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Chapter 12 Autocorrelation

Autocorrelation refers to the correlation of error terms across observations, commonly found in time-series data, and can be classified as pure or impure based on its causes. It leads to inefficiencies in Ordinary Least Squares (OLS) estimation, resulting in underestimated standard errors and misleading hypothesis testing. Detection methods include graphical analysis, runs tests, and various statistical tests, while remedies involve using Generalized Least Squares (GLS) or adjusting the model through methods like Cochrane-Orcutt.

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18 views7 pages

Chapter 12 Autocorrelation

Autocorrelation refers to the correlation of error terms across observations, commonly found in time-series data, and can be classified as pure or impure based on its causes. It leads to inefficiencies in Ordinary Least Squares (OLS) estimation, resulting in underestimated standard errors and misleading hypothesis testing. Detection methods include graphical analysis, runs tests, and various statistical tests, while remedies involve using Generalized Least Squares (GLS) or adjusting the model through methods like Cochrane-Orcutt.

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paidam2005
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🧠 MIND MAP: AUTOCORRELATION (Ch.

12 – ECO311)
📌 1. Definition (Nature)
Autocorrelation: When error terms are correlated across observations.
Common in time-series data (e.g. GDP, inflation, stock prices).
🔹 Pure autocorrelation: Data problem (even if the model is specified correctly).
🔹 Impure autocorrelation: Due to specification errors.

⚠️ 2. Why Does It Happen?


Inertia in the data (momentum)
Excluded variables / misspecified functional form
Cobweb phenomenon (e.g. price & quantity adjusting over time)
Use of lags
Data manipulation
Transformation errors
Non-stationarity (advanced)

💥 3. Consequences
OLS remains linear and unbiased, but is no longer efficient.
Underestimated standard errors.
Narrower confidence intervals.
T-stats become too large → false rejection of H0H_0
Invalid hypothesis testing

🔍 4. Detection Methods
🔹 1. Graphical Methods
Plot residuals over time
Plot residuals against residuals(-1)

🔹 2. Runs Test (Non-parametric)


Looks at signs of residuals (positive/negative)

🧪 Steps:
1. Note signs (+/-) of residuals
2. Count number of runs (continuous streaks of + or -)
If RR falls outside this interval → autocorrelation exists

🔹 3. Durbin-Watson (DW) d-test


🔹 4. Durbin’s h-test
🔹 5. Breusch-Godfrey (BG) Test
🛠️ 5. Remedies

🧠 EXAM PREP Q&A – AUTOCORRELATION


❓Q1: What is autocorrelation?
A: It's when error terms from different time periods are correlated, violating a key OLS
assumption.

❓Q2: Why is autocorrelation a problem?


A: It makes:

OLS inefficient
Standard errors underestimated
t-stats inflated → misleading conclusions

❓Q3: Which test to use if your model includes lagged Y?


A: Use Durbin’s h-test. DW test is invalid in that case.

❓Q4: How do you interpret DW d-statistic?


d=2d = 2: no autocorrelation
d<2d < 2: positive autocorrelation
d>2d > 2: negative autocorrelation

❓Q5: What are the null and alternative hypotheses in Breusch-Godfrey test?
H0H_0: No autocorrelation
H1H_1: Autocorrelation exists

If test statistic > chi-squared critical → reject H0H_0

❓Q6: What do you do if autocorrelation is found?


A:

Use GLS if pp is known


Estimate p^\hat{p}, and apply:
Cochrane-Orcutt
First-difference method
Robust standard errors

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