The Pyramids of Giza are one of the most visited monuments in Egypt. The number of visitors per quarter has been recorded (in thousands) as shown in the accompanying table: $$\begin{array}{l}
\text { Year }\
\begin{array} { | l | c c c c | }
\hline \text { Quarter } & 1995 & 1996 & 1997 & 1998 \
\hline \text { Winter } & 210 & 215 & 218 & 220 \
\text { Spring } & 260 & 275 & 282 & 290 \
\text { Summer } & 480 & 490 & 505 & 525 \
\text { Autumn } & 250 & 255 & 265 & 270 \
\hline
\end{array}
\end{array}$$ a. Plot the time series.
b. Discuss why exponential smoothing is not recommended as a forecasting method in this case.
c. Calculate the four-quarter centred moving averages.
d. Use the moving averages computed in (c) to calculate the seasonal (quarterly) indexes.
e. Use the seasonal indexes computed in (d) to deseasonalise the original time-series data, and plot the deseasonalised time series.
f. Use regression analysis to develop the trend line.
g. Use the seasonal indexes calculated in (d) and the linear trend calculated in (f) to forecast the number of visitors in the next four quarters and describe the seasonal fluctuations in the number of visitors.

Question

The Pyramids of Giza are one of the most visited monuments in Egypt. The number of visitors per quarter has been recorded (in thousands) as shown in the accompanying table: $$\begin{array}{l}
\text { Year }\
\begin{array} { | l | c c c c | } 
\hline \text { Quarter } & 1995 & 1996 & 1997 & 1998 \
\hline \text { Winter } & 210 & 215 & 218 & 220 \
\text { Spring } & 260 & 275 & 282 & 290 \
\text { Summer } & 480 & 490 & 505 & 525 \
\text { Autumn } & 250 & 255 & 265 & 270 \
\hline
\end{array}
\end{array}$$ a. Plot the time series.
b. Discuss why exponential smoothing is not recommended as a forecasting method in this case.
c. Calculate the four-quarter centred moving averages.
d. Use the moving averages computed in (c) to calculate the seasonal (quarterly) indexes.
e. Use the seasonal indexes computed in (d) to deseasonalise the original time-series data, and plot the deseasonalised time series.
f. Use regression analysis to develop the trend line.
g. Use the seasonal indexes calculated in (d) and the linear trend calculated in (f) to forecast the number of visitors in the next four quarters and describe the seasonal fluctuations in the number of visitors.

Quizplus · Accepted Answer

The Answer of The Pyramids of Giza are one of the most visited monuments in Egypt. The number of visitors per quarter has been recorded (in thousands) as shown in the accompanying table: $$\begin{array}{l}
\text { Year }\
\begin{array} { | l | c c c c | } 
\hline \text { Quarter } & 1995 & 1996 & 1997 & 1998 \
\hline \text { Winter } & 210 & 215 & 218 & 220 \
\text { Spring } & 260 & 275 & 282 & 290 \
\text { Summer } & 480 & 490 & 505 & 525 \
\text { Autumn } & 250 & 255 & 265 & 270 \
\hline
\end{array}
\end{array}$$ a. Plot the time series.
b. Discuss why exponential smoothing is not recommended as a forecasting method in this case.
c. Calculate the four-quarter centred moving averages.
d. Use the moving averages computed in (c) to calculate the seasonal (quarterly) indexes.
e. Use the seasonal indexes computed in (d) to deseasonalise the original time-series data, and plot the deseasonalised time series.
f. Use regression analysis to develop the trend line.
g. Use the seasonal indexes calculated in (d) and the linear trend calculated in (f) to forecast the number of visitors in the next four quarters and describe the seasonal fluctuations in the number of visitors.

The Pyramids of Giza Are One of the Most Visited