
on Econometric Time Series 
By:  del Barrio Castro, Tomás; Osborn, Denise R. 
Abstract:  Seasonality is pervasive across a wide range of economic time series and it substantially complicates the analysis of unit root nonstationarity in such series. This paper reviews recent contributions to the literature on nonstationary seasonal processes, focussing on periodically integrated (P I) and seasonally integrated (SI) processes. Whereas an SI process captures seasonal nonstationarity essentially through an annual lag, a P I process has (a restricted form of) seasonallyvarying autoregressive coefficients. The fundamental properties of both types of process are compared, noting in particular that a simple SI process observed S times a year has S unit roots, in contrast to the single unit root of a P I process. Indeed, for S > 2 and even (such as processes observed quarterly or monthly), an SI process has a pair of complexvalued unit roots at each seasonal frequency except the Nyquist frequency, where a single real root applies. Consequently, recent literature concerned with testing the unit roots implied by SI processes employs complexvalued unit root processes, and these are discussed in some detail. A key feature of the discussion is to show how the demodulator operator can be used to convert a unit root process at a seasonal frequency to a conventional zerofrequency unit root process, thereby enabling the wellknown properties of the latter to be exploited. Further, circulant matrices are introduced and it is shown how they are employed in theoretical analyses to capture the repetitive nature of seasonal processes. Discriminating between SI and P I processes requires care, since testing for unit roots at seasonal frequencies may lead to a P I process (erroneously) appearing to have an SI form, while an application to monthly US industrial production series illustrates how these types of seasonal nonstationarity can be distinguished in practice. Although univariate processes are discussed, the methods considered in the paper can be used to analyze cointegration, including cointegration across different frequencies 
Keywords:  Periodic Integration, Seasonal Integration, Vector of Seasons, Circulant Matrices, Demodulator Operator, Industrial Production. 
JEL:  C32 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:117935&r=ets 
By:  Takamitsu Kurita (Faculty of Economics, Kyoto Sangyo University); Mototsugu Shintani (Faculty of Economics, The University of Tokyo) 
Abstract:  We develop methodology for testing cointegrating rank in vector autoregressive (VAR) models in the presence of Fouriertype smooth nonlinear deterministic trends in cointegrating relations. The limiting distribution of loglikelihood ratio test statistics is derived and approximated limit quantiles are tabulated. A sequential procedure to select cointegrating rank is evaluated by Monte Carlo simulations. Our empirical application to economic data also demonstrates the usefulness of the proposed methodology in a practical context. 
Date:  2023–06 
URL:  http://d.repec.org/n?u=RePEc:tky:fseres:2023cf1216&r=ets 
By:  James A. Duffy; Sophocles Mavroeidis; Sam Wycherley 
Abstract:  This paper studies a class of multivariate threshold autoregressive models, known as censored and kinked structural vector autoregressions (CKSVAR), which are notably able to accommodate series that are subject to occasionally binding constraints. We develop a set of sufficient conditions for the processes generated by a CKSVAR to be stationary, ergodic, and weakly dependent. Our conditions relate directly to the stability of the deterministic part of the model, and are therefore less conservative than those typically available for general vector threshold autoregressive (VTAR) models. Though our criteria refer to quantities, such as refinements of the joint spectral radius, that cannot feasibly be computed exactly, they can be approximated numerically to a high degree of precision. Our results also permit us to provide a treatment of unit roots and cointegration in the CKSVAR, for the case where the model is configured so as to generate linear cointegration. 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2307.06190&r=ets 
By:  Cees Diks; Bram Wouters 
Abstract:  A novel method for noise reduction in the setting of curve time series with error contamination is proposed, based on extending the framework of functional principal component analysis (FPCA). We employ the underlying, finitedimensional dynamics of the functional time series to separate the serially dependent dynamical part of the observed curves from the noise. Upon identifying the subspaces of the signal and idiosyncratic components, we construct a projection of the observed curve time series along the noise subspace, resulting in an estimate of the underlying denoised curves. This projection is optimal in the sense that it minimizes the mean integrated squared error. By applying our method to similated and real data, we show the denoising estimator is consistent and outperforms existing denoising techniques. Furthermore, we show it can be used as a preprocessing step to improve forecasting. 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2307.02154&r=ets 
By:  Yoshihiro Yajima; Yasumasa Matsuda 
Abstract:  We consider Gaussian semiparametric estimation (GSE) for twodimensional intrinsically stationary random fields (ISRFs) observed on a regular grid and derive its asymptotic properties. Originally GSE was proposed to estimate long memory time series models in a semiparametric way either for stationary or nonstationary cases. We try an extension of GSE for time series to anisotropic ISRFs observed on two dimensional lattice that include isotropic fractional Brownian fields (FBF) as special cases, which have been employed to describe many physical spatial behaviours. The GSE extended to ISRFs is consistent and has a limiting normal distribution with variance independent of any unknown parameters as sample size goes to infinity, under conditions we specify in this paper. We conduct a computational simulation to compare the performances of it with those of an alternative estimator on the spatial domain. 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:toh:dssraa:136&r=ets 
By:  Josep Lluís CarrioniSilvestre (AQRIREA Research Group. Departament d’Econometria, Estadística i Economia Aplicada. Universitat de Barcelona. Av. Diagonal, 690. 08034 Barcelona. Spain.); Andreu Sansó (Department d’Economia Aplicada. Universitat de les Illes Balears and MOTIBO Research Group, Balearic Islands Health Research Institute (Idisba).) 
Abstract:  This paper focuses on testing the stability of the unconditional variance when the stochastic processes may have heavytailed distributions. Finite sample distributions that depend both on the effective sample size and the tail index are approximated using Extreme Value distributions and summarized using response surfaces. A modification of the Iterative Cumulative Sum of Squares (ICSS) algorithm to detect the presence of multiple structural breaks is suggested, adapting the algorithm to the tail index of the underlying distribution of the process. We apply the algorithm to eighty absolute logexchange rate returns, finding evidence of (i) infinite variance in about a third of the cases, (ii) finite changing unconditional variance for another third of the time series  totalling about one hundred structural breaks  and (iii) finite constant unconditional variance for the remaining third of the time series. 
Keywords:  CUMSUMQ test, Unconditional variance, Multiple structural changes, Heavy tails, Generalized Extreme Value distribution. JEL classification: C12, C22. 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:ira:wpaper:202309&r=ets 
By:  Viet Hoang Dinh; Didier Nibbering; Benjamin Wong 
Abstract:  We show how random subspace methods can be adapted to estimating local projections with many controls. Random subspace methods have their roots in the machine learning literature and are implemented by averaging over regressions estimated over different combinations of subsets of these controls. We document three key results: (i) Our approach can successfully recover the impulse response function in a Monte Carlo exercise where we simulate data from a real business cycle model with fiscal foresight. (ii) Our results suggest that random subspace methods are more accurate than factor models if the underlying large data set has a factor structure similar to typical macroeconomic data sets such as FREDMD. (iii) Our approach leads to differences in the estimated impulse response functions relative to standard methods when applied to two widelystudied empirical applications. 
Keywords:  Local Projections, Random Subspace, Impulse Response Functions, Large Data Sets 
JEL:  C22 E32 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:een:camaaa:202334&r=ets 
By:  Davide Brignone; Alessandro Franconi; Marco Mazzali 
Abstract:  Externalinstrument identification leads to biased responses when the shock is not invertible and the measurement error is present. We propose to use this identification strategy in a structural Dynamic Factor Model, which we call Proxy DFM. In a simulation analysis, we show that the Proxy DFM always successfully retrieves the true impulse responses, while the Proxy SVAR systematically fails to do so when the model is either misspecified, does not include all relevant information, or the measurement error is present. In an application to US monetary policy, the Proxy DFM shows that a tightening shock is unequivocally contractionary, with deteriorations in domestic demand, labor, credit, housing, exchange, and financial markets. This holds true for all raw instruments available in the literature. The variance decomposition analysis highlights the importance of monetary policy shocks in explaining economic fluctuations, albeit at different horizons. 
Date:  2023–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2307.06145&r=ets 
By:  Bram van Os (Erasmus University Rotterdam) 
Abstract:  We present a comprehensive framework for constructing dynamic density models by combining optimization with concepts from information theory. Specifically, we propose to recursively update a timevarying conditional density by maximizing the loglikelihood contribution of the latest observation subject to a KullbackLeibler divergence (KLD) regularization centered at the onestep ahead predicted density. The resulting Relative Entropy Adaptive Density (READY) update has attractive optimality properties, is reparametrization invariant and can be viewed as an intuitive regularized estimator of the pseudotrue density. Popular existing models, such as the ARMA(1, 1) and GARCH(1, 1), can be retrieved as special cases. Furthermore, we show that standard scoredriven models with inverse Fisher scaling can be derived as convenient local approximations of the READY update. Empirical usefulness is illustrated by the modeling of employment growth and asset volatility. 
Date:  2023–06–29 
URL:  http://d.repec.org/n?u=RePEc:tin:wpaper:20230037&r=ets 