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on Econometric Time Series |
| By: | Diego Ardila (ETH Zurich); Didier Sornette (Swiss Finance Institute; ETH Zürich - Department of Management, Technology, and Economics (D-MTEC)) |
| Abstract: | We propose to date and analyze the financial cycle using the Maximum Overlap Discrete Wavelet Transform (MODWT). Our presentation points out limitations of the methods derived from the classical business cycle literature, while stressing their connection with wavelet analysis. The fundamental time-frequency uncertainty principle imposes replacing point estimates of turning points by interval estimates, which are themselves function of the scale of the analysis. We use financial time series from 19 OECD countries to illustrate the applicability of the tool. |
| Keywords: | Financial cycle, wavelet transform, multi-scale analysis, BBQ algorithm, turning points, interval estimates |
| JEL: | C40 E30 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp1629&r=ets |
| By: | Damien Ackerer (Ecole Polytechnique Fédérale de Lausanne; Ecole Polytechnique Fédérale de Lausanne - Swiss Finance Institute); Damir Filipović (Ecole Polytechnique Fédérale de Lausanne; Ecole Polytechnique Fédérale de Lausanne - Swiss Finance Institute); Sergio Pulido (Laboratoire de Mathématiques et Modélisation d'Évry (LaMME); Université d'Évry-Val-d'Essonne, ENSIIE, UMR CNRS 8071) |
| Abstract: | We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the the joint distribution of any finite sequence of log returns admits a Gram-Charlier A expansion in closed-form. We use this to derive closed-form series representations for option prices whose payoff is a function of the underlying asset price trajectory at finitely many time points. This includes European call, put, and digital options, forward start options, and forward start options on the underlying return. We derive sharp analytical and numerical bounds on the series truncation errors. We illustrate the performance by numerical examples, which show that our approach offers a viable alternative to Fourier transform techniques. |
| Keywords: | Jacobi process, option pricing, polynomial model, stochastic volatility |
| JEL: | C32 G12 G13 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp1635&r=ets |
| By: | Barnichon, Régis; Matthes, Christian |
| Abstract: | This paper proposes a new method to estimate the (possibly non-linear) dynamic effects of structural shocks by using Gaussian basis functions to parametrize impulse response functions. We apply our approach to the study of monetary policy and obtain two main results. First, regardless of whether we identify monetary shocks from (i) a timing restriction, (ii) sign restrictions, or (iii) a narrative approach, the effects of monetary policy are highly asymmetric: A contractionary shock has a strong adverse effect on unemployment, but an expansionary shock has little effect. Second, an expansionary shock may have some expansionary effect, but only when the labor market has some slack. In a tight labor market, an expansionary shock generates a burst of inflation and no significant change in unemployment. |
| Date: | 2016–07 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11374&r=ets |
| By: | Alonso, Andrés M.; Sánchez, Ismael; Ugaz, Willy |
| Abstract: | Memory charts like EWMA-S2 or CUSUM-S2 can be designed to be optimal to detect a specific shift in the process variance. However, this feature could be a serious inconvenience since, for instance, if the charts are designed to detect small shift, then, they can be inefficient to detect moderate or large shifts. In the literature, several alternatives have been proposed to overcome this limitation, like the use of control charts with variable parameters or adaptive control charts. This paper proposes new adaptive EWMA control charts for the dispersion (AEWMA-S2) based on a timevarying smoothing parameter that takes into account the potential misadjustment in the process variance. The obtained control charts can be interpreted as a combination of EWMA control charts designed to be efficient for different shift values. Markov chain procedures are established to analyse and design the proposed charts. Comparisons with other adaptive and traditional control charts show the advantages of the proposals. |
| Keywords: | Statistical Process Control; CUSUM; EWMA; Average Run Length; Adaptive control charts |
| Date: | 2016–07 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:23413&r=ets |
| By: | Ana Paula Martins |
| Abstract: | This paper focuses on two applications of time series methods. The first proposes a simple transformation of the unit root form of stationary testing to infer about the validity of smoothing by second-order running averages of a series, or of the variables in a linear model (here opposing co-integration testing). The second one advances a simple iterative algorithm to correct for MA(1) autocorrelation of the residuals of the general linear model, not requiring the estimation of the error process parameter. |
| Keywords: | Smoothing Tests under First Order Autoregressive Processes, Running Averages, Negative Unit Roots, Moving Average Autocorrelation Correction in Linear Models. |
| JEL: | C22 C12 C13 |
| Date: | 2016–01–12 |
| URL: | http://d.repec.org/n?u=RePEc:eei:rpaper:eeri_rp_2016_12&r=ets |
| By: | Jitendra Kuma; Anoop Chaturvedi; Umme Afifa |
| Abstract: | The present paper studies the panel data auto regressive (PAR) time series model for testing the unit root hypothesis. The posterior odds ratio (POR) is derived under appropriate prior assumptions and then empirical analysis is carried out for testing the unit root hypothesis of Net Asset Value of National Pension schemes (NPS) for different fund managers. The unit root hypothesis for the model with linear time trend and linear time trend with augmentation term is carried out. The estimated autoregressive coefficient is far away from one in case of linear time trend only so, testing is not executed but in consideration of augmentation term, it is close to one. Therefore, we performed the unit root hypothesis testing using the derived POR. In all cases unit root hypothesis is rejected therefore all NPS series are concluded trend stationary. |
| Keywords: | Panel data, Stationarity, Autoregressive time series, Unit root, Posterior odds ratio, New Pension Scheme, Net Asset Value. |
| JEL: | C11 C12 C22 C23 C39 |
| Date: | 2016–01–14 |
| URL: | http://d.repec.org/n?u=RePEc:eei:rpaper:eeri_rp_2016_14&r=ets |
| By: | Joshua C.C. Chan; Angelia L. Grant |
| Abstract: | This paper reconciles two widely used trend-cycle decompositions of GDP that give markedly different estimates: the correlated unobserved components model yields output gaps that are small in amplitude, whereas the Hodrick-Prescott (HP) filter generates large and persistent cycles. By embedding the HP filter in an unobserved components model, we show that this difference arises due to differences in the way the stochastic trend is modeled. Moreover, the HP filter implies that the cyclical components are serially independent—an assumption that is decidedly rejected by the data. By relaxing this restrictive assumption, the new model provides comparable model fit relative to the standard correlated unobserved components model. |
| Keywords: | trend-cycle decomposition, HP filter, structural break |
| JEL: | C11 C52 E32 |
| Date: | 2016–07 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2016-44&r=ets |
| By: | Chang, C-L.; McAleer, M.J.; Wang, Y. |
| Abstract: | There is substantial empirical evidence that energy and financial markets are closely connected. As one of the most widely-used energy resources worldwide, natural gas has a large daily trading volume. In order to hedge the risk of natural gas spot markets, a large number of hedging strategies can be used, especially with the rapid development of natural gas derivatives markets. These hedging instruments include natural gas futures and options, as well as Exchange Traded Fund (ETF) prices that are related to natural gas stock prices. The volatility spillover effect is the delayed effect of a returns shock in one physical, biological or financial asset on the subsequent volatility or co-volatility of another physical, biological or financial asset. Investigating volatility spillovers within and across energy and financial markets is a crucial aspect of constructing optimal dynamic hedging strategies. The paper tests and calculates spillover effects among natural gas spot, futures and ETF markets using the multivariate conditional volatility diagonal BEKK model. The data used include natural gas spot and futures returns data from two major international natural gas derivatives markets, namely NYMEX (USA) and ICE (UK), as well as ETF data of natural gas companies from the stock markets in the USA and UK. The empirical results show that there are significant spillover effects in natural gas spot, futures and ETF markets for both USA and UK. Such a result suggests that both natural gas futures and ETF products within and beyond the country might be considered when constructing optimal dynamic hedging strategies for natural gas spot prices. |
| Keywords: | Energy, natural gas, spot, futures, ETF, NYMEX, ICE, optimal hedging strategy, covolatility spillovers, diagonal BEKK |
| JEL: | C58 D53 G13 G31 O13 |
| Date: | 2016–06–03 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureir:93116&r=ets |
| By: | Søren Johansen (University of Copenhagen and CREATES); Morten Ørregaard Nielsen (Queen's University and CREATES) |
| Abstract: | In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive unified treatment of deterministic terms in the additive model X_{t}= gamma Z_{t}+Y_{t}, where Z_{t} belongs to a large class of deterministic regressors and Y_{t} is a zero-mean CVAR. We suggest an extended model that can be estimated by reduced rank regression and give a condition for when the additive and extended models are asymptotically equivalent, as well as an algorithm for deriving the additive model parameters from the extended model parameters. We derive asymptotic properties of the maximum likelihood estimators and discuss tests for rank and tests on the deterministic terms. In particular, we give conditions under which the estimators are asymptotically (mixed) Gaussian, such that associated tests are chi^2-distributed. |
| Keywords: | Additive formulation, cointegration, deterministic terms, extended model, likelihood inference, VAR model |
| JEL: | C32 |
| Date: | 2016–07 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1363&r=ets |
| By: | Gianluca Cubadda (DEF and CEIS, University of Rome "Tor Vergata"); Barbara Guardabascio (ISTAT); Alain Hecq (Maastricht University) |
| Abstract: | This paper introduces a new modelling for detecting the presence of commonalities in a set of realized volatility measures. In particular, we propose a multivariate generalization of the heterogeneous autoregressive model (HAR) that is endowed with a common index structure. The Vector Heterogeneous Autoregressive Index model has the property to generate a common index that preserves the same temporal cascade structure as in the HAR model, a feature that is not shared by other aggregation methods (e.g., principal components). The parameters of this model can be easily estimated by a proper switching algorithm that increases the Gaussian likelihood at each step. We illustrate our approach with an empirical analysis aiming at combining several realized volatility measures of the same equity index for three di?erent markets. |
| Keywords: | Common volatility, HAR models, index models, combinations of realized volatil¬ities, forecasting |
| JEL: | C32 |
| Date: | 2016–07–22 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:391&r=ets |
| By: | In Choi (Department of Economics, Sogang University, Seoul); Sun Ho Hwang (Department of Economics, Sogang University, Seoul) |
| Abstract: | This paper proposes a new, optimal estimator of the AR(1) coefficient that minimixes the prediction mean-squared-error. This estimator can be used to generate an optimal predictor. The new estimator¡®s asymptotic distributions are derived for the cases of stationarity and a near unit root. The optimal estimator is also derived for the AR(p) model ( p¡Ã2) and its asymptotic distributions are reported. Simulation results confirm advantages of using the optimal estimator for prediction. |
| Keywords: | Autoregressive model, prediction, near unit root |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:sgo:wpaper:1607&r=ets |
| By: | In Choi (School of Economics, Sogang University, Seoul) |
| Abstract: | This paper proposes new estimators for the panel autoregressive (PAR) mod- els with short time dimensions (T) and large cross sections (N). These estimators are based on the cross-sectional regression model using the ?rst time series obser- vations as a regressor and the last as a dependent variable. The regressors and errors of this regression model are correlated. The ?rst estimator is the maximum likelihood estimator (MLE) under the assumption of normal distributions. This estimator is called the cross-sectional MLE (CSMLE). The second estimator is the bias-corrected pooled least squares estimator (BCPLSE) that eliminates the asymptotic bias of PLSE by using the CSMLE. The CSMLE and BCPLSE are extended to the PAR model with endogenous time-variant and time-invariant regressors. The CSMLE and BCPLSE provide consistent estimates of the PAR coe¡Ë cients for stationary, unit root and explosive PAR models, estimate the co- e¡Ë cients of time-invariant regressors consistently and can be computed as long as T 2: Their ?nite sample properties are compared with those of some other estimators for the PAR model of order 1. The estimators of this paper are shown to perform quite well in ?nite samples. |
| Keywords: | dynamic panels, maximum likelihood estimator, pooled least squares estimator, stationarity, unit root, explosiveness |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:sgo:wpaper:1610&r=ets |