Regarding the same physical, chemical and biological conditions (genetic relationship) in each sequence, GR deviations show the same deviation trend within each sequence.
The basic idea of PID control is easy to explain: deviation of the controlled quantity (BG in our case) from the target is corrected by adapting the control parameter (insulin) using a linear combination of absolute deviation, trend, and the sum of past deviations.
A common type of algorithm is the PID algorithm in which deviation of the blood glucose value from the target range is corrected by adjusting the dose of insulin using a linear combination of absolute deviation, trend, and the sum of past deviations [ 53].
For other application areas, features can look completely different, as for example summarised in Lemke et al. (2009) for the area of time series forecasting, where features can include, for example, length, seasonality, autocorrelation, standard deviation and trends of the series.
For crude oil and mentha oil futures, the near month volatility trend of daily returns is almost constant, and the magnitude of rolling standard deviation (volatility trend) is the highest for the far month contract.
I have removed an upward trend, because for short-run analysis it is interesting to look at deviations from trends.
Error bars on the points in Fig. 5 are quite small, so the jump between the blue HZ43 points around 2010 is real, as is the deviation from trend in 2014.
where σ is the standard deviation of trend α and r is the correlation coefficient of the regression between foF2res and time.
The residual, or deviation from trend z t = y t −τ t is commonly referred to as the business cycle component, and is the object of economic interest.
