Flashcards Econometrics
Alternative Hypothesis
Definition:
The hypothesis that contradicts the null hypothesis. It represents what we expect to be true if the null hypothesis is false.
Example: If the null hypothesis states that the mean income is $50,000, the alternative hypothesis could be that the mean income is different from $50,000.
Importance: It is the hypothesis that researchers typically wish to support.
AR(1) Serial Correlation
Definition: A time series process where the errors are correlated such that each error depends on the previous one.
Mathematical Representation:
Where:
= current error term
= correlation coefficient (between -1 and 1)
= white noise error term.
Importance: It helps in understanding patterns in time series data, often indicating a persistence effect.
Adjusted R-Squared
Definition:
A measure of goodness-of-fit in multiple regression that adjusts the R-squared value by accounting for the number of explanatory variables relative to the number of observations, penalizing for adding variables that don’t improve the model significantly.
Mathematical Representation:
Where:
= R-squared
= number of observations
= number of explanatory variables.
Importance: Adjusted R-Squared provides a more accurate measure of model fit, especially in models with multiple predictors.
Asymptotic Bias
Definition:
The difference between the expected value of an estimator and the true value of the parameter as the sample size approaches infinity.
Importance: It indicates whether an estimator will yield correct results with very large samples.
Asymptotic Confidence Interval
Definition:
A confidence interval that is approximately valid for large sample sizes, relying on the assumption that sample distribution approximates the true distribution.
Importance: Useful when exact confidence intervals are challenging to derive for smaller sample sizes.
Asymptotic Normality
Definition:
The property that, as the sample size increases, the sampling distribution of the estimator converges to a normal distribution.
Importance: It justifies the use of normal-based inference methods in large samples.
Asymptotic Properties
Definition:
Characteristics of estimators that hold when the sample size becomes very large, such as consistency, normality, and efficiency.
Importance: They help in determining the reliability of estimators as sample size increases.
Asymptotic Standard Error
Definition:
The standard error of an estimator that is valid for large samples. It provides an estimate of the variability of an estimator in large samples.
Importance: It is crucial for hypothesis testing and constructing confidence intervals in large samples.
Asymptotic t Statistic
Definition:
A t-statistic that follows an approximate standard normal distribution for large samples.
Importance: It allows for hypothesis testing in large sample scenarios where the exact distribution may be unknown.
Asymptotic Variance
Definition:
The variance of an estimator as the sample size approaches infinity, used to determine the efficiency of an estimator in large samples.
Importance: Lower asymptotic variance implies a more efficient estimator.
Asymptotically Efficient
Definition:
An estimator that has the smallest possible asymptotic variance among all consistent estimators.
Importance: It is the optimal choice for estimation in large samples.
Augmented Dickey-Fuller Test
Definition:
A statistical test used to determine whether a unit root is present in a time series sample. It includes lagged changes of the variable as regressors.
Importance: It is a fundamental test for checking stationarity in time series data.
Attenuation Bias
Definition:
A bias in an estimator that pulls its expected value towards zero, often caused by measurement error in an explanatory variable.
Importance: Attenuation bias leads to underestimating the strength of relationships in regression analysis.
Asymptotically Uncorrelated
Definition:
A time series process where the correlation between observations diminishes as the time interval between them increases.
Importance: It implies a lack of long-term persistence, which simplifies statistical analysis.
Autocorrelation
Definition:
The correlation of a variable with itself over successive time intervals.
Mathematical Representation:
Where:
= autocorrelation coefficient at lag .
Importance: Understanding autocorrelation is essential for identifying trends and dependencies in time
