
on Econometric Time Series 
By:  Loann D. Desboulets (AixMarseille Univ., CNRS, EHESS, Centrale Marseille, AMSE) 
Abstract:  In this paper we investigate on Multivariate GARCH models to assess the comovements between stock prices of american firms listed on main markets and fundamentals. Comovements can be seen as correlations. The latter are usually estimated via standard GARCH models such as the Dynamic Conditional Correlation (Engle, 2002) or the BabaEngleKraftKroner (Baba et al., 1990). Nevertheless more flexible models such as the Orthogonal GARCH of Alexander (2001) can be used as well. We also introduce a new Semiparametric Orthogonal GARCH as a natural nonlinear extension of the Orthogonal GARCH. A Montecarlo simulation is conducted to evaluate finite sample performance of each model before applying them to the data. Empirical results show evidence that during crises, prices are less correlated with fundamentals that in normal periods. 
Keywords:  nonparametric, Multivariate GARCH, dynamic correlation, PCA 
Date:  2017–10 
URL:  http://d.repec.org/n?u=RePEc:aim:wpaimx:1851&r=ets 
By:  Donatien Hainaut (ESC Rennes School of Business); Franck Moraux (CREM  Centre de recherche en économie et management  UNICAEN  Université de Caen Normandie  NU  Normandie Université  UR1  Université de Rennes 1  UNIVRENNES  Université de Rennes  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  This study proposes a new Markov switching process with clustering eects. In this approach, a hidden Markov chain with a nite number of states modulates the parameters of a selfexcited jump process combined to a geometric Brownian motion. Each regime corresponds to a particular economic cycle determining the expected return, the diusion coecient and the longrun frequency of clustered jumps. We study rst the theoretical properties of this process and we propose a sequential MonteCarlo method to lter the hidden state variables. We next develop a Markov Chain MonteCarlo procedure to t the model to the S&P 500. Finally, we analyse the impact of such a jump clustering on implied volatilities of European options. 
Keywords:  switching regime,Hawkes process,selfexcited jumps 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01909772&r=ets 
By:  Prosper Dovonon; Frank Kleibergen (Sans nom); Alastair Hall 
Abstract:  We explore the local power properties of diﬀerent test statistics for conducting inference in moment condition models that only identify the parameters locally to second order. We consider the conventional Wald and LM statistics, and also the Generalized Anderson Rubin (GAR) statistic (Anderson and Rubin, 1949; Dufour, 1997; Staiger and Stock, 1997; Stock and Wright, 2000), KLM statistic (Kleibergen, 2002, 2005) and the GMM extension of Moreira’s (2003) (GMMM) conditional likelihood ratio statistic. The GAR, KLM and GMMM statistics are socalled “identiﬁcation robust” since their (conditional) limiting distribution is the same under ﬁrstorder, weak and therefore also second order identiﬁcation. For inference about the model speciﬁcation, we consider the identiﬁcationrobust J statistic (Kleibergen, 2005) and the GAR statistic. Interestingly, we ﬁnd that the limiting distribution of the Wald statistic under local alternatives not only depends on the distance to the null hypothesis but also on the convergence rate of the Jacobian. We speciﬁcally analyze two empirically relevant models with second order identiﬁcation. In the panel autoregressive model of order one, our analysis indicates that the Wald test of a unit root value of the autoregressive parameter has better power compared to the corresponding GAR test which, in turn, dominates the KLM, GMMM and LM tests. For the conditionally heteroskedastic factor model, we compare Kleibergen’s (2005) J and the GAR statistics to Hansen’s (1982) overidentifying restrictions test (previously analyzed in this context by Dovonon and Renault, 2013) and ﬁnd the power ranking depends on the sample size. Collectively, our results suggest that tests with meaningful power can be conducted in secondorder identiﬁed models. 
Keywords:  Generalized Method of Moments estimation,Firstorder identiﬁcation failure,Identiﬁcationrobust inference, 
Date:  2018–12–17 
URL:  http://d.repec.org/n?u=RePEc:cir:cirwor:2018s36&r=ets 
By:  Peter C.B. Phillips (Cowles Foundation, Yale University); Yonghui Zhang (Renmin University of China); Xiaohu Wang (The Chinese University of Hong Kong) 
Abstract:  The usual t test, the t test based on heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators, and the heteroskedasticity and autocorrelation robust (HAR) test are three statistics that are widely used in applied econometric work. The use of these significance tests in trend regression is of particular interest given the potential for spurious relationships in trend formulations. Following a longstanding tradition in the spurious regression literature, this paper investigates the asymptotic and finite sample properties of these test statistics in several spurious regression contexts, including regression of stochastic trends on time polynomials and regressions among independent random walks. Concordant with existing theory (Phillips, 1986, 1998; Sun, 2004, 2014), the usual t test and HAC standardized test fail to control size as the sample size n \to \infty in these spurious formulations, whereas HAR tests converge to welldefined limit distributions in each case and therefore have the capacity to be consistent and control size. However, it is shown that when the number of trend regressors K \to \infty, all three statistics, including the HAR test, diverge and fail to control size as n \to \infty. These findings are relevant to high dimensional nonstationary time series regressions. 
Keywords:  HAR inference, KarhunenLoève representation, Spurious regression, tstatistics 
JEL:  C12 C14 C23 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2153&r=ets 
By:  Lajos Horvath; Lorenzo Trapani 
Abstract:  We propose a test to discern between an ordinary autoregressive model, and a random coefficient one. To this end, we develop a full edged estimation theory for the variances of the idiosyncratic innovation and of the random coefficient, based on a twostage WLS approach. Our results hold irrespective of whether the series is stationary or nonstationary, and, as an immediate result, they afford the construction of a test for "relevant" randomness. Further, building on these results, we develop a randomised test statistic for the null that the coefficient is nonrandom, as opposed to the alternative of a standard RCA(1) model. Monte Carlo evidence shows that the test has the correct size and very good power for all cases considered. MSC 2010 subject classifications: Primary 62G10, 62H25; secondary 62M10. 
Keywords:  Random Coefficient AutoRegression, WLS estimator, randomised test. 
URL:  http://d.repec.org/n?u=RePEc:not:notgts:18/03&r=ets 
By:  GilAlana, Luis A.; Yaya, OlaOluwa S 
Abstract:  In this paper we present a testing procedure for fractional orders of integration in the context of nonlinear terms approximated by Fourier functions. The procedure is a natural extension of the linear method proposed in Robinson (1994) and similar to the one proposed in Cuestas and GilAlana (2016) based on Chebyshev polynomials in time. The test statistic has an asymptotic standard normal distribution and several Monte Carlo experiments conducted in the paper show that it performs well in finite samples. Various applications using real life time series, such as US unemployment rates, US GNP and Purchasing Power Parity (PPP) of G7 countries are presented at the end of the paper. 
Keywords:  Fractional unit root; Chebyshev polynomial; Monte Carlo simulation; Nonlinearity; Smooth break; Fourier transform 
JEL:  C12 C15 C22 
Date:  2018–11–16 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:90516&r=ets 
By:  Chaohua Dong; Jiti Gao; Oliver Linton 
Abstract:  We consider nonlinear moment restriction semiparametric models where both the dimension of the parameter vector and the number of restrictions are divergent with sample size and an unknown smooth function is involved. We propose an estimation method based on the sieve generalized method of moments (sieveGMM). We establish consistency and asymptotic normality for the estimated quantities when the number of parameters increases modestly with sample size. We also consider the case where the number of potential parameters/covariates is very large, i.e., increases rapidly with sample size, but the true model exhibits sparsity. We use a penalized sieve GMM approach to select the relevant variables, and establish the oracle property of our method in this case. We also provide new results for inference. We propose several new test statistics for the overidentification and establish their large sample properties. We provide a simulation study and an application to data from the NLSY79 used by Carneiro et al. [14]. 
Keywords:  generalized method of moments, high dimensional models, moment restriction, overidentification, penalization, sieve method, sparsity. 
JEL:  C12 C14 C22 C30 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:msh:ebswps:201823&r=ets 
By:  Henry Stone 
Abstract:  In this paper we use convolutional neural networks to find the H\"older exponent of simulated sample paths of the rBergomi model, a recently proposed stock price model used in mathematical finance. We contextualise this as a calibration problem, thereby providing a very practical and useful application. 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1812.05315&r=ets 
By:  Jitendra Kumar; Varun Agiwal 
Abstract:  Present paper proposes an autoregressive time series model to study the behaviour of merger and acquire concept which is equally important as other available theories like structural break, de trending etc. The main motivation behind newly proposed merged autoregressive (MAR) model is to study the impact of merger in the parameters as well as acquired series. First, we recommend the estimation setup using popular classical least square and posterior distribution under Bayesian method with different loss function. Then, we obtain Bayes factor, full Bayesian significance test and credible interval to know the significance of the merger series. A simulation as well as empirical study is illustrated. 
Keywords:  Autoregressive model, Break point, Merger series, Bayesian inference. 
JEL:  C32 G34 C11 
Date:  2018–12–16 
URL:  http://d.repec.org/n?u=RePEc:eei:rpaper:eeri_rp_2018_16&r=ets 
By:  Lorenzo Trapani 
Abstract:  We propose a procedure to decide between the null hypothesis of (strict) stationarity and the alternative of nonstationarity, in the context of a Random Coefficient AutoRegression (RCAR). The procedure is based on randomising a diagnostic which diverges to positive infinity under the null, and drifts to zero under the alternative. Thence, we propose a randomised test which can be used directly and  building on it  a decision rule to discern between the null and the alternative. The procedure can be applied under very general circumstances: albeit developed for an RCAR model, it can be used in the case of a standard AR(1) model, without requiring any modifications or prior knowledge. Also, the test works (again with no modification or prior knowledge being required) in the presence of infinite variance, and in general requires minimal assumptions on the existence of moments. 
Keywords:  Random Coefficient AutoRegression, Stationarity, Unit Root, Heavy Tails, Randomised Tests. 
URL:  http://d.repec.org/n?u=RePEc:not:notgts:18/02&r=ets 
By:  Carlo Fezzi; Luca Mosetti 
Abstract:  Electricity price forecasting models are typically estimated via rolling windows, i.e. by using only the most recent observations. Nonetheless, the current literature does not provide much guidance on how to select the size of such windows. This paper shows that determining the appropriate window prior to estimation dramatically improves forecasting performances. In addition, it proposes a simple twostep approach to choose the best performing models and window sizes. The value of this methodology is illustrated by analyzing hourly datasets from two large power markets with a selection of ten different forecasting models. Incidentally, our empirical application reveals that simple models, such as the linear regression, can perform surprisingly well if estimated on extremely short samples. 
Keywords:  electricity price forecasting, dayahead market, parameter instability, bandwidth selection, artificial neural networks 
JEL:  C22 C45 C51 C53 Q47 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:trn:utwprg:2018/10&r=ets 
By:  Tan, Fei 
Abstract:  This article is concerned with frequencydomain analysis of dynamic linear models under the hypothesis of rational expectations. We develop a unified framework for conveniently solving and estimating these models. Unlike existing strategies, our starting point is to obtain the model solution entirely in the frequency domain. This solution method is applicable to a wide class of models and permits straightforward construction of the spectral density for performing likelihoodbased inference. To cope with potential model uncertainty, we also generalize the wellknown spectral decomposition of the Gaussian likelihood function to a composite version implied by several competing models. Taken together, these techniques yield fresh insights into the model’s theoretical and empirical implications beyond what conventional timedomain approaches can offer. We illustrate the proposed framework using a prototypical new Keynesian model with fiscal details and two distinct monetaryfiscal policy regimes. The model is simple enough to deliver an analytical solution that makes the policy effects transparent under each regime, yet still able to shed light on the empirical interactions between U.S. monetary and fiscal policies along different frequencies. 
Keywords:  solution method, analytic function, Bayesian inference, spectral density, monetary and fiscal policy 
JEL:  C32 C51 C52 C65 E63 H63 
Date:  2018–10–20 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:90487&r=ets 
By:  Luigi Grossi (University of Verona); Fany Nan (European Commission's Joint Research Centre (JRC)) 
Abstract:  In this paper a robust approach to modelling electricity spot prices is introduced. Differently from what has been recently done in the literature on electricity price forecasting, where the attention has been mainly drawn by the prediction of spikes, the focus of this contribution is on the robust estimation of nonlinear SETARX models (SelfExciting Threshold Auto Regressive models with eXogenous regressors). In this way, parameters estimates are not, or very lightly, influenced by the presence of extreme observations and the large majority of prices, which are not spikes, could be better forecasted. A Monte Carlo study is carried out in order to select the best weighting function for Generalized Mestimators of SETAR processes. A robust procedure to select and estimate nonlinear processes for electricity prices is introduced, including robust tests for stationarity and nonlinearity and robust information criteria. The application of the procedure to the Italian electricity market reveals the forecasting superiority of the robust GMestimator based on the polynomial weighting function respect to the nonrobust Least Squares estimator. Finally, the introduction of external regressors in the robust estimation of SETARX processes contributes to the improvement of the forecasting ability of the model. 
Keywords:  Electricity Price, Nonlinear Time Series, Price Forecasting, Robust GMEstimator, Spikes, Threshold Models 
JEL:  C13 C15 C22 C53 Q47 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:ieb:wpaper:doc201810&r=ets 
By:  Pablo MonteroManso; George Athanasopoulos; Rob J Hyndman; Thiyanga S Talagala 
Abstract:  We propose an automated method for obtaining weighted forecast combinations using time series features. The proposed approach involves two phases. First, we use a collection of time series to train a metamodel to assign weights to various possible forecasting methods with the goal of minimizing the average forecasting loss obtained from a weighted forecast combination. The inputs to the metamodel are features extracted from each series. In the second phase, we forecast new series using a weighted forecast combination where the weights are obtained from our previously trained metamodel. Our method outperforms a simple forecast combination, and outperforms all of the most popular individual methods in the time series forecasting literature. The approach achieved second position in the M4 competition. 
Keywords:  time series feature, forecast combination, XGBoost, M4 competition, metalearning. 
JEL:  C10 C14 C22 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:msh:ebswps:201819&r=ets 
By:  Mario Forni; Luca Gambetti; Luca Sala 
Abstract:  The testing procedure suggested in Canova and Sahneh (2018) is essentially the same as the one proposed in Forni and Gambetti (2014), the only one difference being the use of Geweke, Meese and Dent (1983) version of Sims (1972) test in place of a standard Granger causality test. The two procedures produce similar results, both for small and large samples, and perform remarkably well in detecting nonfundamentalness. Neither methods have anything to do with the problem of aggregation. A “structural aggregate model” does not exist. 
Keywords:  Nonfundamentalness, Granger causality, aggregation, structural VAR 
JEL:  C32 E32 
Date:  2018–11 
URL:  http://d.repec.org/n?u=RePEc:mod:recent:139&r=ets 
By:  David Harvey; Stephen Leybourne; Yang Zu 
Abstract:  This paper considers the problem of testing for an explosive bubble in financial data in the presence of timevarying volatility. We propose a weighted least squaresbased variant of the Phillips, Wu and Yu (2011) test for explosive autoregressive behaviour. We find that such an approach has appealing asymptotic power properties, with the potential to deliver substantially greater power than the established OLSbased approach for many volatility and bubble settings. Given that the OLSbased test can outperform the weighted least squaresbased test for other volatility and bubble specifications, we also suggested a union of rejections procedure that succeeds in capturing the better power available from the two constituent tests for a given alternative. Our approach involves a nonparametric kernelbased volatility function estimator for computation of the weighted least squaresbased statistic, together with the use of a wild bootstrap procedure applied jointly to both individual tests, delivering a opowerful testing procedure that is asymptotically sizerobust to a wide range of timevarying volatility specifications. 
Keywords:  Rational bubble; Explosive autoregression; Timevarying volatility; Weighted least squares; Righttailed unit root testing. 
URL:  http://d.repec.org/n?u=RePEc:not:notgts:18/05&r=ets 
By:  Matteo Barigozzi; Lorenzo Trapani 
Abstract:  We develop an online monitoring procedure to detect a change in a large approximate factor model. Our statistics are based on a wellknown property of the (r + 1)th eigenvalue of the sample covariance matrix of the data (having defined r as the number of common factors): whilst under the null the (r + 1)th eigenvalue is bounded, under the alternative of a change (either in the loadings, or in the number of factors itself) it becomes spiked. Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statistic in conjunction with sample conditioning, obtaining a sequence of i.i.d., asymptotically chisquare statistics which are then employed to build the monitoring scheme. Numerical evidence shows that our procedure works very well in finite samples, with a very small probability of false detections and tight detection times in presence of a genuine changepoint. 
Keywords:  large factor model, changepoint, sequential testing, randomised tests. 
URL:  http://d.repec.org/n?u=RePEc:not:notgts:18/04&r=ets 
By:  Yaya, OlaOluwa S; GilAlana, Luis A. 
Abstract:  This paper examines the behaviour of high and low prices of four commodities, namely crude oil, natural gas, gold and silver, and of the corresponding ranges using both daily and intraday data at various frequencies. For this purpose, it applies fractional integration and cointegration techniques; in particular, an FCVAR model is estimated to capture both the longrun equilibrium relationships between high and low commodity prices, referred to as the range, and the longmemory properties of their linear combination. Fractional cointegration in found in all cases, with the range showing stationary and nonstationary patterns and changing substantially across the frequencies. The findings may assist investors in improving their trading strategies since high and low prices serve as entry and exit signals in the market. 
Keywords:  Commodity prices, intraday, fractional integration, fractional cointegration, FCVAR 
JEL:  C22 C32 G11 G15 
Date:  2018–12–05 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:90518&r=ets 