Shewhart methodology for modelling financial series : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University, Palmerston North, New Zealand
Quality management techniques are widely used in industrial applications for monitoring
observable process variation. Among them, the scientific notion of Shewhart principles is
vital for understating variations in any type of process or service. This study extensively
investigates and demonstrates Shewhart methodology for financial data.
Extremely heavy tails noted in the empirical distribution of stock returns led to the
development of new parametric probability distributions for pricing assets and forecasting
market risk. Standard asset pricingmodels have also extended to account the first four
(excess) moments in return distributions. These approaches remain complex, but yet they
are inadequate for capturing extreme volatility caused by infrequent market events.
It is well known that the security markets are always subjected to a certain amount
of variability caused by noise-traders and other frictional price changes. Unforeseen
events which are happening in the world may lead to hugemarket losses. This research
shows that Shewhart methodology for partitioning data into common and special cause
variations adds value tomodelling stock returns.
Applicability of the proposed method is discussed using several scenarios occurring in
an industrial process and a financialmarket. A set of new propositions based on Shewhart
methodology is formed for finer description of the statistical properties in stock returns.
Research issues which are related to the first four moments, co-moments and autocorrelation
in stock returns are identified. New statistical tools such as difference control
charts, odd-even analysis and estimates for co-moments are proposed to investigate the
new propositions and research issues. Finally, several risk measures are proposed, and
considered with respect to investor’s preferences.
The research issues are investigated using partitioned data from S&P 500 stocks and
the findings show that inmost of the scenarios, contradictory conclusions were made as a
result of special cause variations. A modelling approach based on common and special
cause variations is therefore expected to lead appropriate asset pricing and portfolio
management. New statistical tools proposed in this study can be used to other time series
data; a new R-package called QCCTS (Quality Control Charts for Time Series) is developed
for this purpose.