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Nayland College - Mathematics

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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

Decomposing data

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Decompose data into it's Components

Seasonal Decomposition and Forecasting, Part I (Auckland Uni)

Videos - Seasonal Effects

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

(Merit)
Decomposing data separates it into the Trend, Seasonal, & Residual component.

The relative influence of each of the components (as a percentage of the overall variation can be investigated.

What is the total variation of the Data? (over the time period)

What is the Trend Component (% of the total variation of the Data) 
What is the Seasonal Component (% of the total variation of the Data) 
What is the Residual Component (% of the total variation of the Data)

How do these compare?

Discussion MUST be in CONTEXT

A good model has not too much residual component

Residuals - Are there any unusual observations - do they warrant further investigation.

Note: iNZight graphs do not have labels on the vertical axis. For Merit or better you will need to add a lable with units on the vertical axis.

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 3

word docs Class notespdf

Exemplar: Decomposing
From the data sets available on statslc.com

Decomposing

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)

 

Decompose the time series data.

This analyses the data and separates it into the Trend, Seasonal, & Residuals

Smoothed data - Using the Holt - Winters LOWESS technique

Decomposition animation - Adds seasonal and trend and residual to regenerate the raw data

 

Discuss relative effect of seasonal effect vs long term trend using numerical values

What is the Total Variation of the Data? (over the time period) 13 000 visitors

What is the Trend Component (38%) - Less of an influence over total variation than the Seasonal component

What is the Seasonal Component (62%) - Cause of most of the variation in the number of visitors from Germany (Remember the context)

What is the Residual Component (15%) - This is small indicating that the iNZight Additive model is a reasonably good model for this situation

 

These calculations are not so flash when the trend line is not linear:

Residuals - Are there any unusual observations - do they warrant further investigation.)

 

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Discuss the decomposed data for these graphs: (tourist numbers to NZ from different countries of origin)

 

 

 

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