
on Econometric Time Series 
By:  Mikkel PlagborgMøller (Princeton University); Christian K. Wolf (Princeton University) 
Abstract:  We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures, instead, they are simply two dimension reduction techniques with common estimand but different finitesample properties. (ii) VARbased structural identification â€“ including shortrun, longrun, or sign restrictions â€“ can equivalently be performed using LPs, and vice versa. (iii) Structural estimation with an instrument (proxy) can be carried out by ordering the instrument first in a recursive VAR, even under noninvertibility. (iv) Linear VARs are as robust to nonlinearities as linear LPs. 
Keywords:  external instrument, impulse response function, local projection, proxy variable, structural vector autoregression 
JEL:  C32 C36 
Date:  2020–10 
URL:  http://d.repec.org/n?u=RePEc:pri:econom:202016&r= 
By:  Ulrich K. Müller (Princeton University); Mark W. Watson (Princeton University) 
Abstract:  This chapter discusses econometric methods for studying lowfrequency variation and covariation in economic time series. We use the term lowfrequency for dynamics over time spans that are a nonnegligible fraction of the sample period. For example, when studying 70 years of postWWII quarterly data, decadal variation is lowfrequency, and when studying a decade of daily return data, yearly variation is lowfrequency. Much of this chapter is organized around a set of empirical exercises that feature questions about lowfrequency variability and covariability, and there is no better way to introduce the topics to be covered than to look at the data featured in these exercises. 
Keywords:  Econometrics 
JEL:  C01 C10 
Date:  2020–09 
URL:  http://d.repec.org/n?u=RePEc:pri:econom:202013&r= 
By:  Liu, Yanbo (Shandong University); Phillips, Peter C. B. (Yale University); Yu, Jun (Singapore Management Uinversity) 
Abstract:  This study provides new mechanisms for identifying and estimating explosive bubbles in mixedroot panel autoregressions with a latent group structure. A postclustering approach is employed that combines a recursive kmeans clustering algorithm with paneldata test statistics for testing the presence of explosive roots in time series trajectories. Uniform consistency of the kmeans clustering algorithm is established, showing that the postclustering estimate is asymptotically equivalent to the oracle counterpart that uses the true group identities. Based on the estimated group membership, righttailed selfnormalized ttests and coefficientbased Jtests, each with pivotal limit distributions, are introduced to detect the explosive roots. The usual Information Criterion (IC) for selecting the correct number of groups is found to be inconsistent and a new method that combines IC with a Hausmantype specification test is proposed that consistently estimates the true number of groups. Extensive Monte Carlo simulations provide strong evidence that in finite samples, the recursive kmeans clustering algorithm can correctly recover latent group membership in data of this type and the proposed postclustering paneldata tests lead to substantial power gains compared with the time series approach. The proposed methods are used to identify bubble behavior in US and Chinese housing markets, and the US stock market, leading to new findings concerning speculative behavior in these markets. 
Keywords:  Bubbles; Clustering; Mildly explosive behavior; kmeans; Latent membership detection 
JEL:  C22 C33 C51 G01 
Date:  2022–02–15 
URL:  http://d.repec.org/n?u=RePEc:ris:smuesw:2022_001&r= 
By:  Astill, Sam; Harvey, David I; Leybourne, Stephen J; Taylor, AM Robert 
Abstract:  We develop tests for predictability that are robust to both the magnitude of the initial condition and the degree of persistence of the predictor. While the popular Bonferroni Q test of Campbell and Yogo (2006) displays excellent power properties for strongly persistent predictors with an asymptotically negligible initial condition, it can suffer from severe size distortions and power losses when either the initial condition is asymptotically nonnegligible or the predictor is weakly persistent. The Bonferroni ttest of Cavanagh et al. (1995), although displaying power well below that of the Bonferroni Q test for strongly persistent predictors with an asymptotically negligible initial condition, displays superior size control and power when the initial condition is asymptotically nonnegligible. In the case where the predictor is weakly persistent, a conventional regression ttest comparing to standard normal quantiles is known to be asymptotically optimal under Gaussianity. Based on these properties, we propose two asymptotically size controlled hybrid tests that are functions of the Bonferroni Q, Bonferroni t, and conventional t tests. Our proposed hybrid tests exhibit very good power regardless of the magnitude of the initial condition or the persistence degree of the predictor. An empirical application to the data originally analysed by Campbell and Yogo (2006) shows our new hybrid tests are much more likely to find evidence of predictability than the Bonferroni Q test when the initial condition of the predictor is estimated to be large in magnitude. 
Keywords:  predictive regression; initial condition; unknown regressor persistence; Bonferroni tests; hybrid tests 
Date:  2022–03–03 
URL:  http://d.repec.org/n?u=RePEc:esy:uefcwp:32447&r= 
By:  Gabriel Borrageiro; Nick Firoozye; Paolo Barucca 
Abstract:  Financial time series are both autocorrelated and nonstationary, presenting modelling challenges that violate the independent and identically distributed random variables assumption of most regression and classification models. The prediction with expert advice framework makes no assumptions on the datagenerating mechanism yet generates predictions that work well for all sequences, with performance nearly as good as the best expert with hindsight. We conduct research using S&P 250 daily sampled data, extending the academic research into crosssectional momentum trading strategies. We introduce a novel ranking algorithm from the prediction with expert advice framework, the naive Bayes asset ranker, to select subsets of assets to hold in either longonly or long/short portfolios. Our algorithm generates the best total returns and riskadjusted returns, net of transaction costs, outperforming the longonly holding of the S&P 250 with hindsight. Furthermore, our ranking algorithm outperforms a proxy for the regressthenrank crosssectional momentum trader, a sequentially fitted curds and whey multivariate regression procedure. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.12186&r= 