Time Series Analysis and Tests Quiz

A statistical test used to determine the presence of heteroscedasticity in a regression model. It involves splitting the sample into two sub-samples and comparing the variances of the residuals from each sub-sample.

The ratio of the two residual variances from the two sub-samples in the Goldfeld-Quandt test. The larger variance should be placed in the numerator.

The null hypothesis in the Goldfeld-Quandt test, stating that the variances of the disturbances in the regression model are equal across different values of the independent variable.

The alternative hypothesis in the Goldfeld-Quandt test, stating that the variances of the disturbances in the regression model are unequal across different values of the independent variable.

A statistical test for heteroscedasticity that makes few assumptions about the form of the heteroscedasticity. It involves regressing the squared residuals on the explanatory variables and their squares and cross-products.

The auxiliary regression used in White's test, where the squared residuals are regressed on the explanatory variables and their squares and cross-products. The R-squared from this regression is then used to create a test statistic.

The value calculated in White's test by multiplying the R-squared from the auxiliary regression by the number of observations. It follows a chi-square distribution under the null hypothesis of homoscedasticity.

The degrees of freedom for the chi-square distribution used in White's test. It is equal to the number of regressors in the auxiliary regression excluding the constant term.

A lagged value is a past value of a variable. It is the value of the variable at a previous point in time.

Autocorrelation occurs when the errors in a regression model are correlated with each other over time. This means that the errors are not independent, and there is a pattern or relationship in the residual values.

Positive autocorrelation is characterized by a cyclical residual plot, where the errors tend to follow a wave-like pattern.

Autocorrelation violates the assumption of independent errors in the classical linear regression model. This violation can lead to biased and inconsistent estimates of the regression coefficients, making the model unreliable.

Autocorrelation is often detected by examining the residual plots over time, looking for patterns. Formal tests like the Durbin-Watson test can also be used to detect autocorrelation.

A statistical test used to determine if the variances of two or more groups are equal. The purpose is to determine whether there is enough evidence to reject the assumption of equal variances.

A statistical property where the variance of the error term is constant across all values of the independent variables in a regression model.

A statistical property where the variance of the error term is NOT constant across all values of the independent variables in a regression model.

A statistical method for estimating the coefficients of a linear regression model that assumes the error terms have a constant variance.

The OLS estimator is the Best Linear Unbiased Estimator (BLUE) when certain assumptions are met (no perfect multicollinearity, homoscedasticity, and no autocorrelation of errors)

The standard errors calculated from OLS may be inaccurate in the presence of heteroscedasticity, leading to misleading inferential conclusions.

A statistical method that addresses heteroscedasticity by transforming the regression equation to ensure homoscedasticity. It's a generalized version of OLS.

A method to correct for heteroscedasticity by dividing the regression equation by the variable that is causing the heteroscedasticity.

A regression test that determines if parameters in a model are stable over time.

The statistic used in the Chow Test to determine the stability of regression parameters over time. Calculated by comparing the RSS from the full sample to RSS from the sub-samples.

The null hypothesis in the Chow Test, implying the same regression parameters apply across both time periods.

The alternative hypothesis in the Chow Test, indicating that the regression parameters differ between the two time periods.

The degrees of freedom associated with the F-distribution used to assess the Chow Test statistic, determined by the number of regressors (k) and the number of observations (T).

A test that checks if there is a correlation between the error terms at different time points, suggesting a pattern in the residuals.

The assumption that the error terms at different time points are independent of each other, meaning that the value of one error term doesn't affect the value of another.

The test statistic that measures the correlation between the error terms at different time points. It follows a Chi-squared distribution with degrees of freedom equal to the order of the autocorrelation.

The condition where the regression coefficients are biased and inefficient due to the presence of autocorrelation, leading to unreliable standard errors and inaccurate statistical inferences.

A method that accounts for autocorrelated residuals by incorporating the known pattern of autocorrelation in the model. This helps to obtain unbiased and efficient coefficient estimates.

The condition where the explanatory variables are strongly correlated with each other, making it difficult to isolate the individual effects of each variable on the dependent variable.

The perfect linear relationship between two or more explanatory variables, which makes it impossible to estimate all coefficients in the regression model.

A situation where explanatory variables are highly correlated, leading to unstable coefficients with large standard errors, even though the model might fit the data well.

A simple way to assess multicollinearity by examining the correlation coefficients between independent variables. High correlations (close to -1 or 1) indicate potential multicollinearity.

A measure of how much the variance of an estimated regression coefficient is inflated due to multicollinearity. A higher VIF indicates a larger effect of multicollinearity.

A statistical test used to check if the functional form (linear, quadratic, etc.) of a regression model is correctly specified. It involves adding higher-order terms of the fitted values to an auxiliary regression.

The process of dropping one or more highly correlated independent variables from a regression model to reduce multicollinearity. This can lead to a simpler model.

Transforming highly correlated variables into ratios to reduce multicollinearity. This can change the interpretation of the coefficients.

Collecting more data points to reduce multicollinearity, potentially by increasing the time span or using a higher frequency of data.

A situation where the assumptions of a classical linear regression model are violated because the error terms (residuals) are correlated with each other.