Overview
1. Choose an economic series that you are interested in working with. (Your economic
variable must be approved by me): https://fred.stlouisfed.org/series/CE16OV#0
2. Prepare data for your analysis.
(a) Download data (not seasonally adjusted) directly from the Federal Reserve Economic Data (FRED) website.
(b) Keep observations from 1960-now.
(c) Report the descriptive statistics.
(d) Plot the series with recession bars. Your graph must have a title and it is self
explained.
Discuss if your series has a trend and/or seasonal patterns.
(e) For MA students: compute and plot 5-year rolling variances. Discuss your results.
3. Identify at least five potential forecasting models. Explain briefly why you choose
them.
(a) To identify potential forecasting models, you have to compute the detrended and
seasonally adjusted variable first, which is computed as the residual from regressing your variable on a linear trend (or a quadratic trend or a log-linear trend) and
seasonal dummy variables.
(b) You then compute and plot the sample ACF and PACF for the detrended and
seasonally adjusted series.
(c) Analyze the sample ACF and PACF to find out five potential models for your
forecasting purpose.
For example, a model with a linear trend plus seasonality plus random noises can
be written as:
1
yt = ?0 + ?1t + ?2D2t + ?3D3t + ?4D4t + ?t
.
Another example, a model with a linear trend plus seasonality plus an ARMA(1,1)
cycle can be written as:
yt = ?0 + ?1t + ?2D2t + ?3D3t + ?4D4t + ?1yt?1 + ?1?t?1 + ?t
.
Note: You might want to include the lagged values of other economic variables,
e.g. xt?1, that could be useful in predicting yt based on economic theory. For
example,
yt = ?0 + ?1t + ?2D2t + ?3D3t + ?4D4t+?1xt?1 + ?1yt?1 + ?1?t?1 + ?t
.
4. Split the sample into two periods: the in-sample period (i.e. 1960-2015) and the outof-sample period (i.e. 2016-now).
Use the in-sample observations (i.e. 1960-2015) to estimate all the potential models
and compute all the required statistics (MSE, s
2
, R2
, adjusted R2
, AIC, SIC).
5. Choose three best models based on these AIC and SIC.
6. Use the models from part (5) to compute simulated forecasts for the out-of-sample
period (i.e. 2016-now). Then compute forecast errors and mean squared forecast
errors (MSFE).
The select the best model based on MSFE.
Note: Undergraduate students use the dynamic method, while graduate students are
required to use both the dynamic and the recursive methods.
7. Use all the data to re-estimate the best model from part (6) and implement forecasts