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on Econometric Time Series |
| By: | Archil Gulisashvili |
| Abstract: | In this paper, we provide a unified approach to various scaling regimes associated with Gaussian stochastic volatility models. The evolution of volatility in such a model is described by a stochastic process that is a nonnegative continuous function of a continuous Gaussian process. If the process in the previous description exhibits fractional features, then the model is called a Gaussian fractional stochastic volatility model. Important examples of fractional volatility processes are fractional Brownian motion, the Riemann-Liouville fractional Brownian motion, and the fractional Ornstein-Uhlenbeck process. If the volatility process admits a Volterra type representation, then the model is called a Volterra type Gaussian stochastic volatility model. The scaling regimes associated with a Gaussian stochastic volatility model are split into three groups: the large deviation group, the moderate deviation group, and the central limit group. We prove a sample path large deviation principle for the log-price process in a Volterra type Gaussian stochastic volatility model, and a sample path moderate deviation principle for the same process in a Gaussian stochastic volatility model. We also study the asymptotic behavior of the distribution function of the log-price, call pricing functions, and the implied volatility in mixed scaling regimes. It is shown that the asymptotic formulas for the above-mentioned quantities exhibit discontinuities on the boundaries, where the moderate deviation regime becomes the large deviation or the central limit regime. It is also shown that the large deviation tail estimates are locally uniform. |
| Date: | 2018–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1808.00421&r=ets |
| By: | Matei Demetrescu; Antonio Rubia; Paulo M.M. Rodrigues |
| Abstract: | A new class of tests for fractional integration in the time domain based on M estimation is developed. This approach offers more robust properties against non-Gaussian errors than least squares or other estimation principles. The asymptotic properties of the tests are discussed under fairly general assumptions, and for different estimation approaches based on direct optimization of the M loss-function and on iterated k-step and reweighted LS numeric algorithms. Monte Carlo simulations illustrate the good finite sample performance of the new tests and an application to daily volatility of several stock market indices shows the empirical relevance of the new tests. |
| JEL: | C12 C22 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w201817&r=ets |
| By: | Roberto Casarin (Department of Economics, University of Venice Cà Foscari); Fausto Corradin (Department of Economics, University of Venice Cà Foscari); Francesco Ravazzolo (Free University of Bozen-Bolzano); Domenico Sartore (Department of Economics, University of Venice Cà Foscari) |
| Abstract: | Factor models (FM) are now widely used for forecasting with large set of time series. Another class of models, which can be easily estimated and used in a large dimensional setting, is multivariate autoregressive models (MAR), where independent autoregressive processes are assumed for the series in the panel. We compare the forecasting abilities of FM and MAR models when assuming both models are misspecified and the data generating process is a vector autoregressive model. We establish which conditions need to be satisfied for a FM to overperform MAR in terms of mean square forecasting error. The condition indicates in presence of misspecification that FM is not always overperforming MAR and that the FM predictive performance depends crucially on the parameter values of the data generating process. Building on the theoretical relationship between FM and MAR predictive performances, we provide a scoring rule which can be evaluated on the data to either select the model, or combine the models in forecasting exercises. Some numerical illustrations are provided both on simulated data and on wel-known large economic datasets. The empirical results show that the frequency of the true positive signals is larger when FM and MAR forecasting performances differ substantially and it decreases as the horizon increases. |
| Keywords: | Factor models, Large datasets, Multivariate autoregressive models, Forecasting, Scoring rules, VAR models. |
| JEL: | C32 C52 C53 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2018:18&r=ets |
| By: | Stanislav Anatolyev; Anna Mikusheva |
| Abstract: | This paper establishes some asymptotic results such as central limit theorems and consistency of variance estimation in factor models. We consider a setting common to modern macroeconomic and financial models where many counties/regions/macro-variables/assets are observed for many time periods, and when estimation of a global parameter includes aggregation of a cross-section of heterogeneous micro-parameters estimated separately for each entity. We establish a central limit theorem for quantities involving both cross-sectional and time series aggregation, as well as for quadratic forms in time-aggregated errors. We also study sufficient conditions when one can consistently estimate the asymptotic variance. These results are useful for making inferences in two-step estimation procedures related to factor models. We avoid structural modeling of cross-sectional dependence but impose time-series independence. |
| Date: | 2018–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1807.06338&r=ets |
| By: | Junpei Komiyama; Hajime Shimao |
| Abstract: | Structural estimation is an important methodology in empirical economics, and a large class of structural models are estimated through the generalized method of moments (GMM). Traditionally, selection of structural models has been performed based on model fit upon estimation, which take the entire observed samples. In this paper, we propose a model selection procedure based on cross-validation (CV), which utilizes sample-splitting technique to avoid issues such as over-fitting. While CV is widely used in machine learning communities, we are the first to prove its consistency in model selection in GMM framework. Its empirical property is compared to existing methods by simulations of IV regressions and oligopoly market model. In addition, we propose the way to apply our method to Mathematical Programming of Equilibrium Constraint (MPEC) approach. Finally, we perform our method to online-retail sales data to compare dynamic market model to static model. |
| Date: | 2018–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1807.06993&r=ets |
| By: | Sílvia GONÇALVES; Benoit PERRON |
| Abstract: | We consider bootstrap methods for factor-augmented regressions with cross sectional dependence among idiosyncratic errors. This is important to capture the bias of the OLS estimator derived recently by Gonçalves and Perron (2014). We first show that a common approach of resampling cross sectional vectors over time is invalid in this context because it induces a zero bias. We then propose the cross-sectional dependent (CSD) bootstrap where bootstrap samples are obtained by taking a random vector and multiplying it by the square root of a consistent estimator of the covariance matrix of the idiosyncratic errors. We show that if the covariance matrix estimator is consistent in the spectral norm, then the CSD bootstrap is consistent, and we verify this condition for the thresholding estimator of Bickel and Levina (2008). Finally, we apply our new bootstrap procedure to forecasting inflation using convenience yields as recently explored by Gospodinov and Ng (2013). |
| Keywords: | factor model, bootstrap, asymptotic bias |
| JEL: | C21 C22 C23 C53 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montec:10-2018&r=ets |
| By: | Nikolay Iskrev |
| Abstract: | We propose two measures of the impact of calibration on the estimation of macroeconomic models. The first quantifies the amount of information introduced with respect to each estimated parameter as a result of fixing the value of one or more calibrated parameters. The second is a measure of the sensitivity of parameter estimates to perturbations in the calibration values. The purpose of the measures is to show researchers how much and in what way calibration affects their estimation results -- by shifting the location and reducing the spread of the marginal posterior distributions of the estimated parameters. This type of analysis is often appropriate since macroeconomists do not always agree on whether and how to calibrate structural parameters in macroeconomic models. The methodology is illustrated using the models estimated in Smets and Wouters (2007) and Schmitt-Grohé and Uribe (2012). |
| JEL: | C32 C51 C52 E32 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w201801&r=ets |
| By: | Lennart (L.F.) Hoogerheide (VU University Amsterdam); Herman (H.K.) van Dijk (Erasmus University, Norges Bank) |
| Abstract: | We suggest to extend the stacking procedure for a combination of predictive densities, proposed by Yao et al in the journal Bayesian Analysis to a setting where dynamic learning occurs about features of predictive densities of possibly misspecified models. This improves the averaging process of good and bad model forecasts. We summarise how this learning is done in economics and finance using mixtures. We also show that our proposal can be extended to combining forecasts and policies. The technical tools necessary for the implementation refer to filtering methods from nonlinear time series and we show their connection with machine learning. We illustrate our suggestion using results from Basturk et al based on financial data about US portfolios from 1928 until 2015. |
| Keywords: | Bayesian learning; predictive density combinations |
| JEL: | C11 C15 |
| Date: | 2018–08–08 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20180063&r=ets |
| By: | Abdolrahman Khoshrou; Eric J. Pauwels |
| Abstract: | In Europe, Germany is taking the lead in the switch from the conventional to renewable energy. This poses new challenges as wind and solar energy are fundamentally intermittent, weather-dependent and less predictable. It is therefore of considerable interest to investigate the evolution of price volatility in this post-transition era. There are a number of reasons, however, that makes the practical studies difficult. For instance, EPEX prices can be zero or negative. Consequently, the standard approach in financial time series analysis to switch to logarithmic measures is inapplicable. Furthermore, in contrast to the stock market prices which are only available for trading days, EPEX prices cover the whole year, including weekends and holidays. Accordingly, there is a lot of underlying variability in the data which has nothing to do with volatility, but simply reflects diurnal activity patterns. An important distinction of the present work is the application of matrix decomposition techniques, namely the singular value decomposition (SVD), for defining an alternative notion of volatility. This approach is systematically more robust toward outliers and also the diurnal patterns. Our observations show that the day-ahead market is becoming less volatile in recent years. |
| Date: | 2018–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1807.07328&r=ets |
| By: | Castro Rozo, César; Jiménez-Rodríguez, Rebeca |
| Abstract: | This paper contributes to better understand the dynamic interaction between U.S. effective exchange rate (EER) and oil price by considering a Time-Varying Parameter VAR model with the use of monthly data from 1974 to 2017. Our findings show a depreciation after an oil price shock in the short-run for any period of time, although the pattern of long-run responses of U.S. EER is diverse across different period of time, with an appreciation being observed before the mid-2000s and a depreciation afterwards. This diversity of response should lead policy makers to react differently in order to counteract such shocks. Furthermore, the reaction of oil price to an appreciation of U.S. EER is negative, with the response being similar in the short-run but different in the long-run for each period of time. Thus, the different responses may generate different adverse effects on investment and the knowledge of such effects may help financial investors to diversify their investments in order to optimize the risk-return profile of their portfolios. |
| Keywords: | Oil price, Exchange rate, TVP-VAR model |
| JEL: | F31 F32 Q31 Q37 |
| Date: | 2018–03–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:87879&r=ets |
| By: | Thomas Walther; Lanouar Charfeddine; Tony Klein; |
| Abstract: | This paper contributes to the large debate regarding the impact of oil price changes on U.S. GDP growth. Firstly, it replicates empirical findings of prominent studies and finds that the proposed oil price measures have a dissipating effect with recent data up to 2016Q4. Secondly, it re-examines the issue and provides evidence that oil price decreases affect the GDP growth, when taking into consideration mixed data sampling technique. Finally, it puts particular focus on nonlinearity and a possible instability and shows that combining Markov switching and mixed data sampling models allows to identify different regimes permanently changing with the Great Moderation. |
| Keywords: | Oil prices, GDP growth, Asymmetry, Nonlinearity, Markov switching models, Mixed Data Sampling |
| JEL: | C24 E32 F43 Q43 |
| Date: | 2018–05 |
| URL: | http://d.repec.org/n?u=RePEc:usg:sfwpfi:2018:16&r=ets |
| By: | Guilherme Demos (ETH Zurich); Didier Sornette (ETH Zürich and Swiss Finance Institute) |
| Abstract: | Inspired by the question of identifying the start time τ of financial bubbles, we address the calibration of time series in which the inception of the latest regime of interest is unknown. By taking into account the tendency of a given model to overfit data, we introduce the Lagrange regularisation of the normalised sum of the squared residuals, χ2np(Φ), to endogenously detect the optimal fitting window size := w∗ ∈ [τ : t̄2] that should be used for calibration purposes for a fixed pseudo present time t̄2. The performance of the Lagrange regularisation of χnp(Φ) defined as χ2λ(Φ) is exemplified on a simple Linear Regression problem with a change point and compared against the Residual Sum of Squares (RSS) := χ2 (Φ) and RSS/(N-p):= χ2np (Φ), where N is the sample size and p is the number of degrees of freedom. Applied to synthetic models of financial bubbles with a well-defined transition regime and to a number of financial time series (US S&P500, Brazil IBovespa and China SSEC Indices), the Lagrange regularisation of χ2λ(Φ) is found to provide well-defined reasonable determinations of the starting times for major bubbles such as the bubbles ending with the 1987 Black-Monday, the 2008 Sub-prime crisis and minor speculative bubbles on other Indexes, without any further exogenous information. It thus allows one to endogenise the determination of the beginning time of bubbles, a problem that had not received previously a systematic objective solution. |
| Keywords: | Financial Bubbles, Time Series Analysis, Numerical Simulation, Sub-Sample Selection, Overfitting, Goodness-of-Fit, Cost Function, Optimization |
| JEL: | C32 C53 G01 G1 |
| Date: | 2017–07 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp1820&r=ets |
| By: | Andrea Cipollini; Fabio Parla |
| Abstract: | In this paper, we use a Global Vector Autoregression (GVAR) model to assess the spatio-temporal mechanism of house price spillovers, also known as “ripple effect”, among 93 Italian provincial housing markets, over the period 2004 - 2016. In order to better capture the local housing market dynamics, we use data not only on house prices but also on transaction volumes. In particular, we focus on estimating, to what extent, exogenous shocks, interpreted as negative housing demand shocks, arising from 10 Italian regional capitals, impact on their house prices and sales and how these shocks spill over to neighbours housing markets. The negative housing market demand shock hitting the GVAR model is identified by using theory-driven sign restrictions. The spatio-temporal analysis carried through impulse response functions shows that there is evidence of a “ripple effect” mainly occurring through transaction volumes. |
| Keywords: | Ripple effect; housing market prices and volumes; Global VAR; sign restrictions |
| JEL: | C32 C33 R21 R50 |
| Date: | 2018–04 |
| URL: | http://d.repec.org/n?u=RePEc:mod:wcefin:0069&r=ets |
| By: | João Cruz; João Nicolau; Paulo M.M. Rodrigues |
| Abstract: | This paper tests for structural changes in the duration of bull regimes of adjusted market capitalization stock indexes comprehending 18 developed and emerging economies, using a novel approach introduced by Nicolau (2016); and investigates whether the structural changes detected in the bull markets' duration are connected to the business cycle. Interestingly, the results show that structural changes in the duration of bull market regimes seem to anticipate periods of economic recession. The results provide statistically significant evidence that decreases in bull markets duration do not occur independently from economic crises, as 13 out of the 18 markets considered in our sample verify such decreases at least 12 months prior to the occurrence of an economic crisis. Additionally, these structural changes seem to affect smaller companies first, and then the larger ones. The association between decreases in the bull market regimes' duration and economic crises is possibly a consequence of the financial markets' leading behavior over the economy, with these structural changes serving as proxies for decreasing confidence in the financial markets, which naturally affects economic stability. |
| JEL: | C12 C22 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w201814&r=ets |