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MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model

In this paper we present a stochastic volatility model assuming that the return shock has a Skew-GED distribution. This allows a parsimonious yet flexible treatment of asymmetry and heavy tails in the conditional distribution of returns. The Skew-GED distribution nests both the GED, the Skew-normal and the normal densities as special cases so that specification tests are easily performed. Inference is conducted under a Bayesian framework using Markov Chain MonteCarlo methods for computing the posterior distributions of the parameters. More precisely, our Gibbs-MH updating scheme makes use of the Delayed Rejection Metropolis-Hastings methodology as proposed by Tierney and Mira (1999), and of Adaptive-Rejection Metropolis sampling. We apply this methodology to a data set of daily and weekly exchange rates. Our results suggest that daily returns are mostly symmetric with fat-tailed distributions while weekly returns exhibit both significant asymmetry and fat tails.

Spurious regressions between I(1) processes with long memory errors

In this paper we develop the asymptotic distribution theory for spurious regression between I(1) processes with long‐memory stationary errors. Our result departs from the standard results of Phillips (Understanding spurious regression in econometrics. J. Economet. 33 (1986), 311–40) in two respects. First, the limit theory we apply is based on a functional central limit theorem for stationary linear processes whose spectral density at frequency zero may diverge or collapse to zero. Second, different limit distributions may apply depending on the form of long memory exhibited by the error term. We also discuss the extension of our analyis to spurious regression with fitted intercept.

Asymptotic inference in time series regressions with a unit root and infinite variance errors

Abstract In this paper, we study the limiting distribution of the OLS estimators and t-statistics of the null hypothesis of a unit root in various regression models when the true generating mechanism is either a driftless random walk or a random walk with drift and the distribution of the error term belongs to the normal domain of attraction of a stable law with characteristic exponent less than two. We show that in the former data generating processes (DGP) the same functional form as in the finite variance case applies with the Levy process replacing the standard Wiener process. On the other hand, under the random walk with drift DGP, we show that different limiting distributions are obtained according to the magnitude of the maximal moment exponent α. Finally, we investigate the consequences of a “local” departure from the finite variance setup and provide simulation evidence on the robustness of the limiting distributions (derived under finite variance) to heavy tails in finite samples.

Investigating asymmetry in US stock market indexes: evidence from a stochastic volatility model

This study provides empirical evidence on asymmetry in financial returns using a simple stochastic volatility model which allows a parsimonious yet flexible treatment of both skewness and heavy tails in the conditional distribution of returns. In particular, it is assumed that returns have a Skew-GED conditional distribution. Inference is conducted under a Bayesian framework using Markov Chain Monte Carlo methods for estimating the properties of the posterior distributions of the parameters. One is also able to perform some specification testing via Bayes factors. The data set consists of daily and weekly returns on the DJ30, S&P500 and Nasdaq US stock market indexes. The estimation results are consistent with the presence of substantial asymmetry and heavy tails in the distribution of US stock market indexes.

Estimation and inference on long run equilibria: a simulation study

In this paper we study the finite sample properties of some asymptotically equivalent estimators of cointegrating relationships and related test statistics: the Fully Modified Least Squares estimator proposed by Phillips and Hansen (1990), the Dynamic OLS estimator of Saikkonen (1991) and Stock and Watson (1993), the maximum likelihood estimator (reduced rank regression estimator) of Johansen (1988). On the basis of previous Monte Carlo results on this topic, the main objective of our simulation experiments is to study the sensitivity of the finite sample distribution of estimators and test statistics to three features of the DGP of the observable variables, namely, the degree of serial correlation of the cointegrating relationship, the condition of weak exogeneity and the signal-to-noise ratio. To this end, we consider 100 different DGPs and four increasing sample sizes. Besides the usual descriptive statistics, further information about the empirical distributions of interest by means of graphical and statistical methods are provided. In particular, we study size distortion of test statistics using P-value discrepancy plots and estimate the maximal moment exponent of the empirical distribution of estimators.

Comments on the Investment-Uncertainty Relationship in a Real Option Model

The paper considers the problem of evaluating the probability of investing in a capital-investment project as a measure of the uncertainty-investment relationship in a real option model. By the use of the contingent claims analysis the opportunity to invest is modelled as an American call option with expiring time. We show that an increase in uncertainty of the project may actually have positive or negative effects on the probability of investing depending on which market parameters are called to restore the asset price equilibrium condition.

The Fragility of the KPSS Stationarity Test

Stationarity tests exhibit extreme size distortions if the observable process is stationary yet highly persistent. In this paper we provide a theoretical explanation for the size distortion of the KPSS test for DGPs with a broad range of first order autocorrelation coefficient. Considering a near-integrated, nearly stationary process we show that the asymptotic distribution of the test contains an additional term, which can potentially explain the amount of size distortion documented in previous simulation studies.

Local Asymptotic Distributions of Stationarity Tests

In this paper, we study the asymptotic behaviour of several test statistics of the null hypothesis of stationarity under a sequence of local alternatives. The sequence of local alternatives is modelled as a nearly stationary process, i.e. a non-stationary process in any finite sample which converges to a stationary process as T ↑ ∞. From the asymptotic distributions, we find that the stationarity tests have non-trivial power under the above sequence of local alternatives. Our results complement those of Wright [Econometric Theory (1999) Vol. 15, pp. 704-709] who found that the Kwiatkowski, Phillips, Schmidt and Shin (KPSS) and the modified range statistics (MRS) tests have power equal to their size under a sequence of fractional alternatives. Finally, a simulation study investigates the power properties of the stationarity tests in finite samples.

Fully modified estimation of cointegrating vectors via var prewhitening: A simulation study

In this paper we investigate, by simulation methods, the finite samples properties of the Fully Modified Least Squares (FMLS) estimator of cointegrating vectors when the long run covariance matrix is estimated via VAR prewhitening. We compare this estimator to the FMLS estimator based on an automatic or a fixed bandwidth kernel estimator of the long run covariance matrix. By and large, FMLS estimator based on VAR prewhitening perform better than FMLS based on fixed bandwidth or automatic bandwidth, with the latter behaving almost in the same way in finite samples. More importantly, the empirical distribution of a Wald test statistic built from VAR prewhitened FMLS is closer to the asymptoticχ2 distribution than those obtained from alternative kernel estimators. Thus, our findings strongly favor the use of VAR prewhitening in the FM correction of the OLS estimator.

A note on the stationarity of a threshold first-order bilinear process

In the present note we study the threshold first-order bilinear model X(t)=aX(t-1)+(b11{X(t-1)