HELP Please!!
Sample autocorrelations at lag1, lag2, and lag3 denoted by r1, r2, and r3 of weekly sales of shampoo bottles was found 0.4551, 0.3376, and 0.2514. Using the criteria of your text, the maximum number (‘n’) of weeks for shampoo bottles sales to be stationary will be
a.104 b.52 c.140
d.None of them
To find the maximum number of weeks for shampoo bottle sales to be stationary using the given sample autocorrelations, we need to refer to a specific criterion. One common criterion is the Box-Jenkins criteria, which suggests that if the absolute values of the sample autocorrelations at lag1, lag2, and lag3 decrease slowly, then the time series is non-stationary.
The Box-Jenkins criteria states that in a stationary time series, the sample autocorrelations should decrease rapidly towards zero.
In this case, the sample autocorrelations at lag1, lag2, and lag3 are given as:
r1 = 0.4551
r2 = 0.3376
r3 = 0.2514
To apply the Box-Jenkins criteria, we need to check if the absolute values of these autocorrelations decrease slowly or not.
Let's calculate the differences between each autocorrelation:
|r1 - r2| = |0.4551 - 0.3376| = 0.1175
|r2 - r3| = |0.3376 - 0.2514| = 0.0862
If the differences between each autocorrelation are less than 0.1 (a common threshold), then the time series can be considered stationary. Otherwise, it is non-stationary.
In this case, the difference between r1 and r2 is 0.1175, which is greater than 0.1. Thus, the time series is non-stationary.
Therefore, the correct answer is d. None of them.