Time Series #1

Question 1

What are time series data?

Answer 1

Observations of a variable over time, often correlated across time (serial correlation).

Question 2

What is serial correlation (autocorrelation)?

Answer 2

The correlation of a time-series variable with its lagged values.

Question 3

What are common frequencies of time-series data?

Answer 3

Intra-day, daily, monthly, quarterly, annually etc.

Question 4

How do time-series differ from cross-sectional data?

Answer 4

1. Indexed by time (t) rather than entities (i).
2. Observations are inherently sequential.
3. Bound by start and end dates.

Question 5

What kinds of patterns might time-series exhibit?

Answer 5

Trends, seasonality, cycles and random noise.

Question 6

How are time-series used in finance?

Answer 6

1. Forecasting asset prices
2. Testing financial models like CAPM
3. Measuring volatility
4. Analyzing market efficiency

Question 7

What is the linear model assumption for CLRM?

Answer 7

Yt = α + βXt + Ut

Question 8

What does the random sample assumption state?

Answer 8

Covariance across the residuals must be zero, ensuring no serial correlation.

Question 9

What does the sample variation assumption ensure?

Answer 9

Variance is larger than 0, requiring variability in X.

Question 10

What is the no endogeneity assumption?

Answer 10

Xt and Ut have to be uncorrelated.

Question 11

What is the homoskedasticity assumption?

Answer 11

The variance of errors has to be constant.

Question 12

What is the normality assumption?

Answer 12

The residuals have to be normally distributed, to ensure reliable hypothesis testing.

Question 13

What happens to small and large samples if the normality assumption is violated?

Answer 13

Small sample results become unreliable, however, large samples allow the drop of normality assumption.

Question 14

Why is having no endogeneity in time-series challenging?

Answer 14

Endogeneity often occurs, with Xt and Yt determined simultaneously.

Question 15

What is asymptotic normality?

Answer 15

With large T, the OLS estimates are approximately normally distributed, even without assuming normality.

Question 16

How is normality tested?

Answer 16

Using the Jarque-Bera test, which checks skewness and kurtosis.

Question 17

What does a JB test statistic represent?

Answer 17

It compares the residual distribution’s skewness and kurtosis to a normal distribution.

Question 18

What does a JB test result indicate?

Answer 18

A high JB statistic or a low p-value indicates that the residuals deviate from normality.
If the p-value is above the significance threshold, normality is not rejected.

Question 19

What does it mean if the JB test shows borderline rejection of normality?

Answer 19

It suggests slight deviations from normality, which may be acceptable in large samples but could affect small-sample reliability.

Question 20

What are alternatives if normality is rejected?

Answer 20

1. Transform variables with logs f.e.
2. Winsorize data: use lower and upper bounds
3. Use dummy variables for outliers to exclude them

Question 21

Why does normality matter more for small samples?

Answer 21

Non-normal errors distort hypothesis tests when sample size is insufficient.

Question 22

How do we detect serial correlation?

Answer 22

Using the Breusch-Godfrey test or residual autocorrelation plots.

Question 23

How do you interpret the results of a Breusch-Godfrey test?

Answer 23

If the test statistic exceeds the critical value or the p-value is below the significance level, reject the null hypothesis of no serial correlation. This suggests that autocorrelation exists in the residuals.

Question 24

What are common patterns in residual plots?

Answer 24

1. Cyclical patterns: positive autocorrelation
2. Alternating signs: negative autocorrelation
3. Random scatter: no autocorrelation

Question 25

What are the consequences of serial correlation?

Answer 25

The OLS estimators are inefficient, which means they didn’t choose the smallest variance. This means the standard errors are biased.

Question 26

How is serial correlation corrected?

Answer 26

1. Newey-west standard errors
2. Adding lagged variables to the model

Question 27

What is the Newey-West adjustment?

Answer 27

A correction for standard errors to account for heteroskedasticity and autocorrelation.

Question 28

What are the limitations of Newey-West corrections?

Answer 28

They perform poorly in small samples and require careful lag selection.

Question 29

What do significant results in a serial correlation test imply for a regression model?

Answer 29

The presence of serial correlation indicates that the error terms are not independent. This violates CLRM assumptions and necessitates corrections, such as Newey-West standard errors.

Question 30

How do you interpret corrected standard errors after applying Newey-West adjustments?

Answer 30

Larger standard errors suggest that the original estimates underestimated variability due to serial correlation or heteroskedasticity. Interpretation of coefficients should account for this adjustment.

Question 31

What does it mean if the Newey-West standard errors change significance levels of coefficients?

Answer 31

This indicates that serial correlation or heteroskedasticity significantly impacted the original standard errors. The corrected significance levels are more reliable.

Question 32

How should deviations from normality in residuals impact model interpretation?

Answer 32

In small samples, non-normality can invalidate hypothesis tests. In large samples, reliance on asymptotic normality may still permit valid inference.

Question 33

What is stationarity?

Answer 33

A time series with constant mean, variance and autocorrelation over time.

Question 34

Why is stationarity important?

Answer 34

Non-stationary data lead to spurious regressions.

Question 35

What are common causes of non-stationarity?

Answer 35

Trends, seasonality and structural breaks.

Question 36

How is stationarity tested?

Answer 36

Using tests like the Augmented Dickey-Fuller test.

Question 37

How can non-stationarity be addressed?

Answer 37

By differencing the data or detrending.

Question 38

How are structural breaks identified?

Answer 38

By splitting the sample into subperiods or observing residual patterns.

Question 39

What is the Chow test?

Answer 39

A method to test if coefficients differ across subperiods.

Question 40

How should you interpret the results of a Chow test?

Answer 40

If the null hypothesis is rejected, it indicates that the parameters are not stable across the subperiods, suggesting structural breaks in the relationship.

Question 41

What are examples of structural breaks in finance?

Answer 41

Market crashes or policy changes.

Question 42

Why test for parameter stability?

Answer 42

To ensure coefficients represent consistent relationships over time.

Question 43

What does parameter instability indicate?

Answer 43

Potential model misspecification or external shocks.

Question 44

How does measurement error in explanatory variables affect OLS?

Answer 44

It biases estimates, especially towards zero. (Fama MacBeth example)

Question 45

How is measurement error handled?

Answer 45

Using proxies or adjusting standard errors.

Question 46

Why is measurement error in dependent variables less critical?

Answer 46

It does not bias parameter estimates but may increase error variance.

Question 47

What causes measurement errors in financial variables?

Answer 47

1. Illiquidity in markets
2. Estimated quantities like GDP or inflation

Question 48

What is the role of portfolio betas in addressing measurement errors?

Answer 48

Aggregating betas reduces noise in explanatory variables?

Question 49

What does a high R2 value in time-series regression suggest?

Answer 49

A high R2 indicates that a substantial portion of the variation in the dependent variable is explained by the independent variables. However, it does not imply causation, especially if the data exhibit trends.

Question 50

What do we conclude if the p-values of lagged variables are significant in regression?

Answer 50

It implies that past values (lags) of the independent variable have explanatory power for the current dependent variable, suggesting temporal dependencies.

Question 51

How do you interpret p-values from parameter stability tests across subperiods?

Answer 51

If the p-value is above the significance level, the null hypothesis of equal coefficients cannot be rejected, indicating stable relationships across subperiods.