Interpreting Residuals and D-value

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Questions and Answers

What are the consequences of using ordinary least squares procedures when the error terms in the regression model are positively autocorrelated?

The estimated regression coefficients become biased and have the minimum variance property.

The MSE overestimates the variance of the error terms.

The s(bk) calculated according to ordinary least squares procedures overestimates the true standard deviation of the estimated regression coefficient.

The estimated regression coefficients are still unbiased, but they no longer have the minimum variance property and may be quite inefficient. (correct)

What is a major cause of positively autocorrelated error terms in business and economic regression applications involving time series data?

Inclusion of all relevant variables in the model.

Application of independent normal random variables.

Use of ordinary least squares procedures.

Omission of one or several key variables from the model. (correct)

What is a characteristic of error terms correlated over time in time series data?

They have independent distributions at each time point.

They are always normally distributed.

They do not affect regression applications involving time series data.

They are said to be autocorrelated or serially correlated. (correct)

What assumption about error terms is often not appropriate for regression applications involving time series data?

The assumption of uncorrelated or independent error terms. Signup and view all the answers

When the residuals are uncorrelated, what is the approximate value of D?

$D \approx 2$ Signup and view all the answers

If the residuals are positively correlated, what is the relationship between D and 2?

$D < 2$ Signup and view all the answers

In the example provided in the text, what type of correlation were the residuals found to have when using a straight-line model to predict sales data over a 35-year period?

Positively correlated Signup and view all the answers

What are the remedial measures suggested once residual correlation has been established?

Adding more predictor variables or using transformed variables Signup and view all the answers

What does the Breusch-Godfrey Test involve for testing autocorrelation in error terms?

Estimating the linear regression model, obtaining the residuals, and regressing them on all regressors from the initial model Signup and view all the answers

What is a common cause of autocorrelated error terms?

Omission of key predictor variables Signup and view all the answers

What do the Cochrane-Orcutt and Hildreth-Lu procedures estimate in relation to autocorrelation?

The autocorrelation parameter $\rho$ required for transformation Signup and view all the answers

How are transformed variables obtained in relation to addressing autocorrelated errors?

By subtracting a fraction of the previous value from the current value Signup and view all the answers

How can one estimate the transformed model when dealing with autocorrelated errors?

Using ordinary least squares methods Signup and view all the answers

What is the equation for the autoregressive error regression model discussed in the text?

$Y_t = \beta_0 + \beta_1 X_t + u_t$, where $u_t = \rho u_{t-1} + v_t Signup and view all the answers

What method involves finding the value of $\rho$ that minimizes the Sum of Squared Errors (SSE) to examine if the transformation has eliminated autocorrelation?

Method One Signup and view all the answers

Which type of financial data has the dimensions of both time series and cross-sectional data?

Panel data Signup and view all the answers

What does Method Two, the First Differences Procedure, assume about $\rho$?

$\rho \approx 1$ Signup and view all the answers

What is the key characteristic of financial data mentioned in the text?

Noisy and non-normal Signup and view all the answers

Which method uses recursive residuals to estimate the autoregressive parameter and transform the data accordingly?

Method Two Signup and view all the answers

Which method can be used to convert asset prices into returns?

Log method Signup and view all the answers

What is a disadvantage of log returns?

The sum of log returns is not the same as the log of the sum of returns Signup and view all the answers

What are the steps involved in building an econometric model?

Stating the problem, collecting data, choosing estimation method, evaluating statistically, theoretically, and using the model Signup and view all the answers

What should be checked when reading articles in empirical finance?

Motivation and data quality Signup and view all the answers

What does EViews offer for time series analysis?

Diagnostic tests and simplicity Signup and view all the answers

What are potential violations of assumptions in the Constant Linear Regression Model (CLRM)?

Mean, variance, non-stochastic X matrix, homoscedasticity Signup and view all the answers

What should be done when violations of CLRM assumptions are detected?

Investigate causes and consequences, test for violations of assumptions Signup and view all the answers

What do research results depend on?

Data quality and research design Signup and view all the answers

In what ways can log returns be interpreted?

As continuously compounded returns Signup and view all the answers

What is the Durbin-Watson test used for?

To determine if the autocorrelation parameter (ρ) is zero Signup and view all the answers

What does a first-order autoregressive error model refer to?

A generalized multiple regression model with error terms following an AR(1) process Signup and view all the answers

What property affects the estimation of regression coefficients in the first-order autoregressive error model?

Autocorrelation Signup and view all the answers

How can the presence of autocorrelated errors be detected?

Through a plot of residuals against time and formal statistical tests like the Durbin-Watson Test Signup and view all the answers

What does the autocorrelation parameter (ρ) determine in the first-order autoregressive error model?

The correlation between error terms at different time points Signup and view all the answers

What is a consequence of positively autocorrelated error terms in a simple linear regression model with time series data?

Indication of greater precision of regression coefficients than is actually the case when OLS methods are used Signup and view all the answers

What does the variance-covariance matrix of the error terms for the first-order autoregressive generalized regression model depend on?

The autocorrelation parameter and the variance of the error terms. Signup and view all the answers

What does a small value of the Durbin-Watson test statistic indicate?

The presence of autocorrelation in the error terms. Signup and view all the answers

Study Notes

Simple linear regression model with time series data has positively autocorrelated error terms, which affect the applicability of confidence intervals and tests using t and F distributions.
Positively autocorrelated error terms show a systematic pattern and can lead to an indication of greater precision of regression coefficients than is actually the case when OLS methods are used.
The presence of autocorrelated errors can be detected through a plot of residuals against time and formal statistical tests like the Durbin-Watson Test.
The Durbin-Watson Test is a widely used test for the first-order autoregressive error model to determine if the autocorrelation parameter () is zero, indicating independent error terms.
The first-order autoregressive error model is a generalized multiple regression model where the random error terms follow a first-order autoregressive (AR(1)) process.
The properties of error terms for the first-order autoregressive error model include a non-zero mean, variance, and autocorrelation, which affect the estimation of the regression coefficients.
The autocorrelation parameter () is the coefficient of correlation between adjacent error terms and determines the correlation between error terms at different time points.
The variance-covariance matrix of the error terms for the first-order autoregressive generalized regression model can be stated in terms of the autocorrelation parameter and the variance of the error terms.
The Durbin-Watson test statistic is based on the comparison of the sum of the squared residuals at different time points and is used to assess the presence of a significant autocorrelation in the error terms.
The decision rule for the Durbin-Watson test depends on the alternative hypothesis and the critical values obtained from the test. Small values of the test statistic indicate the presence of autocorrelation.

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Description

This quiz covers the interpretation of residuals and the D-value in the context of correlation. It explains how different levels of correlation between residuals affect the D-value, providing a range and specific values for different correlation scenarios.