Time Series Report - Basic

1. Introduction2. Long term trend3. Seasonal Component4. Residual Component5. Predictions6. Conclusion

(Refer to “Stats enquiry cycle Polar Ice” in workbook)(4 graphs and 1 table to be snipped)

  Basic Moderate Excellent

Purpose/Plan

I plan to investigate the trend and seasonal patterns in Arctic Ice area.

How do the features of Arctic sea ice compare with Antarctic sea ice ?

Develop a theory as to why sea ice areas are trending up/down. Are there reasons for the differences observed?

DataMonthly Arctic Sea

Ice Area data1990 - 2011

Monthly Arctic and Antarctic Sea Ice Area data

1990 - 2011

Monthly Total Sea Ice Area data1990 - 2011

AnalysisDecomposition,

seasonal effects and predictions

Decomposition, seasonal effects, comparison and predictions

Comparison and predictions.Research contextual knowledge.

Conclusion

Description of trend, seasonal pattern, unusual values and predictions (Arctic)

Repeat analysis for Antarctic then compare differences and similarities

Repeat analysis for Total Ice. What do you predict will happen to Sea Ice areas in the future? Use contextual knowledge to explain observed features and differences between series

1. Introduction (purpose statement)

• “From my research into ….. I have learnt…..”• “Polar ice is important…..”• “I want to investigate….. Because…..”• “I want to develop a hypothesis….”• “The research links are listed below….”

How much should I write for a Purpose/Plan?

2. Long term trend

2. Long term trend

The graph of the smoothed trend shows a very gradual decreasing trend. It appears that the mean area of sea ice has decreased on average from about 9.5 million square kilometres to about 8.5 million square kilometres from January 1990 to March 2011.

Or you could write a statement like:“Looking at the raw data the mean area of sea ice in Arctic fluctuated between 13.5 (million square kilometres) and 2.5 (million square kilometres) between 1990 to 2011.”

2. Long term trend

3. Seasonal Component

• There is little variability in the seasonal effects from year to year and the seasonal pattern has stayed fairly constant over the whole time so I can rely on the predictions generated from the Holt-Winters model.

3. Seasonal Component

What does “Estimated seasonal effects mean?

• Seasonal effects – the seasonal pattern of the area of Arctic Sea ice is very consistent. Peak months are usually February/March and trough months are usually August/September.

• Peaks are around 3.5 million km2 above the trend and troughs are around 5 million km2 below the trend.

• These peaks and troughs correspond with the Northern hemisphere’s summer and winter months.

3. Seasonal Component

Other things you could say:

Looking at the graph of the residuals confirms that the predictions should be fairly reliable as the residuals appear to be small as most are no more than 0.5 million km2, above or below the line and have limited variability and no

obvious pattern.

4. Residual Component

Component contribution to series variation

Arctic Sea Ice(Million km2)

Min Max Range Approx. % Contribution

Raw data 3 14 11

Trend 9 10 1

Seasonal -5 4 9 82%(9/11*100 = 82% )

Residual -0.5 0.5 1

Component contribution to series variation continued…

• The main source of variation in the area of Arctic Sea Ice is the seasonal component.

• Around 82% of the overall variation in this series can be accounted for by the seasonal component.

• Trend and residual components account for the remaining variation in the series.

What can I write about residuals?

• Residuals – Residuals are small and the majority fall in the range of plus/minus 0.5 million km2 sea ice. There is one residual of over 1 million km2 sea ice which is in September 2007 which is still small when compared with the range of the data. The range of the raw data is around 11 million km2 ( Max – Min = 14 - 3) so this residual represents less than 10% of this range.

• Any residual less than 10% of overall range is not considered to be of note.

5. Predictions using Holt-Winters

Forecast for a Seasonal High

• Using the Holt-Winters model, I predict that the A.S.I.A for March 2012 will be ____ million Km2.

• It is likely to be between _____ and _____ million Km2.

Forecast for a Seasonal Low

• Using the Holt-Winters model, I predict that the A.S.I.A for September 2012 will be ____ million Km2.

• It is likely to be between ____ and ____ million Km2.

For a good conclusion, write about:-

• What you discovered.• How your analytical findings compare with

published research.• The significance of what you discovered.• A recommendation for ….

Ensure your conclusion matches your purpose / introduction

  Basic Moderate Excellent

Purpose/Plan

I plan to investigate the trend and seasonal patterns in Arctic Ice area.

How do the features of Arctic sea ice compare with Antarctic sea ice ?

Develop a theory as to why sea ice areas are trending up/down. Are there reasons for the differences observed?

DataMonthly Arctic Sea

Ice Area data1990 - 2011

Monthly Arctic and Antarctic Sea Ice Area data

1990 - 2011

Monthly Total Sea Ice Area data1990 - 2011

AnalysisDecomposition,

seasonal effects and predictions

Decomposition, seasonal effects, comparison and predictions

Comparison and predictions.Research contextual knowledge.

Conclusion

Description of trend, seasonal pattern, unusual values and predictions (Arctic)

Repeat analysis for Antarctic then compare differences and similarities

Repeat analysis for Total Ice. What do you predict will happen to Sea Ice areas in the future? Use contextual knowledge to explain observed features and differences between series

Compare and contrast

Perform a similar analysis for Antarctic Sea Ice.• What is different?• What is similar?• Interesting features?

Time Series Report - Moderate

1. Introduction 2. Long term trends (compare)3. Seasonal Components (compare)4. Residual Components (compare)5. Predictions (one for each)6. Conclusion

(Refer to “Stats enquiry cycle Polar Ice” in workbook)8 graphs and 2 tables to be snipped

Create a new series: Total Ice

Create a new series by adding the Arctic and Antarctic raw data together.

Analyse your new series• What is different?• What is similar?

• Interesting features?

Time Series Report - Excellent

1. Introduction 2. Long term trends (compare)3. Seasonal Components (compare)4. Residual Components (compare)5. Repeat analysis for a sensibly created new variable6. Predictions7. Conclusion

(Refer to “Stats enquiry cycle Polar Ice” in workbook)

Advice: be genuine; avoid waffle.