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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




Make Future Estimates (Predictions)

Seasonal Decomposition and Forecasting, Part II (Auckland Uni)

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

Making and discussing predictions (estimates) of the next two cycles of data
Explain a couple of predictions eg Jan 2012 tourist numbers are...
A prediction MUST have correct units (and things like millions)
Just copying the iNZight graph and table of predictions is NOT enough, as these are not rounded and with correct units.

Emphasise that the predictions are estimates of future data values.
Discuss them in context and rounded sensibly.
Discuss what the prediction error means (prediction interval)

How might the forecasts be used (and who might use them) - discuss.
Be careful if the end of the trend line has been influenced by the position in the seasonal cycle of the end point
(more detail below)
This is discussion worth noting, exploring and investigating.
You could also compare Excel predictions with iNZight predictions, and discuss the differences and prediction interval.

Holt-Winter method uses exponential smoothing - where recent data has greater weight, and old data has low weight. The weighting changes by a constant ratio (exponential decay)
Smooth's the trend, seasonal and sub-series, then puts these together and produces a prediction.

Investigate & compare the additive and multiplicative model forecasts


Starter 7

word docs Class notespdf

Exemplar: Predictions
From the data sets available on

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)

Videos - Predictions | Confidence


Predictions uses the Holt-Winter method, which puts greater emphasis on recent data

Graph of predictions with 95% upper and lower limits for predictions (95% confidence interval for prediction interval)

And predictions in table form

By default will give two years of predictions


Prediction need to be rounded appropriately and with units (remember units and scale eg 1000 000km2)

Discuss the predictions in context

Confidence Intervals: We can be 95% sure that the predictions for (time period) will be between ___ and ___

Trend Video (you tube video by Pricilla Allan)



Discuss IN CONTEXT and with appropriate rounding & units

eg the total number of visitors to NZ in Jan 2013 is predicted to be 198 300
We can be 95% confident the number of visitors to NZ for Jan 2013 will be between 187000 and 209500 people.

The is a reasonably large variation in the 95% prediction limits (A variation of 27600 people between the limits in June 2013)


Be careful if the end of the trend line has been influenced by the position in the seasonal cycle of the end point

Here the raw data finishes with more recent data below the trend line, so the trend line drops at the end

As a result the predictions are low...

Here the last 3 data values have been removed to level the end of the trend line

Notice the predictions are more appropriate

Here 3 more data values have been removed making the trend line rise

Notice the predictions are higher


Here are the three situations together:

Trend drops

Trend Flat

Trend Rising


This is discussion worth noting, exploring and investigating for EXCELLENCE



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