Problem 1
Obtain monthly data for Consumer Price Index for All Urban Consumers: All Items, Not Seasonally Adjusted FRED/CPIAUCNS. Use it to construct the time series for month-over-month inflation rate, yt = ∆logCPIt.
(a) Restrict the sample to 1955M1-2013M12. Plot the time series for inflation yt.
(b) Set up and estimate local level model with seasonal component.
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## [6] "sea_dummy5" "sea_dummy6" "sea_dummy7" "sea_dummy8" "sea_dummy9"
## [11] "sea_dummy10" "sea_dummy11"(c) Plot the smoothed level and smoothed seasonal components μt|T and γt|T together with their 90% confidence intervals. Plot the smoothed irregular component εt|T.
(d) Create a 36 period ahead forecast i.e. a forecast for period 2014M1-2016M12. Plot the forecast together with 90% confidence intervals and actual data for the period 2005M1-2016M12. How well does the model perform when it comes to its forecasting ability?
Based on the below plot, I feel like the forecast does a resonable good job at predicting month-over-month inflation. At every point, the actual data seems to be contained within the 90% ci for the forecasted portion of the model.
