Generalized Spectral Tests for High Dimensional Multivariate Martingale Difference Hypotheses

This study proposes new generalized spectral tests for multivariate Martingale Difference Hypotheses, especially suitable for high-dimensionality situations. The new tests are based on the martingale difference divergence covariance (MDD) proposed by Shao and Zhang (2014). It considers block-wise serial dependence of all lags, therefore, is consistent against general block-wise nonparametric Pitman’s local alternatives at the parametric rate n−1/2, where n is the sample size, and free of a user-chosen parameter. In order to cope with the highdimensionality in the sense that the dimension of time series is comparable to or even greater than the sample size, it is pivotal to employ a bias-..

Econometric Time Series

Autoregressive conditional duration modelling of high frequency data

This paper explores the duration dynamics modelling under the Autoregressive Conditional Durations (ACD) framework (Engle and Russell 1998). I test different distributions assumptions for the durations. The empirical results suggest unconditional durations approach the Gamma distributions. Moreover, compared with exponential distributions and Weibull distributions, the ACD model with Gamma distributed innovations provide the best fit of SPY durations.

Econometric Time Series

Multiplicative Component GARCH Model of Intraday Volatility

This paper proposes a multiplicative component intraday volatility model. The intraday conditional volatility is expressed as the product of intraday periodic component, intraday stochastic volatility component and daily conditional volatility component. I extend the multiplicative component intraday volatility model of Engle (2012) and Andersen and Bollerslev (1998) by incorporating the durations between consecutive transactions. The model can be applied to both regularly and irregularly spaced returns. I also provide a nonparametric estimation technique of the intraday volatility periodicity. The empirical results suggest the model can successfully capture the interdependency of intraday r..

Econometric Time Series

Forecasting with VAR-teXt and DFM-teXt Models:exploring the predictive power of central bank communication

This paper explores the complementarity between traditional econometrics and machine learning and applies the resulting model – the VAR-teXt – to central bank communication. The VAR-teXt is a vector autoregressive (VAR) model augmented with information retrieved from text, turned into quantitative data via a Latent Dirichlet Allocation (LDA) model, whereby the number of topics (or textual factors) is chosen based on their predictive performance. A Markov chain Monte Carlo (MCMC) sampling algorithm for the estimation of the VAR-teXt that takes into account the fact that the textual factors are estimates is also provided. The approach is then extended to dynamic factor models (DFM) generat..

Econometric Time Series

An automatic algorithm to date the reference cycle of the Spanish economy

This paper provides an accurate chronology of the Spanish reference business cycle by adapting the multiple change-point model proposed by Camacho, Gadea and Gómez Loscos (2021). In that approach, each individual pair of specific peaks and troughs from a set of indicators is viewed as a realization of a mixture of an unspecified number of separate bivariate Gaussian distributions, whose different means are the reference turning points and whose transitions are governed by a restricted Markov chain. In the empirical application, seven recessions in the period from 1970.2 to 2020.2 are identified, which are in high concordance with the timing of the turning point dates established by the Span..

Econometric Time Series

Coresets for Time Series Clustering

We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors for real-time measurement and rapid drop in storage costs. In particular, we consider the setting where the time series data on N entities is generated from a Gaussian mixture model with autocorrelations over k clusters in Rd. Our main contribution is an algorithm to construct coresets for the maximum likelihood objective for this mixture model. Our algorithm is efficient, and, under a mild assumption on the covariance matrices of the Gaussians, the size of the cor..

Econometric Time Series

Modelling Cycles in Climate Series: the Fractional Sinusoidal Waveform Process

The paper proposes a novel model for time series displaying persistent stationary cycles, the fractional sinusoidal waveform process. The underlying idea is to allow the parameters that regulate the amplitude and phase to evolve according to fractional noise processes. Its advantages with respect to popular alternative specifications, such as the Gegenbauer process, are twofold: the autocovariance function is available in closed form, which opens the way to exact maximum likelihood estimation; secondly the model encompasses deterministic cycles, so that discrete spectra arise as a limiting case. A generalization of the process, featuring multiple components, an additive `red noise' component..

Econometric Time Series

A Unified Framework to Estimate Macroeconomic Stars

We develop a flexible semi-structural time-series model to estimate jointly several macroeconomic "stars" — i.e., unobserved long-run equilibrium levels of output (and growth rate of output), the unemployment rate, the real rate of interest, productivity growth, the price inflation, and wage inflation. The ingredients of the model are in part motivated by economic theory and in part by the empirical features necessitated by the changing economic environment. Following the recent literature on inflation and interest rate modeling, we explicitly model the links between long-run survey expectations and stars to improve the stars' econometric estimation. Our approach permits time variation in ..

Econometric Time Series

Efficient Nonparametric Estimation of Generalized Autocovariances

This paper provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalized autocovariance function of a stationary random process. The generalized autocovariance function is the inverse Fourier transform of a power transformation of the spectral density and encompasses the traditional and inverse autocovariance functions as particular cases. A nonparametric estimator is based on the inverse discrete Fourier transform of the power transformation of the pooled periodogram. The general result on the asymptotic efficiency is then applied to the class of Gaussian stationary ARMA processes and its implications are discussed. Finally, we illus..

Econometric Time Series

Dynamic Interdependence and Volatility Transmission from the American to the Brazilian Stock Market

The main aim of this paper is to verify the dynamic interdependence and transmission of volatility from the American (SP500) to the Brazilian stock market (IBOVESPA and sectoral indexes). Estimates were performed by GARCH/BEKK methodology, considering the period from January 2007 to December 2019. In the periods considered as “critical events†there was a significant increase in the conditional covariance between SP500 and Brazilian stock indexes (IBOVESPA and sector indices), which suggests for the hypothesis of financial contagion. The covariance increased more intensely and persistently during the so-called subprime crisis, one that had a major impact on the Brazilian economy, e..

Econometric Time Series

Kernel-based Time-Varying IV estimation: handle with care

Giraitis, Kapetanios, and Marcellino (Journal of Econometrics, 2020) proposed a kernel-based time-varying coefficients IV estimator. By using entirely different code, We broadly replicate the simulation results and the empirical application on the Phillips Curve but we note that a small coding mistake might have affected some of the reported results. Further, we extend the results by using a different sample and many kernel functions; we find that the estimator is remarkably robust across a wide range of smoothing choices, but the effect of outliers may be less obvious than expected.

Econometric Time Series

Value-at-Risk forecasting model based on normal inverse Gaussian distribution driven by dynamic conditional score

Under the framework of dynamic conditional score, we propose a parametric forecasting model for Value-at-Risk based on the normal inverse Gaussian distribution (Hereinafter NIG-DCS-VaR), which creatively incorporates intraday information into daily VaR forecast. NIG specifies an appropriate distribution to return and the semi-additivity of the NIG parameters makes it feasible to improve the estimation of daily return in light of intraday return, and thus the VaR can be explicitly obtained by calculating the quantile of the re-estimated distribution of daily return. We conducted an empirical analysis using two main indexes of the Chinese stock market, and a variety of backtesting approaches a..

Econometric Time Series

Nonparametric Tests of Conditional Independence for Time Series

We propose consistent nonparametric tests of conditional independence for time series data. Our methods are motivated from the difference between joint conditional cumulative distribution function (CDF) and the product of conditional CDFs. The difference is transformed into a proper conditional moment restriction (CMR), which forms the basis for our testing procedure. Our test statistics are then constructed using the integrated moment restrictions that are equivalent to the CMR. We establish the asymptotic behavior of the test statistics under the null, the alternative, and the sequence of local alternatives converging to conditional independence at the parametric rate. Our tests are implem..

Econometric Time Series

The time-varying evolution of inflation risks

This paper develops a Bayesian quantile regression model with time-varying parameters (TVPs) for forecasting inflation risks. The proposed parametric methodology bridges the empirically established benefits of TVP regressions for forecasting inflation with the ability of quantile regression to model flexibly the whole distribution of inflation. In order to make our approach accessible and empirically relevant for forecasting, we derive an efficient Gibbs sampler by transforming the state-space form of the TVP quantile regression into an equivalent high-dimensional regression form. An application of this methodology points to a good forecasting performance of quantile regressions with TVPs au..

Econometric Time Series

A mixed frequency BVAR for the euro area labour market

We introduce a Bayesian Mixed-Frequency VAR model for the aggregate euro area labour market that features a structural identification via sign restrictions. The purpose of this paper is twofold: we aim at (i) providing reliable and timely forecasts of key labour market variables and (ii) enhancing the economic interpretation of the main movements in the labour market. We find satisfactory results in terms of forecasting, especially when looking at quarterly variables, such as employment growth and the job finding rate. Furthermore, we look into the shocks that drove the labour market and macroeconomic dynamics from 2002 to early 2020, with a first insight also on the COVID-19 recession. Whil..

Econometric Time Series

Testing for long-range dependence in non-stationary time series time-varying regression

We consider the problem of testing for long-range dependence for time-varying coefficient regression models. The covariates and errors are assumed to be locally stationary, which allows complex temporal dynamics and heteroscedasticity. We develop KPSS, R/S, V/S, and K/S-type statistics based on the nonparametric residuals, and propose bootstrap approaches equipped with a difference-based long-run covariance matrix estimator for practical implementation. Under the null hypothesis, the local alternatives as well as the fixed alternatives, we derive the limiting distributions of the test statistics, establish the uniform consistency of the difference-based long-run covariance estimator, and jus..

Econometric Time Series

Sector Volatility Prediction Performance Using GARCH Models and Artificial Neural Networks

Recently artificial neural networks (ANNs) have seen success in volatility prediction, but the literature is divided on where an ANN should be used rather than the common GARCH model. The purpose of this study is to compare the volatility prediction performance of ANN and GARCH models when applied to stocks with low, medium, and high volatility profiles. This approach intends to identify which model should be used for each case. The volatility profiles comprise of five sectors that cover all stocks in the U.S stock market from 2005 to 2020. Three GARCH specifications and three ANN architectures are examined for each sector, where the most adequate model is chosen to move on to forecasting. T..

Econometric Time Series

On the asymptotic behavior of bubble date estimators

In this study, we extend the three-regime bubble model of Pang et al. (2021) to allow the forth regime followed by the unit root process after recovery. We provide the asymptotic and finite sample justification of the consistency of the collapse date estimator in the two-regime AR(1) model. The consistency allows us to split the sample before and after the date of collapse and to consider the estimation of the date of exuberation and date of recovery separately. We have also found that the limiting behavior of the recovery date varies depending on the extent of explosiveness and recovering.

Econometric Time Series

Adaptive Learning on Time Series: Method and Financial Applications

We formally introduce a time series statistical learning method, called Adaptive Learning, capable of handling model selection, out-of-sample forecasting and interpretation in a noisy environment. Through simulation studies we demonstrate that the method can outperform traditional model selection techniques such as AIC and BIC in the presence of regime-switching, as well as facilitating window size determination when the Data Generating Process is time-varying. Empirically, we use the method to forecast S&P 500 returns across multiple forecast horizons, employing information from the VIX Curve and the Yield Curve. We find that Adaptive Learning models are generally on par with, if not better..

Econometric Time Series

Revisiting identification concepts in Bayesian analysis

This paper studies the role played by identification in the Bayesian analysis of statistical and econometric models. First, for unidentified models we demonstrate that there are situations where the introduction of a non-degenerate prior distribution can make a parameter that is nonidentified in frequentist theory identified in Bayesian theory. In other situations, it is preferable to work with the unidentified model and construct a Markov Chain Monte Carlo (MCMC) algorithms for it instead of introducing identifying assumptions. Second, for partially identified models we demonstrate how to construct the prior and posterior distributions for the identified set parameter and how to conduct Bay..

Econometric Time Series

Semimartingale and continuous-time Markov chain approximation for rough stochastic local volatility models

Rough volatility models have recently been empirically shown to provide a good fit to historical volatility time series and implied volatility smiles of SPX options. They are continuous-time stochastic volatility models, whose volatility process is driven by a fractional Brownian motion with Hurst parameter less than half. Due to the challenge that it is neither a semimartingale nor a Markov process, there is no unified method that not only applies to all rough volatility models, but also is computationally efficient. This paper proposes a semimartingale and continuous-time Markov chain (CTMC) approximation approach for the general class of rough stochastic local volatility (RSLV) models. In..

Econometric Time Series

Estimation and Inference with Near Unit Roots

New methods are developed for identifying, estimating and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit root (UR), local unit root (LUR), mildly integrated (MI) and mildly explosive (ME) speciï¬ cations in the new model formulation. It is shown how a new parameterization involving a localizing rate sequence that characterizes departures from unity can be consistently estimated in all cases. Simple pivotal limit distributions that enable valid inference about the form and degree of nonstationarity apply for MI and ME speciï¬ cations and new limit theory holds in UR and LUR cases. Normalizing and variance stabilizi..

Econometric Time Series

Robust Inference with Stochastic Local Unit Root Regressors in Predictive Regressions

This paper explores predictive regression models with stochastic unit root (STUR) components and robust inference procedures that encompass a wide class of persistent and time-varying stochastically nonstationary regressors. The paper extends the mechanism of endogenously generated instrumentation known as IVX, showing that these methods remain valid for short and long-horizon predictive regressions in which the predictors have STUR and local STUR (LSTUR) generating mechanisms. Both mean regression and quantile regression methods are considered. The asymptotic distributions of the IVX estimators are new and require some new methods in their derivation. The distributions are compared to previ..

Econometric Time Series

On Multicointegration

A semiparametric triangular systems approach shows how multicointegration can occur naturally in an I(1) cointegrated regression model. The framework reveals the source of multicointegration as singularity of the long run error covariance matrix in an I(1) system, a feature noted but little explored in earlier work. Under such singularity, cointegrated I(1) systems embody a multicointegrated structure and may be analyzed and estimated without appealing to the associated I(2) system but with consequential asymptotic properties that can introduce asymptotic bias into conventional methods of cointegrating regression. The present paper shows how estimation of such systems may be accomplished und..

Econometric Time Series

Discrete Fourier Transforms of Fractional Processes with Econometric Applications

The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d ≥ 1 2: Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory ..

Econometric Time Series

On Parameter Estimation in Unobserved Components Models subject to Linear Inequality Constraints

We propose a new quadratic-programming-based method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved components models involving inequality constraints on the parameters. For instance, Chat et al. (2016) propose a new model of trend inflation with linear inequality constraints on the stochastic trend. We implement the proposed new method for this model and compare it to the existing approximation. We observe that the proposed new method works as good as the existing approximation in terms of the final trend estimates while achieving greater gains in terms of sample efficie..

Econometric Time Series

CP Factor Model for Dynamic Tensors

Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CP decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynami..

Econometric Time Series

Testing and Estimating Structural Breaks in Time Series and Panel Data in Stata

Identifying structural change is a crucial step in analysis of time series and panel data. The longer the time span, the higher the likelihood that the model parameters have changed as a result of major disruptive events, such as the 2007-2008 financial crisis and the 2020 COVID-19 outbreak. Detecting the existence of breaks, and dating them is therefore necessary not only for estimation purposes but also for understanding drivers of change and their effect on relationships. This article introduces a new community contributed command called xtbreak, which provides researchers with a complete toolbox for analysing multiple structural breaks in time series and panel data. xtbreak can detect th..

Econometric Time Series

Optimal Regime-Switching Density Forecasts

This paper proposes an approach for enhancing density forecasts of non-normal macroeconomic variables using Bayesian Markov-switching models. Alternative views about economic regimes are combined to produce flexible forecasts, which are optimized with respect to standard objective functions of density forecasting. The optimization procedure explores both forecast combinations and Bayesian model averaging. In an application to U.S. GDP growth, the approach is shown to achieve good accuracy in terms of average predictive densities and to produce well-calibrated forecast distributions. The proposed framework can be used to evaluate the contribution of economists' views to density forecast perfo..

Econometric Time Series

A Scalable Inference Method For Large Dynamic Economic Systems

The nature of available economic data has changed fundamentally in the last decade due to the economy's digitisation. With the prevalence of often black box data-driven machine learning methods, there is a necessity to develop interpretable machine learning methods that can conduct econometric inference, helping policymakers leverage the new nature of economic data. We therefore present a novel Variational Bayesian Inference approach to incorporate a time-varying parameter auto-regressive model which is scalable for big data. Our model is applied to a large blockchain dataset containing prices, transactions of individual actors, analyzing transactional flows and price movements on a very gra..

Econometric Time Series