This study has a twofold purpose: to demonstrate the use of the Marquardt compromise method in estimating the unknown parameters contained in the probability call-option pricing models and to test empirically the following models: the Boness, the Black-Scholes, the Merton proportional dividend, the Ingersoll differential tax, and the Ingersoll proportional dividend and differential tax.

Many techniques have been developed to analyze time series. Spectral analysis and cycle regression analysis represent two such techniques. This study combines these two powerful tools to produce two new algorithms; the spectral algorithm and the one-pass algorithm. This research encompasses four objectives. The first objective is to link spectral analysis with cycle regression analysis to determine an initial estimate of the sinusoidal period. The second objective is to determine the best spectral window and truncation point combination to use with cycle regression for the initial estimate of the sinusoidal period. The third is to determine whether the new spectral algorithm performs better than the old T-value algorithm in estimating sinusoidal parameters. The fourth objective is to determine whether the one-pass algorithm can be used to estimate all significant harmonics simultaneously.

The cycle regression analysis algorithm is the most recent addition to a group of techniques developed to detect "hidden periodicities." This dissertation investigates four major aspects of the algorithm. The objectives of this research are 1. To develop an objective method of obtaining an initial estimate of the cycle period? the present procedure of obtaining this estimate involves considerable subjective judgment; 2. To validate the algorithm's success in extracting cycles from multi-cylical data; 3. To determine if a consistent relationship exists among the smallest amplitude, the error standard deviation, and the number of replications of a cycle contained in the data; 4. To investigate the behavior of the algorithm in the predictions of major drops.

In this study a two-part mixed probability density function was derived which described the relative changes in the Standard and Poor's 100 Stock Index over various intervals of time. The density function is a mixture of two different halves of normal distributions. Optimal values for the standard deviations for the two halves and the mean are given. Also, a general form of the function is given which uses linear regression models to estimate the standard deviations and the means. The density functions allow stock market participants trading index options and futures contracts on the S & P 100 Stock Index to determine probabilities of success or failure of trades involving price movements of certain magnitudes in given lengths of time.

The classical normal curve approximation to cumulative hypergeometric probabilities requires that the standard deviation of the hypergeometric distribution be larger than three which limits the usefulness of the approximation for small populations. The purposes of this study are to develop clearly-defined rules which specify when the normal curve approximation to the cumulative hypergeometric probability distribution may be successfully utilized and to determine where maximum absolute differences between the cumulative hypergeometric and normal curve approximation of 0.01 and 0.05 occur in relation to the proportion of the population sampled.

This research was designed to develop and evaluate an automated alternative to the Box-Jenkins method of forecasting. The study involved two major phases. The first phase was the formulation of an automated ARIMA method; the second was the combination of forecasts from the automated ARIMA with forecasts from two other automated methods, the Holt-Winters method and the Stepwise Autoregressive method. The development of the automated ARIMA, based on a decision criterion suggested by Akaike, borrows heavily from the work of Ang, Chuaa and Fatema. Seasonality and small data set handling were some of the modifications made to the original method to make it suitable for use with a broad range of time series. Forecasts were combined by means of both the simple average and a weighted averaging scheme. Empirical and generated data were employed to perform the forecasting evaluation. The 111 sets of empirical data came from the M-Competition. The twenty-one sets of generated data arose from ARIMA models that Box, Taio and Pack analyzed using the Box-Jenkins method. To compare the forecasting abilities of the Box-Jenkins and the automated ARIMA alone and in combination with the other two methods, two accuracy measures were used. These measures, which are free …

This study compared the results for McNemar's test, the t test for related measures, and the chi-square test of independence as cell sized varied in a two-by-two frequency table. In this study. the probability results for McNemar's rest, the t test for related measures, and the chi-square test of independence were compared for 13,310 different combinations of cell sizes in a two-by-two design. Several conclusions were reached: With very few exceptions, the t test for related measures and McNemar's test yielded probability results within .002 of each other. The chi-square test seemed to equal the other two tests consistently only when low probabilities less than or equal to .001 were attained. It is recommended that the researcher consider using the t test for related measures as a viable option for McNemar's test except when the researcher is certain he/she is only interested in 'changes'. The chi-square test of independence not only tests a different hypothesis than McNemar's test, but it often yields greatly differing results from McNemar's test.

This study compared the results of his chi square text of independence and the corrected chi square statistic against Fisher's exact probability test (the hypergeometric distribution) in contection with sampling from a finite population. Data were collected by advancing the minimum call size from zero to a maximum which resulted in a tail area probability of 20 percent for sample sizes from 10 to 100 by varying increments. Analysis of the data supported the rejection of the null hypotheses regarding the general rule-of-thumb guidelines concerning sample size, minimum cell expected frequency and the continuity correction factor. it was discovered that the computation using Yates' correction factor resulted in values which were so overly conservative (i.e. tail area porobabilities that were 20 to 50 percent higher than Fisher's exact test) that conclusions drawn from this calculation might prove to be inaccurate. Accordingly, a new correction factor was proposed which eliminated much of this discrepancy. Its performance was equally consistent with that of the uncorrected chi square statistic and at times, even better.