Econ 427 lecture 7 slides Modeling Seasonals Byron Gangnes

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. Byron Gangnes

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. Byron Gangnes

General seasonal model Byron Gangnes

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. Byron Gangnes

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: Byron Gangnes

Forecasting with seasonals Our example model: At time T+h: Byron Gangnes

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: Byron Gangnes

Forecasting w/ trend and seasonals Do example of visns in Eviews. Byron Gangnes