Passengers (thousands) 150000 145000 140000 135000 130000 125000 120000 115000 110000 Time Series plot of quarterly light rail usage (first quarter 2015 through third quarter 2024) wwww 0 8 12 16 20 Time (Quarters) 24 28 32 36 40 40
Figure 1 below displays the quarterly number of U.S. passengers (in thousands) using light rail as a mode of transportation. The series begins in the first quarter of 2015 and ends with the third quarter of 2024.
We can see a regularity to the series: the first quarter’s ridership tends to be lowest; then there is a progressive rise in ridership going into the second and third quarters, followed by a decline in the fourth quarter. Superimposed on the series are the moving-average
Notice that the seasonal pattern in the time series is not present in the moving averages. The moving averages are a smoothed-out version of the original time series, reflecting only the general trend in the series, which is upward.
Data Analysis Questions:
1. Calculate the moving averages for each observation in the data based on periods 1, 2, 3, and 4. It should be centered on period t = 2.
Label the x and y axes and adjust the values on the plot using Figure 1.
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