Browsing by Subject "Analysis of variance."

Now showing 1 - 4 of 4

Open Access
Comparison of several estimators for the covariance of the coefficient matrix
(1995) Orhan, Mehmet
The standard regression analysis assumes that the variances of the disturbance terms are constant, and the ordinary least squares (OLS) method employs this very crucial assumption to estimate the covariance of the disturbance terms perfectly, but OLS fails to estimate well when the variance of the disturbance terms vary across the observations. A very good method suggested by Eicker and improved by White to estimate the covariance matrix of the disturbance terms in case of heteroskedeisticity was proved to be biased. This paper evaluates the performance of White’s method as well as the OLS method in several different settings of regression. Furthermore, bootstrapping, a new method which very heavily depends on computer simulation is included. Several types of this method are used in several cases of homoskedastic, heteroskedastic, balanced, and unbalanced regressions.
Open Access
Detecting structural change when the change point is unknown
(1995) Başçı, Sıdıka
There are various tests which are used to detect structural change when the change point is unknown. Among these widely used ones are Cumulated Sums (CUSUM) and CUSUM of Squares tests of Brown, Durbin and Evans (1975), Fluctuation test of Sen (1980) and Ploberger, Krämer and Kontrus (1989). More recently, Andrews (1990) suggests Sup F test and shows that it performs better than the above stated tests in terms of power. The problem with these tests is that they all assume stable variance although the regression coefficients change while moving from one regime to the other. In this thesis, we relax this assumption and suggest an alternative test which also allows heteroskedasticity. For this aim, we follow the Bayesian approach. We also present some of the Monte Carlo study results where we find that Bayesian test has superiority over the above stated tests in terms of power.
Open Access
A dynamic importance sampling method for quick simulation of rare events
(1993) Erdoğan, Alper
Simulation of low-probability events may take extremely long times since they occur very rarely. There are various variance reduction methods used to speed up simulations in such cases. In this thesis, a new variance reduction technique is proposed, which is based on expressing the desired probability as the product of a number of greater probabilities and estimating each term in the product in a recursive manner. It turns out that the resulting estimator, when feasible, uses an importance sampling distribution at each step to constrain the samples into a sequence of larger sets which shrink towards the rare set gradually. Moreover, the important samples used in each step are obtained automatically from the outcomes of the experiments in the previous steps. The method is applied to the estimation of overflow probability in a network of queues and remarkable speed-ups with respect to standard simulation are obtained.
Open Access
Formal GARCH performance in a computable dynamic general equilibrium framework
(1998) Yiğitbaşıoğlu, Ali Bora
This study uses a Computable Dynamic General Equilibrium setting based on Brock’s (1979, 1982) intertemporal growth and asset pricing models and applies this framework as a formal test to study the out-of-sample forecast performance of Bollerslev’s (1986) GARCH (1,1) Classical Historical Volatility forecasts. The solution to Brock’s growth model reflects the utility maximizing behavior of the consumer and profit maximizing behavior of producers, and is a framework that has recorded some remarkable successes in mirroring the real economy. All existing studies have used a sample realized variance in the forecast horizon to test the out-of- sample performance of conditional variance forecasting models. The realized variance is simply an approximation to the true distribution of variance in the forecast horizon, and is often an unfair benchmark of performance. Simulation of Brock’s model enables one to obtain the true distribution of asset returns and their variance at all times. The true distribution reflects all the possible states of a simulated economy, which is shown to mimic all the properties observed in empirical financial data. This framework affords the luxury of comparing the out-of-sample forecasts from various models with the true variance in the forecast horizon. The results jointly demonstrate that the GARCH (1,1) model performs significantly better than the Classical Historical Volatility when the true variance is used as the forecast comparison benchmark. It is concluded that the use of realized variance for out-of-sample performance is highly misleading, especially for short-run forecasts.