"An evaluation model for the comparison of three NYSE

indexes "

by Alexia Iasonos, Igor Zurbenko

KEY WORDS: KZ filter, linear regression, time series

decomposition, spectral analysis, AR model

The data used for the analysis were the Dow Jones

Industrial Average, Nasdaq Composite Index and S&P 500

Composite Index daily closing values. A natural logarithm

transformation was used to stabilize

the variance and linearize the data since

exponential growth was apparent in all indexes and

the variance was increasing proportionally to the

mean. Kolmogorov-Zurbenko filter (KZ) was applied to

isolate the daily fluctuations introduced by

seasonality and other stock market forces and retain

the long term component. A strong linear trend existed

for each index, which was obtained by fitting a

regression of the Long term on time. Similarly, the

short term was decomposed by using a KZ filter with

different parameters which were obtained

through spectral analysis. The short term was

perfectly modeled by an Autoregressive model. It was

evident that the three indexes behave the same in the

long term. This model can be used for the comparison

of the stock market and the bond market, as well as,

for the comparison of the stock performance of

different companies.