IID Tests dialog box

 

Use this dialog box to carry independence and identical distribution (iid) tests on data.

 

Input

Specifies the worksheet location of the input data for this operation.

 

Valid Input Range

Provides a reference to the extent of the data available in the currently active worksheet. Use this range as a guide for typing valid extents in the Input Range box.

 

Input Range

Type in this box the range of cells containing the data you want to use as input for this command.

 

Series in Rows

Check this box to indicate that the data specified by the Input Range box is organized in rows as opposed to columns (the default).

 

Refer to Specifying Input Arguments for additional information on this subject.

 

Output

Specifies the worksheet location for placing the results of this operation.

 

New Workbook

Select this option to place the results of this operation in a new document workbook.

 

New Sheet

Select this option to place the results of this operation in a new worksheet.

 

Range Position

Select this option to place the results of this operation starting at the worksheet location specified in the box to the right of this option.

 

Refer to Specifying Output Locations for additional information on this subject.

 

Options

 

Method

Specifies the method used to carry out the test. Select one of the following options:

 

 

Box-Pierce

Box and Pierce (1970) portmanteau test based on the statistic

 

of a finite variance iid sequence , where is approximately distributed as the sum of squares of the independent random variables, , , that is, as a chi-square distribution with degrees of freedom, where the are the sample autocorrelations at lag . Reject the iid hypothesis if

 

,

 

where is the percentile of the chi-square distribution with degrees of freedom.

 

 

Difference Sign

Counts the number, , of values such that , , or equivalently, the number of times the differenced series is positive. For an iid sequence of large , and . Thus is approximately . Reject the iid hypothesis if

 

,

 

where is the percentile of the normal distribution .

 

 

Ljung-Box

Ljung and Box (1978) portmanteau test which replaces the Box-Pierce statistic with

 

,

 

whose distribution better approximates . Reject the iid hypothesis if

 

.

 

 

McLeod-Li

McLeod and Li (1983) portmanteau test based on the statistic of Ljung-Box, but replaces the sample autocorrelation of the data with the sample autocorrelation of the squared data, , giving

 

.

 

Reject the iid hypothesis if

 

.

 

 

Rank

Kendall and Stuart (1976) test which defines as the count of the number of pairs such that , , . For a total of pairs such that in an iid sequence , of large , each event has probability 0.5 and thus the mean of is therefore , and its variance . Thus is approximately . Reject the iid hypothesis if

 

.

 

 

Turning Point

For a sequence of observations, it can be said that there is a turning point at time , , if or . For large , if is the number of turning points of an iid sequence, then the expected value of is , since the probability of a turning point at time is , and its variance . It can be said that is approximately . Reject the iid hypothesis if

 

.

 

 

Maximum Lag

Maximum lag to which the sample autocorrelation function is calculated for the portmanteau methods.

 

 

Degrees of Freedom

Specifies the degrees of freedom of the chi-square distribution on the portmanteau tests. If this value is set to zero, Maximum Lag is used for the number of degrees of freedom of theoretical chi-square distribution. To indicate a different value, type the number of degrees of freedom in this box as an integer greater than zero and smaller than or equal to Maximum Lag.

 

 

Significance Level

Specifies the significance level, , of the underlying distribution at which to reject the iid hypothesis. Type in this box the significance level you want to assign to the test.

 

 

OK

Closes the dialog box and carries out this operation.

 

Cancel

Closes the dialog box without carrying out this operation.

 

 

Sample Output

 

 

For the sample output shown, we reject the iid hypothesis because Q > Q-Critical.