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Whereas the laser beams were activated only intermittently (i.e., every ~5 minutes) for the time-series size measurements, the stir paddle and peristaltic pump stayed on for the entire duration of each run.
For a fixed time series sample size (T) GMM is inconsistent and approaches a shifted Cauchy-distributed random variate as the cross section sample size n → ∞.
In this case, the asymptotic distribution of the FDMLE has bounded support and its density is infinite at the upper bound when the time series sample size T approaching infinity.
Therefore, there are six different alphabets to represent this time series; alphabet size (a)=6 in this case.
We test these hypotheses using time series of size-based prices.
Information from time series and bubble size distribution data was used to identify flow patterns for each of the flow rates studied.
The asymptotic theory holds as long as the cross section (n) or time series (T) sample size is large, regardless of the n/T ratio, which makes the approach appealing for practical work.
Here we apply it on a time series sequence of size n, the categories are the time units and their frequencies are the probability mass function of the amplitude envelope.
The speedup depends on data size and is illustrated in Figure 8, showing processing times for computing statistics over EDR voltage time series of different sizes (logarithmic scale), compared to two classical multi-core parallel processing architectures.
In order to check their adequacy, these methods are compared with other global and local modelling classical approaches using three benchmark time series and different sizes (medium and high) of training data sets.
Section VII evaluates our proposed model by conducting additional experiments on eight different financial time series with different sizes.
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