Name: Ricardo Lu
Student number: 20829257
Part A: Visualization
1.
Generally, the consumption expenditure is increasing with a positive trend over the period. When we
look at the fluctuation over one year, we would observe that most annual increase are followed by a
decrease. We can observe that this time series has an upward linear trend from the graph. We can also
observe irregular component since the graph has a high frequency fluctuation over the period, but it is
hard to observe other components since it is hard to detect a component unless the lower frequency
component has been moved.
2.
We can see that the trend does not seem to be linear. It is increasing. Therefore, the growth rate is
increasing on average from 1960 to 2020 if we ignore short term fluctuations.
3.
We could see from the graph that the annualized growth rate is not constant on average. From 1960 to
1980, the annualized growth rate changed with high frequency in the range of -20% to 60%. From 1980
to 2020, the annualized growth rate changed frequently in the rage of -20% to 40%.
Part B:
1.
From the graph we could see that the quadratic trend fits the original time series better than the linear
trend as the movement of quadratic trend is really closed to the movement of original series. The choice
between linear and quadratic trend depend on the series, as we can see the quarterly consumption
expenditure increases faster at the end of period than at the beginning, which makes the time series do
not seem linear. Therefore, a straight line does not seem to appropriate to model the time series.
2.
From the graph we can see that the linear trend and quadratic trend both fit the log of series well. This
is because the difference between the linear trend and quadratic trend is too small comparing to the
scale of the series, which makes them look same on the graph.
3.
As we look at the detrended series, we could clearly see that the upper linear trend has been removed.
The graph shows that the time series has intensely high fequency during the period, which indicates the
present of irrigular component. We can also observe the cyclical component in the series.
4.
When we look at the graph, we can see that the cycle component oscillates around zero over the period.
Around 1970 the cyclical component is 0.02, which means that the quarterly consumption expenditure
is 2% higher the trend on average. Around the 1977 the cyclical component is bigger that -0.02, which
means that the quarterly consumption expenditure 2% lower than the trend on average.
5.
From the graph we can see the low frequency component has a upward increasing line, which is the
same as the movement of trend. We do not see large fluctuations on this line, which means that there is
no large movement of cycle component around the trend.
6.
The seasonal component for quarter one is -0.03, which means that the series 3% higher than the low
frequency component on average. The seasonal component for quarter two means that the quarterly
consumption expenditure is 4% lower than its low frequency component on average. The seasonal
component for qurater three means that the series is 4% higher than the low frequency component on
average. The seasonal component for quarter four is 0.02, which means the seasonal component for
quarter four is 2% higher than its low frequency component.