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Time Series Regression and EDA
Published in Robert H. Shumway, David S. Stoffer, Time Series: A Data Analysis Approach Using R, 2019
Robert H. Shumway, David S. Stoffer
Perhaps the easiest form of nonstationarity to work with is the trend stationary model wherein the process has stationary behavior around a trend. We may write this type of model as () xt=μt+yt
Forecasting COVID-19 impact on RWI/ISL container throughput index by using SARIMA models
Published in Maritime Policy & Management, 2021
Kaan Koyuncu, Leyla Tavacioğlu, Neslihan Gökmen, Umut Çelen Arican
The concept of stationary has a great priority of the time series analysis. The concept of stationarity is expressed as the mean and variance of a time series is constant and the covariance between the two values of the series depends not only on the examined time but only on the difference between the two-time series. In order to apply the time series models, the series should be adjusted from the trend and seasonality (time-invariant). Correlograms (ACF and PACF graphs) can show a stationarity pattern or a unit root with significant lags. A more subjective way to evaluate stationarity is using (augmented) Dickey-Fuller (ADF) test statistics (Dickey and Fuller 1979). The null hypothesis is that the series have a unit root. The alternative hypothesis is that the time series is stationary (or trend-stationary).
Driver response and recovery following automation initiated disengagement in real-world hands-free driving
Published in Traffic Injury Prevention, 2023
Pnina Gershon, Bruce Mehler, Bryan Reimer
Figure 1a shows the proportions of steering wheel control levels across all events during the 10 sec before and 10 sec after automation-initiated disengagements. Prior to automation-initiated disengagement requests, on average, drivers drove hands-free 78% of the time and rarely had both hands on the steering wheel (3%). Shortly after the onset of disengagement, drivers increased their level of steering wheel control by 53%, grabbing the wheel with at least one hand. A KPSS test on the proportions of hands-free driving indicated that the distribution of hands-free driving was not trend-stationary, but had non-deterministic trends that changed over time (KPSS = 0.952, lag = 5, p< =.01). The PELT changepoint detection algorithm was used to estimate the points in which the statistical properties of the proportions of hands-free driving changed. The analysis yielded two points of change, separating the proportions of hands-free driving after automation disengagement into three segments of trend-stationary periods. Figure 1b, illustrates the segments identified in the proportion of hands-free driving that correspond to lag, response, and recovery time periods. Starting from the onset of an automation disengagement request, the lag period lasted on average 0.6 sec and had proportions of hands-free driving similar to those observed before the disengagement request. Next, a relatively short (0.9 sec) response period was characterized by a sharp decrease in the proportions of hands-free driving. The driver recovery period, represented by stable and low proportions of hands-free driving, started 1.5 sec following the onset of the disengagement request where most of the drivers had at least one hand on the steering wheel. The duration of the recovery period was bounded by the annotation window.