Modelling Stock Prices with Exponential Weighted Moving Average (EWMA)

Using exponentially weighted moving average (EWMA) charts

1. Unlike X -R and Individuals charts (without the Western Electric Handbook rules which aim to increase sensitivity), all of the data collected over time may be used to determine the control status of a process. 2. The EWMA is often superior to the CUSUM charting technique for detecting "larger" shifts. 3. EWMA schemes may be applied for monitoring standard deviations in addition to the proces...

Risk-adjusted survival time monitoring with an updating exponentially weighted moving average (EWMA) control chart.

Monitoring medical outcomes is desirable to help quickly detect performance changes. Previous applications have focused mostly on binary outcomes, such as 30-day mortality after surgery. However, in many applications the survival time data are routinely collected. In this paper, we propose an updating exponentially weighted moving average (EWMA) control chart to monitor risk-adjusted survival t...

Modelling Stock Prices

Moving Average Processes with Infinite Variance

The sample autocorrelation function (acf) of a stationary process has played a central statistical role in traditional time series analysis, where the assumption is made that the marginal distribution has a second moment. Now, the classical methods based on acf are not applicable in heavy tailed modeling. Using the codifference function as dependence measure for such processes be shown it be as...

Optimal portfolios when stock prices follow an exponential Lévy process

We investigate some portfolio problems that consist of maximizing expected terminal wealth under the constraint of an upper bound for the risk, where we measure risk by the variance, but also by the Capital-at-Risk (CaR). The solution of the mean-variance problem has the same structure for any price process which follows an exponential Lévy process. The mean-CaR involves a quantile of the corre...