Fractionally integrated time varying GARCH model

This paper will discuss the current research in building models of conditional variances using the Autoregressive Conditional Heteroskedastic (ARCH) and Generalized ARCH (GARCH) formulations. The discussion will be motivated by a simple asset pricing theory which is particularly appropriate for examining futures contracts with risk averse agents. A new class of models defined to be integrated in variance is then introduced. This new class of models includes the variance analogue of a unit root in the mean as a special case. The models are argued to be both theoretically important for the asset pricing models and empirically relevant. The conditional density is then generalized from a normal to a Student-t with unknown degrees of freedom. By estimating the degrees of freedom, implications about the conditional kurtosis of these models and time aggregated models can be drawn. A further generalization allows the conditional variance to be a non-linear function of the squared innovations. Throughout empirical...

Bivariate FIGARCH and Fractional Cointegration

This work is devoted to the study of long correlations, memory effects and other statistical properties of a sample of high-frequency (tick) data. The high-frequency data sample consists of high-frequency (minute) data for several stocks over a seven-day period which we know is relevant for market crush behaviour in the US market; 10–18 March 2008. The Hurst exponent estimation, the detrended fluctuation analysis and the fractional difference parameter are the tools used for this analysis. It also investigates the underlying volatility processes in high-frequency (tick) data using range of GARCH specifications. The GARCH variants considered include the basic GARCH, IGARCH, ARFIMA (0,,0)-GARCH and FIGARCH models. In all the applications, the methodology provides insight into features of these series volatility.

This paper presents evidence from Monte Carlo simulation aimed at exploring power of heteroskedasticity tests to verify presence of various patterns of non-constant variances in linear models. Three independent MC simulations were set up to investigate impact of error term variance changing with power of the proportionality factor (schemes 1 and 2) or in response to variance multiplication constant applied to a subset of data (scheme 3). Empirical power was shown to vary in accordance with the simulated form of the skedastic function and sample size. Tests mainly showed adequate power for the skedastic function in scheme 1 and to a lesser extent for variance function in scheme 3. On the other hand, skedastic functions simulated in scheme 2 were the most difficult to detect by most heteroskedasticity tests.

Bootstrapping non-stationary stochastic volatility

Long memory and structural breaks in modeling the return and volatility dynamics of precious metals

Quasi score-driven models

Methods for repeated measures data analysis with missing values

Joint and Marginal Diagnostic Tests for Conditional Mean and Variance Specifications

While a variety of specification tests are routinely employed to test for misspecification in linear regression model, such tests and their applications to the truncated and censored regression models are uncommon. This paper develops a regression error specification test (RESET) for the truncated regression model as an extension of the popular RESET for the linear regression model (Ramsey (1969)). The two proposed extensions TRESET1 and TRESET2 developed in the paper are applied to labor force participation data from Mroz (1987). The paper studies the empirical size and power properties of the proposed tests via Monte Carlo experiments. Our simulation results suggest that both TRESET tests have reasonably good size and power properties for the truncated regression model in medium to large samples. However, TRESET2 consistently outperforms TRESET1 both in terms of empirical size and power in our experiments. Â

This study presents two statistical methods for testing the signal-to-noise ratio (SNR) of a log-normal distribution. The proposed statistical tests were based on the generalized confidence interval (GCI) approach and the large sample (LS) approach. To evaluate the performance of the proposed statistical tests, a simulation study was conducted under several values of SNR in a log-normal distribution. The performances of the statistical tests were compared based on the empirical size and power of the test. The simulation results showed that the statistical test based on the GCI approach performed better than the statistical test based on the LS approach in terms of the attained nominal significance level, and the empirical power of the test and is thus recommended for researchers. The performances of the proposed statistical tests also were examined through a numerical example.

Intracerebroventricular injection of streptozotocin in rats produces both oxidative stress in the brain and cognitive impairment

Several previous studies have found fractionally integrated, or long memory behavior, in the conditional mean of inflation. This paper notes that extremely similar phenomena are also apparent in the squared and absolute values of residuals from fractionally filtered inflation series. Hence, the inflation process appears to have a dual long memory feature in both its first and its second conditional moments. We suggest a parametric model of long memory in both the conditional mean and the conditional variance. Some Monte Carlo evidence is presented that supports estimation of the model by approximate maximum likelihood methods. We then report estimated models for the inflation series for several different industrialized countries, including the United States. For nearly all of the countries in our study, there is strong evidence of statistically significant long memory parameters in both the conditional mean and the variance. We note some of the implications for modeling inflation.

This paper proposes the Lagrange multiplier test for the null hypothesis thatthe bivariate time series has only a single common stochastic volatility factor and noidiosyncratic volatility factor. The test statistic is derived by representing the model in alinear state-space form under the assumption that the log of squared measurement error isnormally distributed. The empirical size and power of the test are examined in Monte Carloexperiments. We apply the test to the Asian stock market indices.

Receiver operating characteristic (ROC) surfaces provide a natural extension of ROC curves to three-class diagnostic problems. A key summary index is the volume under the surface (VUS), representing the probability that a randomly chosen observation from each of the three ordered groups is correctly classified. A parametric estimation of VUS typically assumes trinormality of the class distributions. However, a formal method for the verification of this composite assumption has not appeared in the literature. Our approach generalizes the two-class AUC-based GOF test of Zou et al. to the three-class setting by exploiting the parallel structure between empirical and trinormal VUS estimators. We propose a global goodness-of-fit (GOF) test for trinormal ROC models based on the difference between empirical and trinormal parametric estimates of the VUS. To improve stability, a probit transformation is applied and a bootstrap procedure is used to estimate the variance of the difference. The resulting test provides a formal diagnostic for assessing the adequacy of trinormal ROC modeling. Simulation studies illustrate the robustness of the assumption via the empirical size and power of the test under various distributional settings, including skewed and multimodal alternatives. The method’s application to COVID-19 antibody level data demonstrates the practical utility of it. Our findings suggest that the proposed GOF test is simple to implement, computationally feasible for moderate sample sizes, and a useful complement to existing ROC surface methodology.