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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It

3.8 Time Series HOME | Achievement Objectives | Overview | The Statistics Cycle
NZ Grapher: The best choice | iNZight: Getting Started , Importing Data
Using EXCEL: Smoothing, Trend, Seasonal Effects, Graphing, Forecasts, Seasonal Adjustment, Non-Linear models, Comparing Excel & iNZight
Report Writing: Summary | Introduction | Trend | Decompose | Recompose | Seasonal Effect | Forecasts | Robustness | Additive vs Multiplicative model | Comparing | Combining | Conclusion | Practice Assessment

The Trend

3

 

Graphing & Discussing the Long Term Trend

Seasonal Decomposition and Forecasting, Part I (Auckland Uni)

Videos - Long Term Trend

what does this prodice in iNZight?

- Tourist visitors to NZ from different countries Notes.doc
- Alcohol exemplar - class work, sheet.doc & Google Doc
- Homework Travel Destination- Google doc template

Note: Add labels for graph axis. (And units)

Select the ADDITIVE Model to start
(and compare with the multiplicative model later)

NOTE: be careful of quarterly, monthly or total data when describing trends. eg 1500 travellers per month in 2012...

In iNZight the long term trend will need to be described by reading values off the graph.

A Quantitative description the trend MUST be done for Achieve!! (and in context for Merit)

Class example 'Alcohol' Graphs produced, trend line added, discussed, then written about.

Travel Destination Example trend done in class

Travel Purpose & Power Production Trend (Complete for Homework)

O.D.C.A.R.

- Obvious (State the obvious)
- Details (Evidence & Numerical details)
- Context (Relate to the context. What does this mean?)
- Assumptions (check & discuss any statistical assumptions)
- Relate (To references / research and hypothesis made)

Starter 2

Class notespdf

web links iNZight free download and videos on how to get started 

Exemplar
From the data sets available on statslc.com

Example of a trend

EXEMPLARS:
Use iNZight to produce a time series graph and add the trend line. Copy this into your report and discuss

- Alcohol Consumptn: Data csv,| Word Worksheet | Google Doc class write up

- Travel Destination Data csv | Word Write up | Google Doc class work

- Travel Purposes: Data csv

- Electricity Production: Data csv | (Website)

 

(Achieve)
Produce a time series graph then discuss the Long Term Trend
This MUST be quantitative - with numbers and amounts of change.
It is NOT enough to say "the trend steadily increases"
Discuss whether the trend is linear or not.
Discuss the amount of change of the trend.
Discuss the rate of change eg how much increase per month.
eg: The trend increases from 9.5 million km2 in 1990 to about 8.5 million km2 in 2010

(Merit)
As above but the discussion is in context.
eg: The average area of arctic sea ice increases from 9.5 million km2 in 1990 to about 8.5 million km2 in 2010.
Some more detailed description - such as smaller variations in the trend line or possible reasons for the changes.

(Excellence)
Detailed thoughtful discussion:
Explanation for variations in the trend line,
Non-linear trend models,
Piecewise models,
Comparison of iNZight & Excel'
Recent variation in iNZight trend line...

The trend line can vary at the ends due to where the cycle starts and finishes. To avoid this error, use the the trend line values half a cycle from the ends of the raw data as estimates, rather than the end of the trend line (More details below)

OR continue an estimate of the trend line to the end of the data range if you notice that the trend line has been influenced by the cycle finishing point.

 

REMEMBER: there are no indication of units and scales on the vertical axis. You MUST incorporate this, eg. Sea Ice is measured in millions of km2

Discussion: Of the Long Term Trend in very general terms but in context
eg. The Arctic Sea Ice area has decreased from about 9.5 million km2 in 1990 to about 8.5 million km2 in 2010

In more detail: The Arctic sea ice area changes from 9.5 million km2 in Jan 1990 to about 8.5 million km2 in March 2011, which is a change of 1 million km2 over 21 years and 3 months (which is 254 monthly increments) so the average sea ice change is about 4000 km2 per month (1 000 000 ÷ 254)

Trend Video (you tube video by Pricilla Allan)

 

How is the smoothing of the time series and future predictions done in iNZight?

Using the Holt - Winters LOWESS technique

Summary of what students need to know (by Rachel Passmore)

  • Holt –Winters Additive model assumes seasonal pattern is reasonably constant

  • Holt –Winters Multiplicative model is usually better when there is a change in the seasonal pattern - eg seasonal variation increasing (Find out more)

  • Holt-Winters Model uses a technique of exponential smoothing, which is a weighted sum of previous values in a series. More weight is given to more recent values and less weight is given to values from the distant past. This method uses the seasonal LOWESS technique (which stands for LOcally WEighted Seasonal Smoother)

  • Holt-Winters Additive model exponentially smooth's the series in order to produce predictions – the level, the trend and the seasonal sub-series.

  • Students should be able to identify cyclical components and inconsistent seasonal patterns. They should note that such features are incompatible with assumptions underlying Holt-Winters Additive model and suggest a multiplicative model be considered instead. Such a comment would be expected at Excellence level only. Students are NOT expected to calculate a multiplicative model.

Examples:

Traveler numbers from different countries to NZ (Sept 1998 to October 2012 inclusive)

 

Be Careful!!

The trend line can vary at the ends due to where the cycle starts and finishes. To avoid this error, use the trend line values half a cycle from the ends of the raw data as estimates, rather than the end of the trend line

Data set ending in April 2012: Notice the trend line INCREASES
As the data ends just after a peak so the trend line increases.

 

Data set ending in JULY 2012: Notice the trend line remains STEADY
As the data ends at a 'balanced point, so the trend line increases.

 

Data set ending in OCTOBER 2012: Notice the trend line DROPS
As the data ends just after a trough so the trend line drops.

How to cater for this?

To avoid this error, use the trend line values half a cycle from the ends of the raw data as estimates, rather than the end of the trend line. Often an insignificant difference, but avoid discussing the 'possible recent downturn' which isn't there (Excellence point)

This should be discussed if noticed in the trend line.

 

 

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