Relative efficiency of count of sign changes for assessing residual autoregression in least squares regression

摘要: SUMMARY From a constructed example of 100 random samples size 40, in conjunction with the author's ACV method for comparing relative efficiency different tests significance, it is found that simple count sign changes nearly as efficient familiar DurbinWatson test autoregression residuals. Individual decisions based on this are closely similar to those from number runs test. On another actual body data three seem be about equally efficient. A table supplied giving cumulative binomial probabilities assessing significance Probably most workers multivariate regression time series, who computerless, or without von Neumann subprogram their computer, adopt practice counting amongst residuals, purpose probable presence autoregression. If few, residual inferred, i.e. not satisfactory because some significant independent variables have been omitted, linear form assumed valid, etc. The rational; if T sets observations and signs, plus minus, sequence order, frequency r will (T- 1)!/{r!(T- 1 --)!}, total (2T-1 1) almost p = 1. - I arises all signs same inadmissible since sum residuals zero. Incidentally, latter constraint implies values cannot one another, assumed, regards changes, use binomial. With these, effect believed negligible when small, ignored here. main object present note assess compared d statistic developed by Durbin & Watson (1950, 1951). As writer unable cope problem noncentral algebra, recourse made Monte Carlo applied single particular case.