Figure 1. below displays the quarterly number of U.S. passengers (in thousands) using light rail as a mode of transporta
Posted: Thu Apr 28, 2022 1:56 pm
Figure 1. below displays the quarterly
number of U.S. passengers (in thousands) using light rail as a mode
of transportation. The series begins with the first quarter of 2009
and ends with the first quarter of 2014.
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 forecasts based on a span of k =
4.
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 trending in the series, which is upward.
Figure 1. also shows the moving-average
model forecasts and prediction limits projected into the future.
Notice that the moving-average model makes no accommodation for the
trend in its forecasts.
yTREND =SEASON
For each of the estimated levels given by the centered moving
averages, we calculate the ratio of actual sales divided by the
centered moving average and enter = D4 / F4 in cell G4 and then
copy the formula down to cell G20. This ratio tells us how to
seasonally adjust a series.
Because we have more than one seasonal ratio observation for a
given quarter, we average these ratios by quarter. That is, we
compute the average for all the quarter 1 ratios, then the average
for all the quarter 2 ratios, and so on. These averages become our
seasonal ratio estimates.
Show the resulting ratios based on the periods of 1, 2, 3 and 4
in the table below:
Quarter
Seasonality ratio
1
2
3
4
(15p.)
yt = [a + b (t)]
× SR
Show the regression output here:
(20p.)
(15p.)
yt = [a + b (t)]
× SR =?
where SR is the seasonality ratio for
the appropriate quarter corresponding to the value
of t.
(PLEASE DO PARTS 4 AND 5. THANK
YOU!)
number of U.S. passengers (in thousands) using light rail as a mode
of transportation. The series begins with the first quarter of 2009
and ends with the first quarter of 2014.
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 forecasts based on a span of k =
4.
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 trending in the series, which is upward.
Figure 1. also shows the moving-average
model forecasts and prediction limits projected into the future.
Notice that the moving-average model makes no accommodation for the
trend in its forecasts.
yTREND =SEASON
For each of the estimated levels given by the centered moving
averages, we calculate the ratio of actual sales divided by the
centered moving average and enter = D4 / F4 in cell G4 and then
copy the formula down to cell G20. This ratio tells us how to
seasonally adjust a series.
Because we have more than one seasonal ratio observation for a
given quarter, we average these ratios by quarter. That is, we
compute the average for all the quarter 1 ratios, then the average
for all the quarter 2 ratios, and so on. These averages become our
seasonal ratio estimates.
Show the resulting ratios based on the periods of 1, 2, 3 and 4
in the table below:
Quarter
Seasonality ratio
1
2
3
4
(15p.)
yt = [a + b (t)]
× SR
Show the regression output here:
(20p.)
(15p.)
yt = [a + b (t)]
× SR =?
where SR is the seasonality ratio for
the appropriate quarter corresponding to the value
of t.
(PLEASE DO PARTS 4 AND 5. THANK
YOU!)