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Full-Text Articles in Physical Sciences and Mathematics
Asymptotics For The Arc Length Of A Multivariate Time Series And Its Applications As A Measure Of Risk, Tharanga Wickramarachchi
Asymptotics For The Arc Length Of A Multivariate Time Series And Its Applications As A Measure Of Risk, Tharanga Wickramarachchi
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The necessity of more trustworthy methods for measuring the risk (volatility) of financial assets has come to the surface with the global market downturn This dissertation aims to propose sample arc length of a time series, which provides a measure of the overall magnitude of the one-step-ahead changes over the observation time period, as a new approach for quantifying the risk. The Gaussian functional central limit theorem is proven under finite second moment conditions. Without loss of generality we consider equally spaced time series when first differences of the series follow a variety of popular stationary models including autoregressive moving …
Some New Problems In Changepoint Analysis, Jonathan Woody
Some New Problems In Changepoint Analysis, Jonathan Woody
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Climatological studies have often neglected changepoint effects when modeling
various physical phenomena. Here, changepoints are plausible whenever a station location moves or its instruments are changed. There is frequently meta-data to
perform sound statistical inferences that account for changepoint
information. This dissertation focuses on two such problems in changepoint analysis.
The first problem we investigate involves assessing trends
in daily snow depth series. Here, we introduce a stochastic storage model. The model allows for seasonal features, which permits the
analysis of daily data. Changepoint times are shown to greatly influence estimated trends in one snow depth series and are accounted …