huellen; JuanPablo Ortega 
Abstract:  Macroeconomic forecasting has recently started embracing techniques that can deal with largescale datasets and series with unequal release periods. The aim is to exploit the information contained in heterogeneous data sampled at different frequencies to improve forecasting exercises. Currently, MIxedDAta Sampling (MIDAS) and Dynamic Factor Models (DFM) are the two main stateoftheart approaches that allow modeling series with nonhomogeneous frequencies. We introduce a new framework called the MultiFrequency Echo State Network (MFESN), which originates from a relatively novel machine learning paradigm called reservoir computing (RC). Echo State Networks are recurrent neural networks with random weights and trainable readout. They are formulated as nonlinear statespace systems with random state coefficients where only the observation map is subject to estimation. This feature makes the estimation of MFESNs considerably more efficient than DFMs. In addition, the MFESN modeling framework allows to incorporate many series, as opposed to MIDAS models, which are prone to the curse of dimensionality. Our discussion encompasses hyperparameter tuning, penalization, and nonlinear multistep forecast computation. In passing, a new DFM aggregation scheme with Almon exponential structure is also presented, bridging MIDAS and dynamic factor models. All methods are compared in extensive multistep forecasting exercises targeting US GDP growth. We find that our ESN models achieve comparable or better performance than MIDAS and DFMs at a much lower computational cost. 
Date:  2022–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2211.00363&r=ets 
By:  Philipp Ketz 
Abstract:  In this paper, we use the results in Andrews and Cheng (2012), extended to allow for parameters to be near or at the boundary of the parameter space, to derive the asymptotic distributions of the two test statistics that are used in the twostep (testing) procedure proposed by Pedersen and Rahbek (2019). The latter aims at testing the null hypothesis that a GARCHX type model, with exogenous covariates (X), reduces to a standard GARCH type model, while allowing the "GARCH parameter" to be unidentified. We then provide a characterization result for the asymptotic size of any test for testing this null hypothesis before numerically establishing a lower bound on the asymptotic size of the twostep procedure at the 5% nominal level. This lower bound exceeds the nominal level, revealing that the twostep procedure does not control asymptotic size. In a simulation study, we show that this finding is relevant for finite samples, in that the twostep procedure can suffer from overrejection in finite samples. We also propose a new test that, by construction, controls asymptotic size and is found to be more powerful than the twostep procedure when the "ARCH parameter" is "very small" (in which case the twostep procedure underrejects). 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2210.11398&r=ets 
By:  Chaturvedi, Priya; Kumar, Kuldeep 
Abstract:  In the paper, we use generalized autoregressive conditional heteroskedasticitymixed data sampling (GARCHMIDAS) to study the impact of Australia’s commodity price index, Global economic conditions indicator, Global Economic Policy Uncertainty Index, monthly realised volatility of S&P/ASX 200 index and monthly realised volatility of money supply on the volatility of the Australian dollar during the period from 1999 to 2021. The results indicate that exchange rate volatility rises with a rise in fluctuations in S&P/ASX 200 index, money supply volatility, commodity price index and falls with a rise in global economic activity. For the GEPU index, the slope coefficient is positive and significant only in the 3 years lag and not significant in the 1 and 2years lags. This means that a rise in economic turmoil leads to a rise in exchange rate volatility. We also find strong evidence for asymmetry in the shortterm volatility component. The results obtained in the study show that there is comovement of volatility across various financial markets. 
Keywords:  Exchange rate volatility · GARCHMIDAS · Macroeconomic and financial variables · Asymmetry 
JEL:  C58 
Date:  2022–08–18 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:115222&r=ets 
By:  Mostafa Shabani; Martin Magris; George Tzagkarakis; Juho Kanniainen; Alexandros Iosifidis 
Abstract:  Crosscorrelation analysis is a powerful tool for understanding the mutual dynamics of time series. This study introduces a new method for predicting the future state of synchronization of the dynamics of two financial time series. To this end, we use the crossrecurrence plot analysis as a nonlinear method for quantifying the multidimensional coupling in the time domain of two time series and for determining their state of synchronization. We adopt a deep learning framework for methodologically addressing the prediction of the synchronization state based on features extracted from dynamically subsampled crossrecurrence plots. We provide extensive experiments on several stocks, major constituents of the S\&P100 index, to empirically validate our approach. We find that the task of predicting the state of synchronization of two time series is in general rather difficult, but for certain pairs of stocks attainable with very satisfactory performance. 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2210.14605&r=ets 
By:  David Childers; Jesús FernándezVillaverde; Jesse Perla; Christopher Rackauckas; Peifan Wu 
Abstract:  We propose a methodology to take dynamic stochastic general equilibrium (DSGE) models to the data based on the combination of differentiable statespace models and the Hamiltonian Monte Carlo (HMC) sampler. First, we introduce a method for implicit automatic differentiation of perturbation solutions of DSGE models with respect to the model's parameters. We can use the resulting output for various tasks requiring gradients, such as building an HMC sampler, to estimate first and secondorder approximations of DSGE models. The availability of derivatives also enables a general filterfree method to estimate nonlinear, nonGaussian DSGE models by sampling the joint likelihood of parameters and latent states. We show that the gradientbased joint likelihood sampling approach is superior in efficiency and robustness to standard MetropolisHastings samplers by estimating a canonical real business cycle model, a real small open economy model, and a mediumscale New Keynesian DSGE model. 
JEL:  C01 C10 C11 E0 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:30573&r=ets 