In a sample of size 25, you calculate a sample autocorrelation to be 0.35. You need to know if this autocorrelation is statistically significant at the 5% level of significance. Is it? (Keep in mind that the standard error of a sample autocorrelation is 1/(N^0.5), where N is the sample size.

Question

In a sample of size 25, you calculate a sample autocorrelation to be 0.35. You need to know if this autocorrelation is statistically significant at the 5% level of significance. Is it?  (Keep in mind that the standard error of a sample autocorrelation is 1/(N^0.5), where N is the sample size.

BlackTom AI · Accepted Answer

First, identify the given values: a sample size N = 25 and a sample autocorrelation r = 0.35. The standard error of the sample autocorrelation is provided as SE = 1 / sqrt(N) = 1 / 5 = 0.2. Next, compute the test statistic as t = r / SE = 0.35 / 0.2 = 1.75.

Option A: 'Yes, the autocorrelation is statistically significant at the 5% level (t-stat must be 1.96)'. This statement would be true only if the calculated t-statistic met or exceeded 1.96 (for a two-tailed test at 5% significance) or the appropriate critical value for the chosen test. Since 1.75 < 1.96, the t-statistic does not reach the 5% threshold. Therefore, this option incorrectly asserts significance at the 5% level.

Option B: 'No, the autocorrelation is significant at the 10% level (t-stat must be 1.645), but not at the 5% level'. Here, the key is the comparison to the critical values. A t-statistic of 1.75 exceeds 1.645, which means the result would be significant at the 10% level. However, it does not reach 1.96, so it is not significant at the 5% level. This option correctly describes the level at which the result is significant and the level at which it is not.

To summarize the logic in a different framing: compare the computed t = 1.75 to the standard critical thresholds 1.645 (10% level) and 1.96 (5% level). Since 1.645 < 1.75 < 1.96, the outcome sits between those cutoffs. That means it passes the 10% test but fails the 5% test. The conclusion about which option is supported by these comparisons is that the result is not significant at 5% but is significant at 10%.

Similar Questions

What is a fundamental difference between typical time series data and cross-sectional data that violates a standard OLS assumption?

Autocovariance in residuals of time series regression indicates that OLS should never be applied to estimate coefficients

A classical ordinary least squares (OLS) cannot be applied if the dependent variable exhibits autocovariance

If the d-statistic in the Durbin-Watson Test is 0.5,

Consider the following time-series process given by where denotes the lag operator and . What is the lag 3 autocorrelation of , ?

Consider the following time-series process given by where denotes the lag operator and . What is the lag 1 autocorrelation of , ?

Consider the following time-series process given by 𝑦 𝑡 = ( 1 + 0.5 𝐿 + 0.6 𝐿 2 ) 𝜀 𝑡 where 𝐿 denotes the lag operator and 𝜀 𝑡 ∼ 𝑊 𝑁 ( 0 , 3 ) . What is the lag 3 autocorrelation of 𝑦 𝑡 , 𝜌 ( 3 ) ?

Consider the following time-series process given by 𝑦 𝑡 = ( 1 + 0.6 𝐿 + 0.1 𝐿 2 ) 𝜀 𝑡 where 𝐿 denotes the lag operator and 𝜀 𝑡 ∼ 𝑊 𝑁 ( 0 , 8 ) . What is the lag 1 autocorrelation of 𝑦 𝑡 , 𝜌 ( 1 ) ?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler