Econ 427 lecture 7 slides

1. Econ 427 lecture 7 slides Modeling Seasonals

2. Modeling seasonality • Deterministic seasonality refers to perfectly predictable recurring seasonal patterns in a time series • Weather, holidays, agricultural cycles, tradition • Sometimes series are seasonally-adjusted, but many times we want to work with unadjusted series but capture this predictable component • Can use regression models to estimate seasonal components.

3. Estimating seasonal models • We use a set of seasonal dummy variables to allow for predictable recurring patterns in the data • Consider the quarterly case • D1 = (1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0, …) • D2 = (0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0, …) • D3 = (0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0, …) • D4 = (0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1, …) The “1”s indicate that that period is qtr 1 or qtr 2, etc.

4. General seasonal model

5. Model with trend and cycle • For ex, with a quadratic trend plus seasonal factors: • Can also use these “seasonal” dummies to capture trading day and holiday effects. You have a question on problem set 2 that looks at weekday effects.

6. Forecasting with seasonals • Like the time trend (or trend^2, etc.) the dummy variables have a perfectly predictable pattern, so we know at time T what there values will be in coming periods. Once we have estimates of the parameters, we can easily calculate the optimal forecast:

7. Forecasting with seasonals • Our example model: • At time T+h:

8. Forecasting with seasonals • The expected value of this given the information available at time time T: • All the RHS vars except epsilon are known at time T. • Then we operationalize it by replacing unknown true params with our OLS estimates:

9. Forecasting w/ trend and seasonals • Do example of visns in Eviews.