Model Selection I

The precision of prognostications, deductions, and interpretations hinges heavily upon the precise model elected. Hence, if this step is bypassed and analysis is commenced directly (which might encompass estimation or hypothesis testing, for instance), the fruits of one’s labor could potentially dissipate.

According to Hendry and Richard (1983), a model chosen for empirical analysis should satisfy the following criteria:

• Ensure admissibility of the data

• Align with established theory

• Contain weakly exogenous regressors

• Demonstrate parameter constancy

• Exhibit data coherency

• Be encompassing

• Omission of relevant variable(s)

• Including unnecessary variable(s)

• Adoption of wrong functional form

• Errors of measurement

• Incorrect specification of the stochastic error term

To identify the specification errors one can choose either “mechanical choice methods” or “theory based approaches”.

The presence of omitted variables introducing bias in the OLS estimator. 

it leads to overfitting of the model

1) Conduct an F-test for the joint hypothesis.

2) If the null hypothesis is rejected (indicating evidence against linearity), proceed to perform individual t-tests for each coefficient. 

What equation (2.7) states is that instead of utilizing the true values of Yi and Xi , we substitute them with their proxies, Yi * and X1 * , which might contain measurement errors. Therefore, in Equation (2.7), we introduce the bias of measurement errors.

In-sample forecasting provides insights into how well the chosen model fits the data within a specific sample. On the other hand, out-of-sample forecasting focuses on evaluating how effectively a fitted model predicts future values of the dependent variable, considering the given values of the independent variables.

Goodness of fit is a statistical measure that evaluates how effectively a model aligns with or represents the observed data. It quantifies the level of agreement between the predicted values generated by a model and the actual values observed within a dataset.

By examination of residuals

The CV estimate of variance is a method used to estimate the variance or error in a regression model by employing CV techniques.

It aims to provide a more robust and accurate estimate of the model’s error compared to traditional methods.

The CV estimate of variance is calculated by taking the average of the squared residuals across all folds and dividing it by the degrees of freedom. The degrees of freedom are typically adjusted to account for the number of model parameters estimated.

Skewness measures the lack of symmetry in a distribution.

The skewness of Y is determined by its first, second, and third moments.

Because the probabilities of observing values of Y above and below its mean are equal.

Positive skewness

Negative skewness

Measureing the extent to which the variance of the variable Y is influenced by extreme values.