in the time series analysis chapter of scheweser. it says that in order to test the correlation of residuals you apply this formula which has 1/T as the standard error. Here it says that T is basically the initial observations in the data minus the order of regressive function. So if there were 50 observations and it is a AR(1) function. then T is 49. But in the example it also says that a function such as xt= x(t-1) + x(t-4). is Ar(1) function with a seasonal lag not a AR(2) function but calculates T by subtracting from the initial observation. So basically how do you find out T? in various situations? in the function such as above. Secondly it says that degree freedom is (T-2). is it alsways the case or is its actually T-k-1 depending ont he numebr of variables??? I hope i havent made it sound to complicated??
floyd, there are 3 things here 1) get t-statistics of the autocorrelations for different lags 2) get critical t values for those autocorrelations from t table 3) compare t-statistics from step 1 with t critical value from step 2, to reject or fail to reject your hypothesis. For 1) Mostly, t-statistics of the autocorrelations would be provided by the model and would be given in the table. But, if in the exam, it is not provided, then it could be calculated as the (autocorrelation value / standard error) where, standard error = 1 / sqrt T Here T is the number of observations. (NO adjustment to T here for any degrees of freedom) For 2) It is for getting the Critical t value from the t table, that you would need degrees of freedom. And degrees of freedom would be n-k-1. (where k is the number of independent variables and ‘-1’ is for the ‘intercept’) To answer your confusion, you dont need to use degree of freedom to calculate standard error in step 1. You just need degrees of freedom in step 2 to get t critical value from the t table.
rusbus I think I got part 2 but part 1 i think you may be under some confusion about part1. lets say if you have 3 values from data about erm number of cars on road. and you want to use a one lagged function on it. that is c(t)= c(t-1) +Z then you can only plot 2 data points on the graph understand? these would be these would be the third value against the second and the second against the first. And you have to find the regression line that best passes through this plots. SO u lose one observation. this is my uderstanding of it. and scweser has does it as well if you look the example there were 40 observations n he took 39. secondly what i dont understand how many will u lose if it is a function such as xt= x(t-1) + x(t-4). Here it says that T is basically the initial observations in the data minus the order of regressive function. So if there were 50 observations and it is a AR(1) function. then T is 49. But in the example it also says that a function such as xt= x(t-1) + x(t-4). is Ar(1) function with a seasonal lag not a AR(2) function but it calculates T by subtracting 2 and not 1 from the initial observation. for this case got it?
i may also point out that if the question directly gives the observations n not intial data then u dont need to chanege
floyd, here is general theory. 1) Come up with estimate (formula). 2) Figure out distribution of the estimate 3) Based on the distribution come up with confidence interval/critical values 4) Compare value of the estimate to critical value. In case of auto-correlation coefficient estimates, their distributions have mean of 0 and variance of 1/T (for any lag in iid case of returns) -> 1/sqrt(T) is used. In case of regressions, variance of the estimate depends of 1/(T-k-1) -> T-k-1 is used. I have to go to a meeting. Hope, that helps.
the question what exactly is T? please read above post to see my question
floyd Wrote: ------------------------------------------------------- > the question what exactly is T? please read above > post to see my question T is the number of observation. You should use the appropriate statistic based on the distribution of the estimate. Variance of the autocorrelation estimate is 1/T -> use that.