Neas-Seminars



Time series Mod 6: Bartlett's Test

Posted By NEAS 6/7/2005 1:11:54 PM
Add to Favorites2
Author Message
NEAS
 Posted 6/7/2005 1:11:54 PM
Supreme Being

Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)

Group: Administrators
Last Active: 4/15/2014 9:29:33 AM
Posts: 3,134, Visits: 420

Time Series, Module 6: "Characterizing Time Series: The Autocorrelation Function"

(The attached PDF file has better formatting.)

Bartlett’s Test

Updated: June 7, 2005

 

Jacob: The autocorrelation function of a white noise process is identically zero. Bartlett’s test says that the sample autocorrelations are normally distributed. Which is correct?

Rachel: The autocorrelations are zero; these are the theoretical values. The sample autocorrelations are the observed values; because of random fluctuations, they are not exactly zero. Instead, they are normally distributed with a mean of zero and a standard deviation of 1//T.

Jacob: Why does the distribution of the sample autocorrelations depend on T? Suppose we examine the autocorrelation of lag 10. What difference does it make if the time series have 100 values or 1,000 values?

Rachel: The sample autocorrelation function is an estimate of the autocorrelation function. If the sample is very large, the sample autocorrelations have a mean of zero and a very small standard deviation; this is an unbiased and consistent estimator for a function which is identically zero. If the sample is small, the observed (sample) autocorrelations have random fluctuations that make them diverge from zero. Bartlett’s test tells us how much they diverge from zero.

Jacob: How do we use Bartlett’s test to determine if a time series is a white noise process?

Rachel: Suppose a time series has 400 values, and we observe sample autocorrelations for the first 100 lags. We have 100 numbers for a normal distribution with a mean of 0 and a standard deviation of 1//T = 1/20. Using the cumulative normal distribution table, we infer that 5% of the autocorrelations should have absolute values of 1.96 × (1/20) . 10% or greater. If the actual percentage of 6% or 4%, we presume the time series is a white noise process. If the actual percentage if 15%, we presume the time series is not a white noise process.

 TimeSeries.Module6.intuition.Bertletts.test.pdf (201 views, 32.31 KB)
serina
 Posted 7/8/2005 1:49:51 PM
Junior Member

Junior Member - (12 reputation)Junior Member - (12 reputation)Junior Member - (12 reputation)Junior Member - (12 reputation)Junior Member - (12 reputation)Junior Member - (12 reputation)Junior Member - (12 reputation)Junior Member - (12 reputation)Junior Member - (12 reputation)

Group: Forum Members
Last Active: 8/8/2005 3:43:00 PM
Posts: 7, Visits: 1
12

according to last question:

if the actual percentage >=10%,we presume the time series is not white noise process;

if the actual percentage <10%,we presume the time series is a white noise process. is this right? why?

how to determine if a time series is a white noise process?

thanks in advance.

 

sdexamtaker
 Posted 7/12/2005 8:00:12 PM
Junior Member

Junior Member - (11 reputation)Junior Member - (11 reputation)Junior Member - (11 reputation)Junior Member - (11 reputation)Junior Member - (11 reputation)Junior Member - (11 reputation)Junior Member - (11 reputation)Junior Member - (11 reputation)Junior Member - (11 reputation)

Group: Forum Members
Last Active: 7/21/2005 8:03:00 PM
Posts: 5, Visits: 1
11
See page 496 of the text. If the percentage is greater than 10%, we have a statistically significant chance that the true autocorrellation coefficient is not zero, which would mean it is not a white noice process. If less than 10%, the test would indicate the coefficient is zero, meaning a white noise process is likely for that coefficient. This test only applies to individual autocorrellation coefficients, though.
NEAS
 Posted 12/19/2005 12:03:06 PM
Supreme Being

Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)Supreme Being - (3,942 reputation)

Group: Administrators
Last Active: 4/15/2014 9:29:33 AM
Posts: 3,134, Visits: 420

Jacob: How do we work the Bartlett’s problems? Suppose we have 225 observations and a significance level of 10%.

Rachel: Bartlett’s test uses 2 sided Z values.

We use 2 sided because the sample autocorrelation may be positive or negative.

We use Z values, not t values, since we know the variance if the time series is white noise.

The Z value for a significance level of 10% is 1.645. The standard deviation for a time series with 225 observations is 1 / /225 = 1/15 = 6.67%. The sample autocorrelation at a 90% confidence interval is 1.645 × 6.67% = 10.97% . 11%.

Jacob: Does that mean that if the sample autocorrelation is more than 11% the time series is not white noise?

Rachel: We can make only statistical statements: If the time series is white noise, the probability is less than 10% of getting a sample autocorrelation whose absolute value is more than 11%.

Jacob: Why does the textbook use 5% for the regression analysis course and 10% for the time series course?

Rachel: The textbook says this is the common practice. One rationale is that we can always add observations in most regression analysis projects. If we do a social science study and get a p-value of 8.5%, we say: "Let’s do some more interviews or collect more data to see if we can get a p-value less than 5%."

For time series, we can’t add observations. If we have a time series of 100 quarters, we must wait another five years to get 120 quarters. Many p-values are between 5% and 10%, so we use 10%.

A second rationale is that many regression analysis studies seek true causes. To know what increases sales, we may examine several dozen independent variables. To know the true cause, we use a strong significance level.

Most time series studies are proxies: we don’t know the true causes, but we try to find a simple formula. We do not need to be sure of the time series because it is just a proxy.

A third rationale is that most regression analysis studies are theory. A study may examine why citizens vote Democratic or Republican, looking at a dozen independent variables. The study is aimed at policy wonks and academics, who want to know the true relation. If we are not sure, we just say: "I don’t know."

Most time series studies are aimed at business persons, who want to know whether to raise or lower prices or raise or lower advertising. There is no middle ground. A business person must give a recommendation; one can’t say "I don’t know." We use a less stringent significance level.

yandavi
 Posted 1/7/2010 7:16:12 PM
Forum Member

Forum Member - (27 reputation)Forum Member - (27 reputation)Forum Member - (27 reputation)Forum Member - (27 reputation)Forum Member - (27 reputation)Forum Member - (27 reputation)Forum Member - (27 reputation)Forum Member - (27 reputation)Forum Member - (27 reputation)

Group: Forum Members
Last Active: 1/12/2010 1:31:00 PM
Posts: 27, Visits: 1
27
I agree with Serina.  The way they describe the results (where Rachel speaks) is a bit ambiguous.

Similar Topics

Expand / Collapse

Reading This Topic

Expand / Collapse

Back To Top