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The trends reported in the text and summarized in Table 1 were estimated employing a method that accounts for residual serial correlation and time series error, and subbasin trends may not sum linearly [ Johnston and DiNardo, 1997].
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This article studies parametric component and nonparametric component estimators in a semiparametric regression model with linear time series errors; their r-th mean consistency and complete consistency are obtained under suitable conditions.
After specifying a model for { R k, t }, we have a regression model with time series errors, that can be fit using standard maximum likelihood methods.
In Akron, Model 3 has higher sensitivities than Model 1, suggesting that the time series errors are less relevant in outbreak signature detection for the test data.
The plots of the sample autocorrelation and partial autocorrelations functions of the time series innovations lie inside the dotted confidence bounds for a white noise process (i.e., are samples of uncorrelated time series errors).
We selected the order of the SARIMA model for the time series errors, { X k, t }, as defined by (4) in the Appendix using standard identification techniques based on the sample autocorrelation and partial autocorrelation (e.g., [ 18]).
As a result, the equation required no time-series error term.
After correcting the time series for errors and rainfall-induced variation, a ~100 km2 area where vegetation was severely impacted by ash was highlighted using bi-temporal comparison and principal component analysis.
For each time series, the maximum error rate (compared to observed traffic volume) was 22.4 %, while the average error rate was 6.9%%.
As mentioned earlier the error time series was first formed by getting the error between the numerical estimation and corresponding observation at the current time step.
Figure 10 illustrates the distribution of the time series of positioning errors for GPS-only, BDS-only and the integration of GPS and BDS.
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