5: Forecasting and Panels Flashcards
What do we do in forecasting?
We want to use time series to predict the future.
What are ARIMA models?
Auto-Regressive Integrated Moving Average models.
They are one way to forecast future value.
What are the three parameters of ARIMA models?
ARIMA(p,d,q):
- p is the order of the autoregressive part (number of lags we want to include). Look at the PACF: If we have n significant spikes, then no significant spikes, the optimal order is probably n.
- d is the order of the first differencing involved. If lag-1 autocorrelation is 0 or negative, if they are all small and no significant, no need for a higher order differencing. If lag-1 autocorrelation is negative and big, you are probably overdifferencing.
- q is the order of the moving average part. Look at the ACF: if we have a decay in correlation until lag m, then no further significant, the optimal order is probably m.
Can we use ARIMA models on series that are not stationary?
Yes, since they remove the moving average, by removing the first difference. Creates stationarity, necessary for assuming future follows the past
What are RANDOM variations around the moving average called?
White noise
What is panel data?
Cross-sectional time series: entities are observed over time.
The second level (time) could also be a sub-unit within the entity.
With panel data, you can control for unobserved heterogeneity.
Why do we use fixed effect models?
- Observations are NOT independent (nested within groups).
- Unobserved characteristics of the groups are correlated with the variables of the model.
- We are interested in the variation within groups, net of the effect of the group characteristics.
What do we use fixed effect models for?
To measure the impact of a variable that varies over time.
- Assuming unobserved characteristics of the entity may bias the predictors.
- Assuming that time-invariant characteristics are unique to the entity (test with Hausman)
What are the effects when alpha depends on the entity (not constant)?
- Lines at different levels, different intercepts
- Same slope (ß) for lines
- Every entity is affected equally by ß, but starts at different points.
How many dummy variables should we include in a fixed effect model?
Example: for 8 entities, we include 7 dummies (1 is the baseline).
Dummies add/remove on the fixed effect.
What test do we use to see if a fixed effect model is preferable to OLS?
An F-test to test whether individual effects are significantly different from 0. If p-value < 0.05, the fixed effects model is preferable.
Can also be done for time fixed effect. If p-value > 0.05, there is no need to use time fixed effect
What is cross-sectional dependence and what tests are connected to it?
Testing that residuals are not correlated across entities (in the cross-section). Also called contemporaneous correlation. Only a problem with long time series.
- Breusch-Pagan LM test. p-value > 0.05 : no cross-sectional dependence.
- PesaranCD test
What is serial correlation and what test is connected to it?
When a variable correlated with itself over time. Only a problem with long time series.
- Breusch-Godfrey/Woolridge:
Null hypothesis: no serial correlation. p-value > 0.05 : no serial correlation.
How do we test for heteroscedasticity?
Breusch-Pagan test.
Null hypothesis: homoscedasticity.
p-value < 0.05 : there is heteroscedasticity.
If reject null: Use heteroscedasticity corrected variance covariance matrix.
How do we test for stationarity?
Augmented Dickey-Fuller test (ADF).
p-value < 0.05 : no unit roots.
