|
on Econometric Time Series |
| By: | Javier Hualde (Universidad Pública de Navarra); Morten Ørregaard Nielsen (Queen's University and CREATES) |
| Abstract: | We consider truncated (or conditional) sum-of-squares estimation of a parametric fractional time series model with an additive deterministic structure. The latter consists of both a drift term and a generalized power law trend. The memory parameter of the stochastic component and the power parameter of the deterministic trend component are both considered unknown real numbers to be estimated and belonging to arbitrarily large compact sets. Thus, our model captures different forms of nonstationarity and noninvertibility as well as a very flexible deterministic specification. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to non-uniform convergence of the objective function over a large admissible parameter space and due to the competition between stochastic and deterministic components. As expected, parameter estimates related to the deterministic component are shown to be consistent and asymptotically normal only for parts of the parameter space depending on the relative strength of the stochastic and deterministic components. In contrast, we establish consistency and asymptotic normality of parameter estimates related to the stochastic component for the entire parameter space. Furthermore, the asymptotic distribution of the latter estimates is unaffected by the presence of the deterministic component, even when this is not consistently estimable. We also include a small Monte Carlo simulation to illustrate our results. |
| Keywords: | Asymptotic normality, Consistency, Deterministic trend, Fractional process, Generalized polynomial trend, Generalized power law trend, Noninvertibility, Nonstationarity, Sum-of-squares estimation |
| JEL: | C22 |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1458&r= |
| By: | BENSALMA, Ahmed |
| Abstract: | Recently the generalization of the standard Dickey-Fuller test to the fractional case has been proposed. The proposed test, called fractional Dickey-Fuller test can be applied to sample generated from a type I or a type II fractional process. Depending on whether the test is applied to sample generated from a type I or type II process, it is referred to as a test with or without prehistoric influence respectively. The main and the first objective of this paper is to study the impact induced by a pre-sample of the finite sample null distribution. In fact, the recently proposed test is built based on a composite null hypothesis rather than a sample one. The second objective is to highlight the theoretical justifications for the choice of the null composite hypothesis. All the theoretical results are illustrated with simulated and real data sets. Furthermore, to facilitate the reproducibility of our simulation data and figures we provide all the necessary supplementary material consisting of EViews programs. |
| Keywords: | ARFIMA; fractional integration, Dickey-Fuller test; Fractional Dickey-Fuller test; type I and type II fractional Brownian motion. |
| JEL: | C12 C15 C4 C5 |
| Date: | 2021–04–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:107408&r= |
| By: | Lajos Horvath; Lorenzo Trapani |
| Abstract: | We propose a family of CUSUM-based statistics to detect the presence of changepoints in the deterministic part of the autoregressive parameter in a Random Coefficient AutoRegressive (RCA) sequence. In order to ensure the ability to detect breaks at sample endpoints, we thoroughly study weighted CUSUM statistics, analysing the asymptotics for virtually all possible weighing schemes, including the standardised CUSUM process (for which we derive a Darling-Erdos theorem) and even heavier weights (studying the so-called R\'enyi statistics). Our results are valid irrespective of whether the sequence is stationary or not, and no prior knowledge of stationarity or lack thereof is required. Technically, our results require strong approximations which, in the nonstationary case, are entirely new. Similarly, we allow for heteroskedasticity of unknown form in both the error term and in the stochastic part of the autoregressive coefficient, proposing a family of test statistics which are robust to heteroskedasticity, without requiring any prior knowledge as to the presence or type thereof. Simulations show that our procedures work very well in finite samples. We complement our theory with applications to financial, economic and epidemiological time series. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2104.13440&r= |
| By: | Pincheira, Pablo; Hardy, Nicolas |
| Abstract: | In this paper, we show that traditional comparisons of Mean Squared Prediction Error (MSPE) between two competing forecasts may be highly controversial. This is so because when some specific conditions of efficiency are not met, the forecast displaying the lowest MSPE will also display the lowest correlation with the target variable. Given that violations of efficiency are usual in the forecasting literature, this opposite behavior in terms of accuracy and correlation with the target variable may be a fairly common empirical finding that we label here as "the MSPE Paradox." We characterize "Paradox zones" in terms of differences in correlation with the target variable and conduct some simple simulations to show that these zones may be non-empty sets. Finally, we illustrate the relevance of the Paradox with two empirical applications. |
| Keywords: | Mean Squared Prediction Error, Correlation, Forecasting, Time Series, Random Walk. |
| JEL: | C1 C10 C12 C18 C2 C22 C4 C40 C5 C52 C53 C58 E0 E00 E30 E31 E37 E44 E47 E52 E58 F30 F31 F37 G00 G12 G15 G17 Q0 Q00 Q02 Q1 Q2 Q3 Q33 Q4 Q43 Q47 |
| Date: | 2021–04–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:107403&r= |
| By: | Miranda-Agrippino, Silvia (Bank of England, CfM and CEPR); Ricco, Giovanni (University of Warwick, OFCE-Sciences Po and CEPR) |
| Abstract: | We propose a Bayesian approach to Local Projections that optimally addresses the empirical bias-variance tradeo inherent in the choice between VARs and LPs. Bayesian Local Projections (BLP) regularise the LP regression models by using informative priors, thus estimating impulse response functions potentially better able to capture the properties of the data as compared to iterative VARs. In doing so, BLP preserve the exibility of LPs to empirical model misspeci cations while retaining a degree of estimation uncertainty comparable to a Bayesian VAR with standard macroeconomic priors. As a regularised direct forecast, this framework is also a valuable alternative to BVARs for multivariate out-of-sample projections. |
| Keywords: | Local Projections ; VARs JEL Classification: C11 ; C14 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:1348&r= |
| By: | David T. Frazier; Ruben Loaiza-Maya; Gael M. Martin; Bonsoo Koo |
| Abstract: | We propose a new method for Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach constructs a posterior predictive using a variational approximation to a loss-based, or Gibbs, posterior that is directly focused on predictive accuracy. The theoretical behavior of the new prediction approach is analyzed and a form of optimality demonstrated. Applications to both simulated and empirical data using high-dimensional Bayesian neural network and autoregressive mixture models demonstrate that the approach provides more accurate results than various alternatives, including misspecified likelihood-based predictions. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2104.14054&r= |
| By: | Ramis Khbaibullin (Bank of Russia, Russian Federation); Sergei Seleznev (Bank of Russia, Russian Federation) |
| Abstract: | We illustrate the ability of the stochastic gradient variational Bayes algorithm, which is a very popular machine learning tool, to work with macrodata and macromodels. Choosing two approximations (mean-field and normalizing flows), we test properties of algorithms for a set of models and show that these models can be estimated fast despite the presence of estimated hyperparameters. Finally, we discuss the difficulties and possible directions of further research. |
| Keywords: | Stochastic gradient variational Bayes, normalizing flows, mean-field approximation, sparse Bayesian learning, BVAR, Bayesian neural network, DFM. |
| JEL: | C11 C32 C32 C45 E17 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:bkr:wpaper:wps61&r= |
| By: | Alqaralleh, Huthaifa; Canepa, Alessandra; Chini, Zanetti (University of Turin) |
| Abstract: | In this study we examine the impact of the Covid-19 pandemic on stock market contagion. Empirical analysis is conducted on six major stock markets using a novel wavelet-copula-GARCH procedure to account for both the time and frequency domain of stock market correlation. We find evidence of contagion in the stock markets under consideration during the Covid-19 pandemic |
| Date: | 2021–03 |
| URL: | http://d.repec.org/n?u=RePEc:uto:dipeco:202110&r= |
| By: | Erniel B. Barrios; Paolo Victor T. Redondo |
| Abstract: | Contagion arising from clustering of multiple time series like those in the stock market indicators can further complicate the nature of volatility, rendering a parametric test (relying on asymptotic distribution) to suffer from issues on size and power. We propose a test on volatility based on the bootstrap method for multiple time series, intended to account for possible presence of contagion effect. While the test is fairly robust to distributional assumptions, it depends on the nature of volatility. The test is correctly sized even in cases where the time series are almost nonstationary. The test is also powerful specially when the time series are stationary in mean and that volatility are contained only in fewer clusters. We illustrate the method in global stock prices data. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2104.14412&r= |
| By: | Christina Anderl; Guglielmo Maria Caporale |
| Abstract: | This paper re-examines the UIP relation by estimating first a benchmark linear Cointegrated VAR including the nominal exchange rate and the interest rate differential as well as central bank announcements, and then a Cointegrated Smooth Transition VAR (CVSTAR) model incorporating nonlinearities and also taking into account the role of interest rate expectations. The analysis is conducted for five inflation targeting countries (the UK, Canada, Australia, New Zealand and Sweden) and three non-targeters (the US, the Euro-Area and Switzerland) using daily data from January 2000 to December 2020. We find that the nonlinear framework is more appropriate to capture the adjustment towards the UIP equilibrium, since the estimated speed of adjustment is substantially faster and the short-run dynamic linkages are stronger. Further, interest rate expectations play an important role: a fast adjustment only occurs when the market expects the interest rate to increase in the near future, namely central banks are perceived as more credible when sticking to their goal of keeping inflation at a low and stable rate. Also, central bank announcements have a more sizeable short-run effect in the nonlinear model. Finally, UIP holds better in inflation targeting countries, where monetary authorities appear to achieve a higher degree of credibility. |
| Keywords: | UIP, exchange rate, nonlinearities, asymmetric adjustment, CVAR (Cointegrated VAR), CVSTAR (Cointegrated Smooth Transition VAR), interest rate expectations, interest rate announcements |
| JEL: | C32 F31 G15 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9027&r= |