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# P1.T2.509. Box-Pierce and Ljung-Box Q-statistics

#### Nicole Seaman

##### Chief Admin Officer
Staff member
Subscriber
Learning outcomes: Calculate the sample mean and sample autocorrelation, and describe the Box-Pierce Q- statistic and the Ljung-Box Q-statistic. Describe sample partial autocorrelation

Questions:

509.1. If a time series is reasonably approximated as white noise, then each of the following is true EXCEPT which is not true of a white noise process?

a. Serial correlations (aka, autocorrelations) are zero
b. Observations in the time series are normally distributed
c. In a large sample, the distribution of the sample autocorrelations is approximately normal with mean of zero
d. In a large sample, the distribution of the sample autocorrelations is approximately normal with variance of 1/T

509.2. For a certain time series, you have produced a correlogram with an autocorrelation function that includes twenty four monthly observations; m = degrees of freedom = 24. Your calculated Box-Pierce Q-statistic is 19.50 and your calculated Ljung-Box Q-statistic is 27.90. You want to determined if the series is
white noise. Which is your best conclusion (please note this requires a lookup)?

a. With 95.0% confidence, you accept the series as white noise (more accurately, you fail to reject the null)
b. With 95.0% confidence, you accept the series as partial white noise (due to Box-Pierce) but reject the null (due to Ljung-Box)
c. With 95.0% confidence, you reject both null hypotheses and conclude the series is not white noise
d. With 95.0% confidence, you reject both null hypotheses but conclude the series is white noise because the sum of the statistics is greater than the critical value

509.3. In regard to the Box-Pierce and Ljung-Box Q-statistics, each of the following is TRUE except which is false?

a. The Box-Pierce Q-statistic is used to test whether the residuals in a time series are white noise
b. The Ljung-Box Q-statistic is used to test whether a time series exhibits a linear trend under the null hypothesis of a unit root
c. The Box-Pierce Q-statistic is approximately distributed as a chi-squared random variable under the null hypothesis that autocorrelations are jointly zero in a time series
d. Selection of the number of lags being tested (aka, maximum displacement, m) in the Ljung-Box test is a balance between conducting a joint test (i.e., can't be too small) and quality of the distribution approximations (i.e., can't be too large)

Answers here:

#### kbaradzina

##### New Member
Hello, where could I find the answers to these questions? Thank you in advance! Kind regards

Learning outcomes: Calculate the sample mean and sample autocorrelation, and describe the Box-Pierce Q- statistic and the Ljung-Box Q-statistic. Describe sample partial autocorrelation

Questions:

509.1. If a time series is reasonably approximated as white noise, then each of the following is true EXCEPT which is not true of a white noise process?

a. Serial correlations (aka, autocorrelations) are zero
b. Observations in the time series are normally distributed
c. In a large sample, the distribution of the sample autocorrelations is approximately normal with mean of zero
d. In a large sample, the distribution of the sample autocorrelations is approximately normal with variance of 1/T

509.2. For a certain time series, you have produced a correlogram with an autocorrelation function that includes twenty four monthly observations; m = degrees of freedom = 24. Your calculated Box-Pierce Q-statistic is 19.50 and your calculated Ljung-Box Q-statistic is 27.90. You want to determined if the series is
white noise. Which is your best conclusion (please note this requires a lookup)?

a. With 95.0% confidence, you accept the series as white noise (more accurately, you fail to reject the null)
b. With 95.0% confidence, you accept the series as partial white noise (due to Box-Pierce) but reject the null (due to Ljung-Box)
c. With 95.0% confidence, you reject both null hypotheses and conclude the series is not white noise
d. With 95.0% confidence, you reject both null hypotheses but conclude the series is white noise because the sum of the statistics is greater than the critical value

509.3. In regard to the Box-Pierce and Ljung-Box Q-statistics, each of the following is TRUE except which is false?

a. The Box-Pierce Q-statistic is used to test whether the residuals in a time series are white noise
b. The Ljung-Box Q-statistic is used to test whether a time series exhibits a linear trend under the null hypothesis of a unit root
c. The Box-Pierce Q-statistic is approximately distributed as a chi-squared random variable under the null hypothesis that autocorrelations are jointly zero in a time series
d. Selection of the number of lags being tested (aka, maximum displacement, m) in the Ljung-Box test is a balance between conducting a joint test (i.e., can't be too small) and quality of the distribution approximations (i.e., can't be too large)

Answers here:I

#### Nicole Seaman

##### Chief Admin Officer
Staff member
Subscriber
Hello, where could I find the answers to these questions? Thank you in advance! Kind regards
Hello @kbaradzina

Thank you for using Bionic Turtle! The answers to these questions are accessed by clicking on the "Answers here: In forum" link at the end of the original post above. However, the answers and explanations are only available to paid members, as they are part of our FRM study packages. You can view all of our study packages here on our Features & Pricing page: https://www.bionicturtle.com/features-pricing-2/. Each of our study packages includes full access to the free and paid sections of the forum. Please let me know if have any other questions about the study prep services that we offer. Thank you,

Nicole