
on Econometric Time Series 
By:  Cristina Amado (NIPE/Center for Research in Economics and Management, University of Minho, Portugal; and CREATES and Aarhus University) 
Abstract:  Nonstationarity and outlying observations are commonly encountered in financial time series. It is thus expected that models are able to accommodate these stylized facts and the techniques used are suitable to specify such models. In this paper we relax the assumption of stationarity and consider the problem of detecting smooth changes in the unconditional variance in the presence of outliers. It is found by simulation that the misspecifi cation test for constancy of the unconditional variance in GARCH models can be severely adversely affected in the presence of additive outliers. An outlier robust specifi cation procedure is also proposed to mitigate the effects of outliers for building multiplicative timevarying volatility models. The outlier robust variant of the test is shown to perform better than the conventional test in terms of size and power. An application to commodity returns illustrates the usefulness of the robust specifi cation procedure. 
Keywords:  Conditional heteroskedasticity; Testing parameter constancy; Model specification; Timevarying unconditional variance; Outliers. 
JEL:  C12 C32 C51 C52 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:nip:nipewp:11/2022&r=ets 
By:  Ramis Khabibullin (Independent Researcher); Sergei Seleznev (Bank of Russia, Russian Federation) 
Abstract:  This paper presents a fast algorithm for estimating hidden states of Bayesian state space models. The algorithm is a variation of amortized simulationbased inference algorithms, where numerous artificial datasets are generated at the first stage, and then a flexible model is trained to predict the variables of interest. In contrast to those proposed earlier, the procedure described in this paper makes it possible to train estimators for hidden states by concentrating only on certain characteristics of the marginal posterior distributions and introducing inductive bias. Illustrations using the examples of stochastic volatility model, nonlinear dynamic stochastic general equilibrium model and seasonal adjustment procedure with breaks in seasonality show that the algorithm has sufficient accuracy for practical use. Moreover, after pretraining, which takes several hours, finding the posterior distribution for any dataset takes from hundredths to tenths of a second. 
Keywords:  amortized simulationbased inference, Bayesian state space models, neural networks, seasonal adjustment, stochastic volatility, SVDSGE. 
JEL:  C11 C15 C32 C45 
Date:  2022–12 
URL:  http://d.repec.org/n?u=RePEc:bkr:wpaper:wps104&r=ets 
By:  Alexander Chudik; M. Hashem Pesaran; Mahrad Sharifvaghefi 
Abstract:  This paper is concerned with the problem of variable selection when the marginal effects of signals on the target variable as well as the correlation of the covariates in the active set are allowed to vary over time, without committing to any particular model of parameter instabilities. It poses the issue of whether weighted or unweighted observations should be used at the variable selection stage in the presence of parameter instability, particularly when the number of potential covariates is large. Amongst the extant variable selection approaches, we focus on the One Covariate at a time Multiple Testing (OCMT) method. This procedure allows a natural distinction between the selection and forecasting stages. We establish three main theorems on selection, estimation post selection, and insample fit. These theorems provide justification for using unweighted observations at the selection stage of OCMT and downweighting of observations only at the forecasting stage. The benefits of the proposed method as compared to Lasso, Adaptive Lasso and Boosting are illustrated by Monte Carlo studies and empirical applications to forecasting monthly stock market returns and quarterly output growths. 
Keywords:  parameter instability, highdimensionality, variable selection, One Covariate at a time Multiple Testing (OCMT) 
JEL:  C22 C52 C53 C55 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_10223&r=ets 
By:  Faria, Gonçalo; Verona, Fabio 
Abstract:  Predictability is time and frequency dependent. We propose a new forecasting method  forecast combination in the frequency domain  that takes this fact into account. With this method we forecast the equity premium and real GDP growth rate. Combining forecasts in the frequency domain produces markedly more accurate predictions relative to the standard forecast combination in the time domain, both in terms of statistical and economic measures of outofsample predictability. In a realtime forecasting exercise, the flexibility of this method allows to capture remarkably well the sudden and abrupt drops associated with recessions and further improve predictability. 
Keywords:  forecast combination, frequency domain, equity premium, GDP growth, Haar filter, wavelets 
JEL:  C58 G11 G17 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:zbw:bofrdp:12023&r=ets 
By:  Michael Dueker; Laura E. Jackson; Michael T. Owyang; Martin Sola 
Abstract:  Smoothtransition autoregressive (STAR) models, competitors of Markovswitching models, are limited by an assumed timeinvariant threshold level. We augment the STAR model with a timevarying threshold that can be interpreted as a “tipping level” where the mean and dynamics of the VAR shift. Thus, the timevarying latent threshold level serves as a demarcation between regimes. We show how to estimate the model in a Bayesian framework using a Metropolis step and an unscented Kalman filter proposal. To show how allowing time variation in the threshold can affect the results, we present two applications: a model of the natural rate of unemployment and a model of regimedependent government spending. 
Keywords:  Regime switching, smoothtransition autoregressive model, unemployment, nonlinear models. 
JEL:  C22 E31 G12 
Date:  2022–12 
URL:  http://d.repec.org/n?u=RePEc:udt:wpecon:2022_04&r=ets 
By:  Francesco Cordoni; Nicolas Doremus; Alessio Moneta 
Abstract:  We propose a statistical identification procedure for structural vector autoregressive (VAR) models that present a nonlinear dependence (at least) at the contemporaneous level. By applying and adapting results from the literature on causal discovery with continuous additive noise models to structural VAR analysis, we show that a large class of structural VAR models is identifiable. We spell out these specific conditions and propose a scheme for the estimation of structural impulse response functions in a nonlinear setting. We assess the performance of this scheme in a simulation experiment. Finally, we apply it in a study on the effects of monetary policy on the economy. 
Keywords:  Structural VAR models; Causal Discovery; Nonlinearity; Additive Noise Models; Impulse response functions. 
Date:  2023–01–27 
URL:  http://d.repec.org/n?u=RePEc:ssa:lemwps:2023/07&r=ets 
By:  Chaohua Dong; Jiti Gao; Yundong Tu; Bin Peng 
Abstract:  Robust Mestimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing the resultant estimators rests on the nonsmoothness of these losses. Generalized functions have advantages over ordinary functions in several aspects, especially generalized functions possess derivatives of any order. Generalized functions incorporate local integrable functions, the socalled regular generalized functions, while the socalled singular generalized functions (e.g. Dirac delta function) can be obtained as the limits of a sequence of sufficient smooth functions, socalled regular sequence in generalized function context. This makes it possible to use these singular generalized functions through approximation. Nevertheless, a significant contribution of this paper is to establish the convergence rate of regular sequence to nonsmooth loss that answers a call from the relevant literature. For parameter estimation where objective function may be nonsmooth, this paper first shows as a general paradigm that how generalized function approach can be used to tackle the nonsmooth loss functions in Section two using a very simple model. This approach is of general interest and applicability. We further use the approach in robust Mestimation for additive singleindex cointegrating time series models; the asymptotic theory is established for the proposed estimators. We evaluate the finitesample performance of the proposed estimation method and theory by both simulated data and an empirical analysis of predictive regression of stock returns. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.06631&r=ets 
By:  Zhang, Xinyu; Tong, Howell 
Abstract:  Principal component analysis (PCA) is a most frequently used statistical tool in almost all branches of data science. However, like many other statistical tools, there is sometimes the risk of misuse or even abuse. In this paper, we highlight possible pitfalls in using the theoretical results of PCA based on the assumption of independent data when the data are time series. For the latter, we state with proof a central limit theorem of the eigenvalues and eigenvectors (loadings), give direct and bootstrap estimation of their asymptotic covariances, and assess their efficacy via simulation. Specifically, we pay attention to the proportion of variation, which decides the number of principal components (PCs), and the loadings, which help interpret the meaning of PCs. Our findings are that while the proportion of variation is quite robust to different dependence assumptions, the inference of PC loadings requires careful attention. We initiate and conclude our investigation with an empirical example on portfolio management, in which the PC loadings play a prominent role. It is given as a paradigm of correct usage of PCA for time series data. 
Keywords:  bootstrap; inference; limiting distribution; PCA; portfolio management; time series; 11771239; 71973077 
JEL:  C1 
Date:  2022–04–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:113566&r=ets 
By:  Mikihito Nishi 
Abstract:  In this study, we propose a test for the coefficient randomness in autoregressive models where the autoregressive coefficient is local to unity, which is empirically relevant given the results of earlier studies. Under this specification, we theoretically analyze the effect of the correlation between the random coefficient and disturbance on tests' properties, which remains largely unexplored in the literature. Our analysis reveals that the correlation crucially affects the power of tests for coefficient randomness and that tests proposed by earlier studies can perform poorly when the degree of the correlation is moderate to large. The test we propose in this paper is designed to have a power function robust to the correlation. Because the asymptotic null distribution of our test statistic depends on the correlation $\psi$ between the disturbance and its square as earlier tests do, we also propose a modified version of the test statistic such that its asymptotic null distribution is free from the nuisance parameter $\psi$. The modified test is shown to have better power properties than existing ones in large and finite samples. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.04853&r=ets 
By:  Sylvia Fr\"uhwirthSchnatter; Darjus Hosszejni; Hedibert Freitas Lopes 
Abstract:  Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotationbased identification such as the positive lower triangular (PLT) constraint. To fill this gap, we review the advantages of variance identification in sparse factor analysis and introduce the generalized lower triangular (GLT) structures. We show that the GLT assumption is an improvement over PLT without compromise: GLT is also unique but, unlike PLT, a nonrestrictive assumption. Furthermore, we provide a simple counting rule for variance identification under GLT structures, and we demonstrate that within this model class the unknown number of common factors can be recovered in an exploratory factor analysis. Our methodology is illustrated for simulated data in the context of postprocessing posterior draws in Bayesian sparse factor analysis. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.06354&r=ets 