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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 …
New Results In Multivariate Time Series With Applications, Nan Su
New Results In Multivariate Time Series With Applications, Nan Su
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This dissertation presents some new results in stationary multivariate time series.
The asymptotic properties of the sample autocovariance are established, that is, we derive a multivariate version of Bartlett's Classic Formula.
The estimation of the autocovariance function plays a crucial role in time series analysis,
in particular for the identification problem.
Explicit formula for vector autoregressive $(p)$ and vector moving average $(q)$ processes are presented as examples.
We also address linear processes driven by non-independent errors,
a feature that permits consideration of multivariate GARCH processes.
We next compare several techniques to discriminate
two multivariate stationary signals. The compared methods include …