LINEAR FILTERING AND THE ARIMA APPROACH TO SEASONAL ADJUSTMENT AND STOCK OPTION PRICING

This dissertation explores some aspects of seasonal adjustment, linear filtering, and stock option pricing relating to the ARIMA time series model. An observed time series Z(,t) is decomposed into an additive nonseasonal component N(,t) and seasonal component S(,t) . This decomposition is achieved with a one-sided linear filter applied to the observed series. The derived estimator of N(,t) is shown to be optimal in the sense of giving minimum mean square error given only the past values of the series Z(,t) . The advantages of this one-sided procedure are that it utilizes a fixed set of weights, requires no forecasted values for its use, is unambiguous in its implementation, and does not require revisions. A comparison is made with existing empirical and two-sided procedures.;An ARIMA approach is utilized in developing estimators of call and put stock options. The ARIMA model for the underlying stock provides the volatility measure which, together with the distributional assumptions of future stock price, gives the information required to establish option prices. Estimators are derived for European options and adapted for use for American options. The ARIMA option estimators are shown to satisfy the basic properties of stock options. Comparisons are made between the ARIMA estimates and the Black-Scholes estimates on five underlying stocks.;The use of a one-sided linear filter leads to questions of the phase shift induced by the linear filter. The broader question of time delay between an input and output process is considered. A time domain measure of time delay between an input and output process is developed through the cross-covariance function by connecting the cross-covariances to the phase derivative measure of time delay in the frequency domain. This time delay measure is applied to the optimal one-sided seasonally adjusted trend component for a stochastic process which can be considered as an underlying mechanism for the Census X-11 seasonal adjustment filters.