Pi Mu Epsilon - Mathematical Association of America

Thursday MAA Session #9 August 2, 2012
2:40–2:55
Censored Distributions in Stochastic Simulation of Financial Market Data
Valentina M. Semenova
Dartmouth College
Certain financial market data, such as interest rate and volatility, are non-negative. At the same
time, they are often modeled by stochastic processes without lower bound, such as OrnsteinUhlenbeck
process. In order to make distribution more realistic, it is necessary to bound it at 0. There
are 2 possibilities for bounding: censored distribution and truncated distribution. It is examined
how use of truncated distribution modifies statistical moments and correlations. It will be shown
that use of censored distribution within the stochastic modeling framework of interest rates and
volatilities produce more realistic results than unbounded or truncated distribution. Financial data
illustrations include short interest rates and volatilities of foreign exchange rates.
3:00–3:15
Using Wavelet Transformations to Analyze Carbon Uptake
Tyler J. Heaps
Augsburg College
The objective of this study was to apply wavelet transformations to analyze long-term records of
carbon uptake at different measurement sites throughout the United States. Wavelet transformations,
such as the Haar wavelet transform (HWT), were used to compress the information and
reduce the biased and non-useful data. The data were collected from Ameriflux, a network of
tower sites that provide quantitative information throughout the United States, and analyzed using
MatLab.
Wavelets are useful in modeling a time series on different time scales. The wavelet approach was
helpful in analyzing the carbon uptake at a given site, which may have half-hourly data collected
over many years. A key measurement analyzed was net ecosystem exchange (NEE), which measures
the rate that carbon enters and leaves the ecosystem. The wavelet decomposed NEE was
compared to wavelet decompositions of other environmental measurements such as incoming solar
radiation and air temperature. My results indicate a moderate linear correlation between the
incoming solar radiation and carbon uptake. The smaller differences of solar radiation tended to
cause an efflux of carbon into the atmosphere over a 4-6 year period. In shorter time scales, there
was no linear correlation between the air temperature and NEE, but over a larger time scale, the
higher temperatures allowed for uptake of carbon by the biosphere. Future research would examine
the robustness of our findings across a latitudinal gradient and sites with similar vegetation.
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