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on Econometric Time Series |
| By: | Giovanni Barone-Adesi (University of Lugano and Swiss Finance Institute); Robert F. Engle (New York University, Leonard Stern School of Business); Loriano Mancini (University of Zurich and Swiss Banking Institute) |
| Abstract: | We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework we allow for different distributions of the historical and the pricing return dynamics enhancing the model flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. Using our GARCH model and a nonparametric approach we obtain decreasing state price densities per unit probability as suggested by economic theory, validating our GARCH pricing model. Implied volatility smiles appear to be explained by the negative asymmetry of the filtered historical innovations. A new simplified delta hedging scheme is presented based on conditions usually found in option markets, namely the local homogeneity of the pricing function. We provide empirical evidence and we quantify the deterioration of the delta hedging in the presence of large volatility shocks. |
| Date: | 2004–10 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp03&r=ets |
| By: | Alastair Hall; Atsushi Inoue; James M. Nason; Barbara Rossi |
| Abstract: | We propose a new information criterion for impulse response function matching estimators of the structural parameters of macroeconomic models. The main advantage of our procedure is that it allows the researcher to select the impulse responses that are most informative about the deep parameters, therefore reducing the bias and improving the efficiency of the estimates of the model’s parameters. We show that our method substantially changes key parameter estimates of representative dynamic stochastic general equilibrium models, thus reconciling their empirical results with the existing literature. Our criterion is general enough to apply to impulse responses estimated by vector autoregressions, local projections, and simulation methods. |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedawp:2007-10&r=ets |
| By: | Giampiero Gallo (Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti"); Margherita Velucchi (Università degli Studi di Firenze, Dipartimento di Statistica) |
| Abstract: | We analyze several measures of volatility (realized variance, bipower variation and squared daily returns) as estimators of integrated variance of a continuous time stochastic process for an asset price. We use a Multiplicative Error Model to describe the evolution of each measure as the product of its conditional expectation and a positive valued iid innovation. By inserting past values of each measure and asymmetric effects based on the sign of the return in the specification of the conditional expectation, one can investigate the information content of each indicator relative to the others. The results show that there is a directed dynamic relationship among measures, with squared returns and bipower variance interdependent with one another, and affecting realized variance without any feed-back from the latter. |
| Keywords: | Volatility, Multiplicative Error Models, Realized Variance, Bi-power Variance, Squared Returns, Jumps. |
| JEL: | C22 C51 C53 |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:fir:econom:wp2007_01&r=ets |
| By: | Christian T. Brownlees (Università degli Studi di Firenze, Dipartimento di Statistica); Giampiero Gallo (Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti") |
| Abstract: | Nonlinear time series models can exhibit components such as long range trends and seasonalities that may be modeled in a flexible fashion. The resulting unconstrained maximum likelihood estimator can be too heavily parameterized and suboptimal for forecasting purposes. The paper proposes the use of a class of shrinkage estimators that includes the Ridge estimator for forecasting time series, with a special attention to GARCH and ACD models. The local large sample properties of this class of shrinkage estimators is investigated. Moreover, we propose symmetric and asymmetric focused selection criteria of shrinkage estimators. The focused information criterion selection strategy consists of picking up the shrinkage estimator that minimizes the estimated risk (e.g. MSE) of a given smooth function of the parameters of interest to the forecaster. The usefulness of such shrinkage techniques is illustrated by means of a simulation exercise and an intra-daily financial durations forecasting application. The empirical application shows that an appropriate shrinkage forecasting methodology can significantly outperform the unconstrained ML forecasts of rich flexible specifications. |
| Keywords: | Forecasting, Shrinkage Estimation, FIC, MEM, GARCH, ACD |
| JEL: | C22 C51 C53 |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:fir:econom:wp2007_02&r=ets |
| By: | Teräsvirta, Timo (Dept. of Economic Statistics, Stockholm School of Economics); Zhao, Zhenfang (Dept. of Economic Statistics, Stockholm School of Economics) |
| Abstract: | Financial return series of sufficiently high frequency display stylized facts such as volatility clustering, high kurtosis, low starting and slow-decaying autocorrelation function of squared returns and the so-called Taylor effect. In order to evaluate the capacity of volatility models to reproduce these facts, we apply both standard and robust measures of kurtosis and autocorrelation of squares to first-order GARCH, EGARCH and ARSV models. Robust measures provide a fresh view of stylized facts which is useful because many financial time series can be viewed as being contaminated with outliers. |
| Keywords: | GARCH; EGARCH; ARSV; extreme observations; autocorrelation function; kurtosis; robust measure; confidence region. |
| JEL: | C22 C52 |
| Date: | 2007–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hastef:0662&r=ets |
| By: | Robert M. de Jong; Tiemen Woutersen |
| Abstract: | This paper considers dynamic time series binary choice models. It proves near epoch dependence and strong mixing for the dynamic binary choice model with correlated errors. Using this result, it shows in a time series setting the validity of the dynamic probit likelihood procedure when lags of the dependent binary variable are used as regressors, and it establishes the asymptotic validity of Horowitz’ smoothed maximum score estimation of dynamic binary choice models with lags of the dependent variable as regressors. For the semiparametric model, the latent error is explicitly allowed to be correlated. It turns out that no long-run variance estimator is needed for the validity of the smoothed maximum score procedure in the dynamic time series framework. |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:jhu:papers:538&r=ets |
| By: | Badi H. Baltagi (Center for Policy Research, Maxwell School, Syracuse University, Syracuse, NY 13244-1020); Georges Bresson; Alain Pirotte |
| Abstract: | This paper studies the performance of panel unit root tests when spatial effects are present that account for cross-section correlation. Monte Carlo simulations show that there can be considerable size distortions in panel unit root tests when the true specification exhibits spatial error correlation. These tests are applied to a panel data set on net real income from the 1000 largest French communes observed over the period 1985-1998. |
| Keywords: | Nonstationarity, panel data, spatial dependence, cross-section correlation, unit root tests |
| JEL: | C23 |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:max:cprwps:88&r=ets |
| By: | Gael M. Martin; Andrew Reidy; Jill Wright |
| Abstract: | This paper presents a comprehensive empirical evaluation of option-implied and returns-based forecasts of volatility, in which recent developments related to the impact on measured volatility of market microstructure noise are taken into account. The paper also assesses the robustness of the performance of the option-implied forecasts to the way in which those forecasts are extracted from the option market. Using a test for superior predictive ability, model-free implied volatility, which aggregates information across the volatility 'smile', and at-the-money implied volatility, which ignores such information, are both tested as benchmark forecasts. The forecasting assessment is conducted using intraday data for three Dow Jones Industrial Average (DJIA) stocks and the S&P500 index over the 1996-2006 period, with future volatility proxied by a range of alternative noise-corrected realized measures. The results provide compelling evidence against the model-free forecast, with its poor performance linked to both the bias and excess variability that it exhibits as a forecast of actual volatility. The positive bias, in particular, is consistent with the option market factoring in a substantial premium for volatility risk. In contrast, implied volatility constructed from liquid at-the-money options is given strong support as a forecast of volatility, at least for the DJIA stocks. Neither benchmark is supported for the S&P500 index. Importantly, the qualitative results are robust to the measure used to proxy future volatility, although there is some evidence to suggest that any option-implied forecast may perform less well in forecasting the measure that excludes jump information, namely bi-power variation. |
| Keywords: | Volatility Forecasts; Quadratic Variation; Intraday Volatility Measures |
| JEL: | C10 C53 G12 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2007-5&r=ets |
| By: | George Kapetanios (Queen Mary, University of London); Andrew P. Blake (Bank of England) |
| Abstract: | The martingale difference restriction is an outcome of many theoretical analyses in economics and finance. A large body of econometric literature deals with tests of that restriction. We provide new tests based on radial basis function neural networks. Our work is based on the test design of Blake and Kapetanios (2000, 2003a,b). However, unlike that work we can provide a formal theoretical justification for the validity of these tests using approximation results from Kapetanios and Blake (2007). These results take advantage of the link between the algorithms of Blake and Kapetanios (2000, 2003a,b) and boosting. We carry out a Monte Carlo study of the properties of the new tests and find that they have superior power performance to all existing tests of the martingale difference hypothesis we consider. An empirical application to the S&P500 constituents illustrates the usefulness of our new test. |
| Keywords: | Martingale difference hypothesis, Neural networks, Boosting |
| JEL: | C14 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp601&r=ets |
| By: | George Kapetanios (Queen Mary, University of London) |
| Abstract: | The investigation of the presence of structural change in economic and financial series is a major preoccupation in econometrics. A number of tests have been developed and used to explore the stationarity properties of various processes. Most of the focus has rested on the first two moments of a process thereby implying that these tests are tests of covariance stationarity. We propose a new test for strict stationarity, that considers the whole distribution of the process rather than just its first two moments, and examine its asymptotic properties. We provide two alternative bootstrap approximations for the exact distribution of the test statistic. A Monte Carlo study illustrates the properties of the new test and an empirical application to the constituents of the S&P 500 illustrates its usefulness. |
| Keywords: | Covariance stationarity, Strict stationarity, Bootstrap, S&P500 |
| JEL: | C32 C33 G12 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp602&r=ets |
| By: | Michael McAller (School of Economics and Commerce, University of Western Australia); Marcelo C. Medeiros (Department of Economics, PUC-Rio) |
| Abstract: | In this paper we propose a flexible model to capture nonlinearities and long-range dependence in time series dynamics. The new model is a multiple regime smooth transition extension of the Heterogenous Autoregressive (HAR) model, which is specifically designed to model the behavior of the volatility inherent in financial time series. The model is able to describe simultaneously long memory, as well as sign and size asymmetries. A sequence of tests is developed to determine the number of regimes, and an estimation and testing procedure is presented. Monte Carlo simulations evaluate the finite-sample properties of the proposed tests and estimation procedures. We apply the model to several Dow Jones Industrial Average index stocks using transaction level data from the Trades and Quotes database that covers ten years of data. We find strong support for long memory and both sign and size asymmetries. Furthermore, the new model, when combined with the linear HAR model, is viable and flexible for purposes of forecasting volatility. |
| Keywords: | Realized volatility, smooth transition, heterogeneous autoregression, financial econometrics,leverage, sign and size asymmetries, forecasting, risk management, model combination. |
| Date: | 2007–04 |
| URL: | http://d.repec.org/n?u=RePEc:rio:texdis:544&r=ets |
| By: | Arvid Raknerud, Terje Skjerpen and Anders Rygh Swensen (Statistics Norway) |
| Abstract: | We use state space methods to estimate a large dynamic factor model for the Norwegian economy involving 93 variables for 1978Q2–2005Q4. The model is used to obtain forecasts for 22 key variables that can be derived from the original variables by aggregation. To investigate the potential gain in using such a large information set, we compare the forecasting properties of the dynamic factor model with those of univariate benchmark models. We find that there is an overall gain in using the dynamic factor model, but that the gain is notable only for a few of the key variables. |
| Keywords: | Dynamic factor model; Forecasting; State space; AR models |
| JEL: | C13 C22 C32 C53 |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:ssb:dispap:504&r=ets |
| By: | Qian Chen (China Academy of Public Finance and Public Policy, Central University of Finance & Economics); David E. Giles (Department of Economics, University of Victoria) |
| Abstract: | We derive saddlepoint approximations for the density and distribution functions of the half-life estimated by OLS from an AR(1) or AR(p) model. Our analytic results are used to prove that none of the integer-order moments of these half-life estimators exist. This provides an explanation for the unreasonably large estimates of persistency associated with the purchasing power parity “puzzle”, and it also explains the excessively wide confidence intervals reported in the empirical PPP literature. |
| Keywords: | Saddlepoint approximation, half-life estimator, PPP puzzle |
| JEL: | C13 C22 F31 F41 |
| Date: | 2007–05–28 |
| URL: | http://d.repec.org/n?u=RePEc:vic:vicewp:0703&r=ets |
| By: | Paul Turner (Dept of Economics, Loughborough University) |
| Abstract: | This paper presents Monte Carlo simulations for the Johansen cointegration test which indicate that the critical values applied in a number of econometrics software packages are inappropriate. This is due to a confusion in the specification of the deterministic terms included in the VECM between the cases considered by Osterwald-Lenum (1992) and Pesaran, Shin and Smith (2000). The result is a tendency to reject the null of no cointegration too often. However, a simple adjustment of the critical values is enough to deal with the problem. |
| Keywords: | Cointegration, Johansen Test. |
| JEL: | C15 C32 |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:lbo:lbowps:2007_12&r=ets |
| By: | Theodoridis, Konstantinos (Cardiff Business School) |
| Abstract: | This Paper describes a procedure for constructing theory restricted prior distributions for BVAR models. The Bayes Factor, which is obtained without any additional computational effort, can be used to assess the plausibility of the restrictions imposed on the VAR parameter vector by competing DSGE models. In other words, it is possible to rank the amount of abstraction implied by each DSGE model from the historical data. |
| Keywords: | BVAR; DSGE Model Evaluation; Gibbs Sampling; Bayes Factor |
| JEL: | C11 C13 C32 C52 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:cdf:wpaper:2007/15&r=ets |