
on Econometric Time Series 
Issue of 2020‒05‒04
twelve papers chosen by Jaqueson K. Galimberti Auckland University of Technology 
By:  Bo Zhang; Jiti Gao; Guangming Pan 
Abstract:  This paper considers a pdimensional time series model of the form x(t)=Π x(t1)+Σ^(1/2)y(t), 1≤t≤T, where y(t)=(y(t1),...,y(tp))^T and Σ is the square root of a symmetric positive definite matrix. Here Π is a symmetric matrix which satisfies that ∥Π ∥_2≤ 1 and T(1∥Π ∥_min) is bounded. The linear processes Y(tj) is of the form ∑_{k=0}^∞b(k)Z(tk,j) where ∑_{i=0}^∞b(i) < ∞ and {Z(ij) } are are independent and identically distributed (i.i.d.) random variables with E Z ij =0, EZ(ij)²=1 and EZ(ij)^4< ∞. We first investigate the asymptotic behavior of the first k largest eigenvalues of the sample covariance matrices of the time series model. Then we propose a new estimator for the highdimensional near unit root setting through using the largest eigenvalues of the sample covariance matrices and use it to test for near unit roots. Such an approach is theoretically novel and addresses some important estimation and testing issues in the highdimensional near unit root setting. Simulations are also conducted to demonstrate the finitesample performance of the proposed test statistic. 
Keywords:  Asymptotic normality, largest eigenvalue, linear process, near unit root test. 
JEL:  C21 C32 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:msh:ebswps:202012&r=all 
By:  Andrea Gazzani (Bank of Italy); Alejandro Vicondoa (Instituto de Economía, Pontificia Universidad Católica de Chile) 
Abstract:  This paper proposes a novel methodology, the Bridge ProxySVAR, which exploits highfrequency information for the identification of the Vector Autoregressive (VAR) models employed in macroeconomic analysis. The methodology is comprised of three steps: (I) identifying the structural shocks of interest in highfrequency systems; (II) aggregating the series of highfrequency shocks at a lower frequency; and (III) using the aggregated series of shocks as a proxy for the corresponding structural shock in lower frequency VARs. We show that the methodology correctly recovers the impact effect of the shocks, both formally and in Monte Carlo experiments. Thus the Bridge ProxySVAR can improve causal inference in macroeconomics that typically relies on VARs identified at lowfrequency. In an empirical application, we identify uncertainty shocks in the U.S. by imposing weaker restrictions relative to the existing literature and find that they induce mildly recessionary effects. 
Keywords:  structural vector autoregression, external instrument, highfrequency identification, proxy variable, uncertainty shocks. 
JEL:  C32 C36 E32 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:bdi:wptemi:td_1274_20&r=all 
By:  David Harris; Hsein Kew; A. M. Robert Taylor 
Abstract:  This paper focuses on the estimation of the location of level breaks in time series whose shocks display nonstationary volatility (permanent changes in unconditional volatility). We propose a new feasible weighted least squares (WLS) estimator, based on an adaptive estimate of the volatility path of the shocks. We show that this estimator belongs to a generic class of weighted residual sum of squares which also contains the ordinary least squares (OLS) and WLS estimators, the latter based on the true volatility process. For fixed magnitude breaks we show that the consistency rate of the generic estimator is unaffected by nonstationary volatility. We also provide local limiting distribution theory for cases where the break magnitude is either localtozero at some polynomial rate in the sample size or is exactly zero. The former includes the Pitman drift rate which is shown via Monte Carlo experiments to predict well the key features of the finite sample behaviour of both the OLS and our feasible WLS estimators. The simulations highlight the importance of the break location, break magnitude, and the form of nonstationary volatility for the finite sample performance of these estimators, and show that our proposed feasible WLS estimator can deliver significant improvements over the OLS estimator under heteroskedasticity. We discuss how these results can be applied, by using level break fraction estimators on the first differences of the data, when testing for a unit root in the presence of trend breaks and/or nonstationary volatility. Methods to select between the break and no break cases, using standard information criteria and feasible weighted information criteria based on our adaptive volatility estimator, are also discussed. Simulation evidence suggests that unit root tests based on these weighted quantities can display significantly improved finite sample behaviour under heteroskedasticity relative to their unweighted counterparts. An empirical illustration to U.S. and U.K. real GDP is also considered. 
Keywords:  Level break fraction, nonstationary volatility, adaptive estimation, feasible weighted estimator, information criteria, unit root tests and trend breaks. 
JEL:  C12 C22 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:msh:ebswps:20208&r=all 
By:  Guglielmo Maria Caporale; Luis A. GilAlana; Miguel MartinValmayor 
Abstract:  This paper provides evidence on the degree of persistence of one of the key components of the CAPM, namely the market risk premium, as well as its volatility. The analysis applies fractional integration methods to data for the US, Germany and Japan, and for robustness purposes considers different time horizons (2, 5 and 10 years) and frequencies (monthly and weekly). The empirical findings in most cases imply that the market risk premium is a highly persistent variable which can be characterized as a random walk process, whilst its volatility is less persistent and exhibits stationary longmemory behaviour. There is also evidence that in the case of the US the degree of persistence has changed as a results of various events; this is confirmed by both endogenous break tests and the associated subsample estimates. Market participants should take this evidence into account when designing their investment strategies. 
Keywords:  CAPM, risk premium, persistence, mean reversion, long memory 
JEL:  C22 G11 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_8211&r=all 
By:  Christiane Baumeister; James D. Hamilton 
Abstract:  This paper examines methods for structural interpretation of vector autoregressions when the identifying information is regarded as imperfect or incomplete. We suggest that a Bayesian approach offers a unifying theme for guiding inference in such settings. Among other advantages, the unified approach solves a problem with calculating elasticities that appears not to have been recognized by earlier researchers. We also call attention to some computational concerns of which researchers who approach this problem using other methods should be aware. 
JEL:  C11 C32 Q43 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:27014&r=all 
By:  Lusompa, Amaze 
Abstract:  It is well known that Local Projections (LP) residuals are autocorrelated. Conventional wisdom says that LP have to be estimated by OLS with Newey and West (1987) (or some type of Heteroskedastic and Autocorrelation Consistent (HAC)) standard errors and that GLS is not possible because the autocorrelation process is unknown. I show that the autocorrelation process of LP is known and that autocorrelation can be corrected for using GLS. Estimating LP with GLS has three major implications: 1) LP GLS can be substantially more efficient and less biased than estimation by OLS with NeweyWest standard errors. 2) Since the autocorrelation process can be modeled explicitly, it is possible to give a fully Bayesian treatment of LP. That is, LP can be estimated using frequentist/classical or fully Bayesian methods. 3) Since the autocorrelation process can be modeled explicitly, it is now possible to estimate timevarying parameter LP. 
Keywords:  Impulse Response, Local Projections, Autocorrelation, GLS 
JEL:  C1 C11 C2 C22 C3 C32 
Date:  2019–11–14 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:99856&r=all 
By:  Faria, Gonçalo; Verona, Fabio 
Abstract:  Any time series can be decomposed into cyclical components fluctuating at different frequencies. Accordingly, in this paper we propose a method to forecast the stock market's equity premium which exploits the frequency relationship between the equity premium and several predictor variables. We evaluate a large set of models and find that, by selecting the relevant frequencies for equity premium forecasting, this method significantly improves in both statistical and economic sense upon standard time series forecasting methods. This improvement is robust regardless of the predictor used, the outofsample period considered, and the frequency of the data used. 
JEL:  C58 G11 G17 
Date:  2020–04–27 
URL:  http://d.repec.org/n?u=RePEc:bof:bofrdp:2020_006&r=all 
By:  Oskar Gustafsson; Mattias Villani; P\"ar Stockhammar 
Abstract:  Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially updated by new function evaluations. An acquisition strategy uses this posterior distribution to decide where to place the next function evaluation. We propose a novel Bayesian optimization framework for situations where the user controls the computational effort, and therefore the precision of the function evaluations. This is a common situation in econometrics where the marginal likelihood is often computed by Markov Chain Monte Carlo (MCMC) methods, with the precision of the marginal likelihood estimate determined by the number of MCMC draws. The proposed acquisition strategy gives the optimizer the option to explore the function with cheap noisy evaluations and therefore finds the optimum faster. Prior hyperparameter estimation in the steadystate Bayesian vector autoregressive (BVAR) model on US macroeconomic time series data is used for illustration. The proposed method is shown to find the optimum much quicker than traditional Bayesian optimization or grid search. 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2004.10092&r=all 
By:  Syed Jawad Hussain Shahzad (Montpellier Business School, Montpellier, France; South Ural State University, Chelyabinsk, Russian Federation); Rangan Gupta (Department of Economics, University of Pretoria, Pretoria, 0002, South Africa); Riza Demirer (Department of Economics and Finance, Southern Illinois University Edwardsville, Edwardsville, IL 620261102, USA); Christian Pierdzioch (Department of Economics, Helmut Schmidt University, Holstenhofweg 85, P.O.B. 700822, 22008 Hamburg, Germany) 
Abstract:  Using highfrequency (daily) data on macroeconomic uncertainties and the partial crossquantilogram approach, we examine the directional predictability of disentangled oilpriceshocks for the entire conditional distribution of uncertainties of five advanced economies (Canada, Euro Area, Japan, the United Kingdom, and the United States). Our results show that oildemand, supply, and financial riskrelated shocks can predict the future path of uncertainty; however, the predictive relationship is contingent on the initial level of macroeconomic uncertainty and the size of the shocks. Our results suggest that macroeconomic uncertainty is indeed predictable at high frequency, and that oilpriceshocks capture valuable predictive information regarding the future path of macroeconomic uncertainties. 
Keywords:  Oil shocks, uncertainty, partial crossquantilograms, directional predictability, developed economies 
JEL:  C22 C32 Q41 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:pre:wpaper:202031&r=all 
By:  Yi He; Sombut Jaidee; Jiti Gao 
Abstract:  We propose a powerful quadratic test for the overall significance of many weak exogenous variables in a dense autoregressive model. By shrinking the classical weighting matrix on the sample moments to be identity, the test is asymptotically correct in high dimensions even when the number of coefficients is larger than the sample size. Our theory allows a nonparametric error distribution and estimation of the autoregressive coefficients. Using random matrix theory, we show that the test has the optimal asymptotic testing power among a large class of competitors against local dense alternatives whose direction is free in the eigenbasis of the sample covariance matrix among regressors. The asymptotic results are adaptive to the predictors' crosssectional and temporal dependence structure, and do not require a limiting spectral law of their sample covariance matrix. The method extends beyond autoregressive models, and allows more general nuisance parameters. Monte Carlo studies suggest a good power performance of our proposed test against high dimensional dense alternative for various data generating processes. We apply our tests to detect the overall significance of over one hundred exogenous variables in the latest FREDMD database for predicting the monthly growth in the US industrial production index. 
Keywords:  Highdimensional linear model, null hypothesis, uniformly power test. 
JEL:  C12 C21 C55 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:msh:ebswps:202013&r=all 
By:  Kartikay Gupta; Niladri Chatterjee 
Abstract:  The leadlag relationship plays a vital role in financial markets. It is the phenomenon where a certain priceseries lags behind and partially replicates the movement of leading timeseries. The present research proposes a new technique which helps better identify the leadlag relationship empirically. Apart from better identifying the leadlag path, the technique also gives a measure for adjudging closeness between financial timeseries. Also, the proposed measure is closely related to correlation, and it uses Dynamic Programming technique for finding the optimal leadlag path. Further, it retains most of the properties of a metric, so much so, it is termed as loose metric. Tests are performed on Synthetic Time Series (STS) with known leadlag relationship and comparisons are done with other stateoftheart models on the basis of significance and forecastability. The proposed technique gives the best results in both the tests. It finds paths which are all statistically significant, and its forecasts are closest to the target values. Then, we use the measure to study the topology evolution of the Foreign Exchange market, as the COVID19 pandemic unfolds. Here, we study the FX currency prices of 29 prominent countries of the world. It is observed that as the crises unfold, all the currencies become strongly interlinked to each other. Also, USA Dollar starts playing even more central role in the FX market. Finally, we mention several other application areas of the proposed technique for designing intelligent systems. 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2004.10560&r=all 
By:  Guglielmo Maria Caporale; Alex Plastun; Viktor Oliinyk 
Abstract:  This paper analyses the explanatory power of the frequency of abnormal returns in the FOREX for the EURUSD, GBRUSD, USDJPY, EURJPY, GBPCHF, AUDUSD and USDCAD exchange rates over the period 19942019. Abnormal returns are detected using a dynamic trigger approach; then the following hypotheses are tested: their frequency is a significant driver of price movements (H1); it does not exhibit seasonal patterns (H2); it is stable over time (H3). For our purposes a variety of statistical methods (both parametric and nonparametric) are applied including ADF tests, Granger causality tests, correlation analysis, (multiple) regression analysis, Probit and Logit regression models. No evidence is found of either seasonal patterns or instability. However, there appears to be a strong positive (negative) relationship between returns in the FOREX and the frequency of positive (negative) abnormal returns. On the whole, the results suggest that the latter is an important driver of price dynamics in the FOREX, is informative about crises and can be the basis of profitable trading strategies, which is inconsistent with market efficiency. 
Keywords:  FOREX, anomalies, price dynamics, frequency of abnormal returns 
JEL:  G12 G17 C63 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_8196&r=all 