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Q1: Consider the GDP information in global_economy. Plot the GDP per capita for each country over time. Which country has the highest GDP per capita? How has this changed over time?

Q2 For each of the following series, make a graph of the data. If transforming seems appropriate, do so and describe the effect.

Q2.1 United StatesGDP from global_economy.

Q2.2- Slaughter of Victorian “Bulls, bullocks and steers” in aus_livestock.

Q2.3 Victorian Electricity Demand from vic_elec.

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Q2.4 Gas production from aus_production.

Q3 Why is a Box-Cox transformation unhelpful for the canadian_gas data?

Because candian_gas data hasstrong seasonal pattern higher demand in winter months,but box-cox is not good at handle additive seasonality.

Q4. What Box-Cox transformation would you select for your retail data (from Exercise 7 in Section 2.10)?

I choose first series because it has Seasonal fluctuations Box-Cox transformation help stabilize the variance and make any underlying patterns more visible.

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Q5 For the following series, find an appropriate Box-Cox transformation in order to stabilise the variance. Tobacco from aus_production, Economy class passengers between Melbourne and Sydney from ansett, and Pedestrian counts at Southern Cross Station from pedestrian.

Q5.1 variance. Tobacco from aus_production

5.2 Economy class passengers between Melbourne and Sydney from ansett.

Q5.3 Pedestrian counts at Southern Cross Station from pedestrian.

Q7. Consider the last five years of the Gas data from aus_production.Plot the time series. Can you identify seasonal fluctuations and/or a trend-cycle?

I can see the seasonal fluctuations, similar patterns that repeat every year. Trend-cycle shows increasing direction.

Q7b.Use classical_decomposition with type=multiplicative to calculate the trend-cycle and seasonal indices.

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Q7.c Do the results support the graphical interpretation from part a?

Yes, the result do support the interpretation especially in the trend section.

Q7.d Compute and plot the seasonally adjusted data.

Q7e. Change one observation to be an outlier (e.g., add 300 to one observation), and recompute the seasonally adjusted data. What is the effect of the outlier?

Outlier does affect moving average used in decomposition, they can distort the trend around the outlier.

Q7f.Does it make any difference if the outlier is near the end rather than in the middle of the time series?

Having end outlier will have a biger affect on seasonal adjustment because methods have less data to average out the end outlier.

Q8. Recall your retail time series data (from Exercise 7 in Section 2.10). Decompose the series using X-11. Does it reveal any outliers, or unusual features that you had not noticed previously?

Using x-11 shows a seasonal pattern with high around end of each year, there are few outliers shown.There was a drop in 2020, which probably due to effect of pandemic.

Q9 Figures 3.19 and 3.20 show the result of decomposing the number of persons in the civilian labour force in Australia each month from February 1978 to August 1995. Write about 3–5 sentences describing the results of the decomposition. Pay particular attention to the scales of the graphs in making your interpretation.Is the recession of 1991/1992 visible in the estimated components?

The trend chart shows upward in the labour force over the period, with beside around year 1991 there is no sharp drop in the trend line. The seasonal chart shows seasonal dips around summer periods. The reminder chart shows more variability. There is a sharp decrease around 1991 that deviates below that the trend would predict. This means somethig unusual beyond regular seasonal vairation. The recession of 1991 is visible in the decomposition, especially in the remainder charts. Around those years, the remainder shows a negative deviation, suggest growth slowed to what trend predicted.