Problem 1 (25 Points)

Everybody is talking about inflation right now. The most popular indicator for inflation is the CPI and reported by the U.S. Bureau of Labor Statistics. Worksheet "CPI" in "Assignment 5.xlsx" contains monthly values of the Consumer Price Index between January 2019 and June 2022 (in column D).

1. Using moving averages over 5 months, what CPI value would you predict for July 2022?
2. Using an exponential smoothing model with a smoothing constant of 0.2, what CPI value would you predict for July 2022? Why is this answer different from the one in part a)?
3. Using an exponential smoothing model with a smoothing constant of 0.8, what CPI value would you predict for July 2012? Why is this answer different from the one in part b)?
4. Make a scatterplot of the monthly CPI between January 2019 and June 2022. What does this scatterplot tell you? Should you have used the forecasting techniques in parts a) - c) in this case? Why? Why not?
5. Develop a simple linear regression model with the 42 months ("Period") as the independent and the corresponding CPI values as the dependent variable. How well does your model fit the data? Do you think this is a better model than the ones used in parts a) - c)? Why? Why not?
6. Using your regression model from part e), predict the CPI value in December 2022. Could you have made such a prediction based on the models from parts a) - c)? Why? Why not?

Data for question 1

Year	Month	Period	CPI-U
2019	Jan	1	251.712
2019	Feb	2	252.776
2019	Mar	3	254.202
2019	Apr	4	255.548
2019	May	5	256.092
2019	Jun	6	256.143
2019	Jul	7	256.571
2019	Aug	8	256.558
2019	Sep	9	256.759
2019	Oct	10	257.346
2019	Nov	11	257.208
2019	Dec	12	256.974
2020	Jan	13	257.971
2020	Feb	14	258.678
2020	Mar	15	258.115
2020	Apr	16	256.389
2020	May	17	256.394
2020	Jun	18	257.797
2020	Jul	19	259.101
2020	Aug	20	259.918
2020	Sep	21	260.280
2020	Oct	22	260.388
2020	Nov	23	260.229
2020	Dec	24	260.474
2021	Jan	25	261.582
2021	Feb	26	263.014
2021	Mar	27	264.877
2021	Apr	28	267.054
2021	May	29	269.195
2021	Jun	30	271.696
2021	Jul	31	273.003
2021	Aug	32	273.567
2021	Sep	33	274.310
2021	Oct	34	276.589
2021	Nov	35	277.948
2021	Dec	36	278.802
2022	Jan	37	281.148
2022	Feb	38	283.716
2022	Mar	39	287.504
2022	Apr	40	289.109
2022	May	41	292.296
2022	Jun	42	296.311