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

Question

BlackTom AI · Accepted Answer

Question restatement: If the d-statistic in the Durbin-Watson Test is 0.5, which statement is implied by the result?

Option a: 'we do not reject the null hypothesis.' In the Durbin-Watson framework, the null hypothesis typically posits no first-order serial correlation in the residuals. A DW value as low as 0.5 suggests a strong positive autocorrelation, making it unlikely to fail to reject the null. Therefore, this option is inconsistent with a DW of 0.5.

Option b: 'there is no serial correlation in the residuals.' This directly contradicts the meaning of a very small DW statistic. A value near 0 indicates strong positive serial correlation, not the absence of it. Hence this statement is incorrect for a DW of 0.5.

Option c: 'there are some problems about the test.' While no statistical test is perfect, this option is vague and does not address the specific interpretation of a DW value of 0.5. The question asks for what the statistic indicates about residuals, not about test validity. This makes the statement not informative about the result indicated by 0.5.

Option d: 'there is serial correlation in the residuals.' This is the direct, correct interpretation for a low Durbin-Watson value like 0.5. A small DW statistic signals positive first-order autocorrelation in the residuals, meaning successive residuals are correlated rather than independent. This aligns with the typical interpretation of DW values significantly below 2.

Additional context to reinforce understanding: The Durbin-Watson statistic ranges from 0 to 4. A value around 2 suggests no autocorrelation. Values substantially below 2 imply positive autocorrelation, while values substantially above 2 imply negative autocorrelation. A DW of 0.5 is far from 2 and points toward meaningful positive serial correlation in the error terms, which has implications for standard errors and model specification. However, the exact decision against a null hypothesis would depend on critical value tables or p-values for the sample size and number of regressors. In any case, the direction indicated by 0.5 is consistent with the presence of serial correlation in residuals, rather than its absence.

ECON7950 (1) [2024 B2] In-Class Quiz 2

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

View Explanation

Log in for full answers

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

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.

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