Dissertation Archive, WMU Graduate College

Dissertation Defense

Candidate: Yasemin Bardakci

Degree of: Doctor of Philosophy

Department: Economics

Title: Essays on the Econometrics of Financial Volatility

Date: Wednesday, June 23, 2004 3:00-5:00 p.m.
5302 Friedmann

Committee: Dr. Matthew L. Higgins, Chair
Dr. Debasri Mukherjee
Dr. Onur Arugaslan

Abstract: My dissertation consists of three essays on the econometric analysis of financial volatility. I am especially interested in forecasting volatility as it plays a crucial role in financial and economic decision-making. My first essay is titled "The Runs Test for Volatility Forecastibility: Extensions and Comparisons with Tests for GARCH". Recently, Diebold and Christoffersen (2000) introduced a test for forecastable volatility based on the number of runs in the hit/miss indicator of a sequence of constant forecast intervals. They claim their test should be useful for detecting volatility dependence in low frequency asset returns for which no parametric model seems appropriate. The most commonly used model for dependence in the second moments is the GARCH process. If the runs test is to be useful, it should have a reasonable power when the true volatility process is GARCH. In this paper, I compare the size and the power of the runs test and the optimal LM test for GARCH by Monte Carlo simulation. I consider data generated from a GARCH process with parameters representative of both high and low frequency asset returns. For high frequency returns the LM test has superior power to the runs test. For low frequency returns however, the tests have very similar power. I also propose a switching variance model, which produces a first order Markov hit sequence for which the runs test is uniformly most powerful. For this process, I find that the runs test has greater power than the LM test. In the final part of the essay, I propose a multivariate version of the runs test and compare it to multivariate tests for GARCH. The multivariate runs test again performs well for low frequency returns.
The second essay of the dissertation is titled "Sampling Properties of Criteria for Evaluating GARCH Forecasts of Asset Return Volatility". I drive the population moments of criteria commonly used to evaluate accuracy of volatility forecasts from GARCH models. I state the existence conditions for the population moments. The criteria include the mean squared error, the mean absolute error and heteroscedasticity adjusted mean square error. Using Monte Carlo simulation, I analyze the sampling properties of these criteria and also the sampling properties of the R2's and t-statistics from the Mincer and Zarnowitz (1969) regression for evaluating volatility forecasts. When volatility is highly persistent, I find that the majority of the sampling distribution of the R2 lies below the population R2. Also, the t-statistics for testing forecast efficiency are unreliable. For a logarithmic version of the Mincer and Zarnowitz regression, I find that R2's tend to be smaller, but inferences concerning forecast efficiency are valid. Among the accuracy criteria I find that the heteroscedasticity adjusted mean-squared error is preferable.
The third essay considers situations when the loss function is not symmetric. Most of the forecast criteria used in the literature consider symmetric loss functions like MSE because of mathematical convenience. However, forecast evaluation results are very sensitive to the proper specification of the loss function. The optimal predictor under MSE is the conditional mean whereas under asymmetric loss it is conditional mean plus a time variant term. In this paper I compare the forecasts of returns from the optimal predictor for a symmetric quadratic loss function (MSE) with the optimal predictor for an asymmetric loss function under the assumption that agents have asymmetric loss functions. In particular, I use the LINLIN asymmetric loss function. I use normal GARCH(1,1), t-GARCH(1,1), and a nonparametric model to predict the time varying variance. The optimal predictor does not necessarily always out-perform the pseudo-optimal predictor.

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