Regression Part-8 Autocorrelation

Question 1

What problem do we face with cross-sectional data?

Answer 1

Heteroskedasticity (variance changes with x variable)

Question 2

What problem do we face with time series data?

Answer 2

Auto correlation or serial correlation (when the residual terms are correlated; When observed errors follow a pattern, they are said to be serially correlated or autocorrelated. or when error term from one time period depends on error term from other time period)

Question 3

What is spatial autocorrelation?

Answer 3

When we observe autocorrelation in cross-sectional data. The correlation is observed over space not time

Question 4

What is a cross-sectional data

Answer 4

Cross-sectional data refer to observations of many different individuals (subjects, objects) at a given time, each observation belonging to a different individual

Question 5

What is a time series data?

Answer 5

observations of an entity made over time

Question 6

Why is time series data difficult to deal with?

Answer 6

There is an order to the observations; Smaller dataset than x-sectional data; Autocorrelation troubles

Question 7

What is the difference between autocorrelation and serial correlation

Answer 7

AC - correlation of a series with itself lagged by a few units
SC - Correlation between two series

Question 8

What are some major reasons for autocorrelation?

Answer 8

1. Inertia - TS exhibit business cycles 2. Specification bias (Omitted variable or Incorrect functional form) 3. cobweb phenomenon 4. Lag 5. Data transformation

Question 9

What is a pure serial corelation?

Answer 9

When there is AC in a correctly specified model

Question 10

What is impure serial corelation?

Answer 10

Caused by omitted variable or incorrect functional form

Question 11

What is positive, negative and no serial correlation?

Answer 11

error terms have the same sign from time to time; error terms have the opposite sign from time to time; when errors are completely uncorrelated with each other

Question 12

What are the consequences of serial correlation?

Answer 12

estimators are LUE and not best cuz OLS wont have the minimum variance estimator; R2 is unreliable (overestimate); variance to be underestimated

Question 13

What are the informal and formal tests to test for AC or serial corelation?

Answer 13

Informal - residuals v time; errors
Formal - Durbin Watson test; Runs test; Breusch-Godfrey test

Question 14

What is the DW test?

Answer 14

Tests for AR(1) of error term

Question 15

What are the conditions for DW test?

Answer 15

1. Model to include intercept
2. X variable should be non-stochastic
3. only for first order AC;
4. error normally distributed
5. No lagged variables of Y in model
6. No missing observations

Question 16

What are the DW statistic values?

Answer 16

1. for positive corelation (rho =1) d= 0
2. for negative correlation (rho =-1) d=4
3. for no correlation (rho =0) d is approx 2