Abstract
Temporal autocorrelation (also called serial correlation) refers to the relationship between successive values (i.e. lags) of the same variable. Although it has long been a major concern in time series models, however, in-depth treatments of temporal autocorrelation in modeling vehicle crash data are lacking. This paper presents several test statistics to detect the amount of temporal autocorrelation and its level of significance in crash data. The tests employed are: 1) the Durbin-Watson (DW); 2) the Breusch-Godfrey (LM); and 3) the Ljung-Box Q (LBQ). When temporal autocorrelation is statistically significant in crash data, it could adversely bias the parameter estimates. As such, if present, temporal autocorrelation should be removed prior to use the data in crash modeling. Two procedures are presented in this paper to remove the temporal autocorrelation: 1) Differencing; and 2) the Cochrane-Orcutt method.
Highlights
Temporal autocorrelation is a special case of correlation, and refers not to the relationship between two or more variables, but to the relationship between successive values of the same variable
Temporal autocorrelation refers to the relationship between successive values of the same variable. It is a major concern in time series models, it is very important to be checked in crash data modeling as well
There are several methods that can be used to detect the existence of the temporal autocorrelation in the crash dataset, such as: 1) the residuals scatter plots; 2) the Durbin-Watson (DW) test; 3) the Durbin h test; 4) the Breusch-Godfrey (LM) test; 5) the Ljung-Box Q (LBQ) test; and 6) correlograms
Summary
Temporal autocorrelation (i.e. serial correlation) is a special case of correlation, and refers not to the relationship between two or more variables, but to the relationship between successive values of the same variable. The presence of correlated error terms means that these types of inferences cannot be made reliably [2] The violation of this assumption occurs because of some temporal (time) component (i.e. heterogeneity due to time) that can affect the observations drawn across the time, such as time series data, panel data in the form of serial correlation, and any other dataset that might be collected over a period of time. If there are factors responsible for inflating the observation at some point in time to an extent larger than expected (i.e. a positive error), it is reasonable to expect that the effects of those same factors linger creating an upward (positive) bias in the error term of a subsequent period This phenomenon is called positive first-order autocorrelation, which is the most common manner in which the assumption of independence of errors is violated. If the temporal autocorrelation is found to be significant in crash data, it must be removed before using the data in the modeling process [4] [5] [6]
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