Achievement Standard 3.1 Time Series is a 3 Credits INTERNAL Assessment

Work through the relevant time series concepts described below.
Complete the Sigma Exercises and the Homework booklet AIS pages listed.
Analyse using Excel and write a report on some time series datasets

Practice assessment

Links to the Statistics NZ website

NCEA Mathematics Achievement Standard AS90641

Determine the trend for time series data
Mathematics: Statistics strand – Level 8

Use graphs, moving averages, separation into smooth and rough (with awareness of additive and multiplicative models) to explore time series.

Background

This is a set of three PowerPoint presentations which demonstrate a suggested method for students to analyse and report on time series data for AS90641. The first presentation shows a basic analysis and forecast. The second two give some suggestions for a more comprehensive analysis and report. These PowerPoints may be used with a data show, or made available to students on individual computers or as printed notes. They could be used as a teaching tool or for individual learning or revision by students.

Basic analysis.ppt | Extra for experts.ppt | Reporting.ppt

Datasets from the spreadsheet  Example sales.xls are used in the analyses. Basic analysis uses the worksheet called Hardware. Extra for experts, and Reports use the worksheet called Clothing.

A set of sample reports is also provided. The basic one is called Report on hardware sales and the advanced is called Report on clothing sales . These follow the same analysis process as the PowerPoints.

Along with them is the spreadsheet  Example sales answers which gives the worked answers and graphs used in the reports. This can also be used to automatically calculate these for any other dataset. There is also a set of other retail sales datasets for extra practice.

QUESTION

COMMENTS

PRACTICE

1) What is Time Series?

Time Series is data which has been recorded over regular time intervals.

Assessment criteria

Abel Tasman Data set

2) What is our aim?

We analyse time series data to investigate trends, cycles, and predict future values.
We want to produce a model to fit the time series data, and investigate improvements and limitations of the model.

3) What type of graph is appropriate for time series?

A line graph is used to graph time series. Correct labelling of axis and time intervals is important.

Learn more about Graphing Time series

Abel Tasman Raw data graph

4) How do we describe features of a time series graph?

When describing features of time series graphs specific values must be referred to

Learn more about features of Time Series Graphs

For a good description and summary read David Barton's p3 to 7

5) What is cyclical variation?

Often time series has some cyclical pattern or consistent pattern over equal periods of time. These are long term cycles.

Learn more about Cyclical variation

6) What is seasonal variation?

Usually time series has a short term cyclical pattern. These cycles can be over a day, week, month or year. These are shorter term cycles.

Learn more about Seasonal variation

Abel Tasman Describing graph

AIS p6

7) What are random movements?

There is always some amount of random variation in data. This is referred as noise. Sometimes outliers or spikes in data can occur.

Learn more about Random movements

Basic time series descriptions and graphing
Ex 1.01 p8
Data sets Q: 1 2 3

AIS p5

8) What is the order of the time series data?

The order of the time series data is the number of data values that cover one seasonal cycle.

eg 2 monthly data has an order of 6 if the seasonal cycle is one year.

Using Excel to graph and discuss
Ex 2.01 p15
Data sets Q: 1 2

9) How do we use Excel to smooth the data?

Smoothing the data evens out the seasonal effects by calculating the moving average.

Learn more about smoothing data

Abel Tasman smoothed data

Using Excel to smooth data
Ex 2.03 p25
Data sets Q: 1 2 3 8 11

AIS p8

pg07_Road_Casualities

10) How do we add a long term trend line?

The fitting of a linear model to the moving average can be used to describe the trend numerically

Learn more about trend line

Abel Tasman Trend Line

AIS p9
AIS p10
AIS p11

pg10 Turnover Supermarket
pg11 Monthly electricity bills

11) What are average seasonal effects?

The difference between the actual data value and the smooth data value is the individual seasonal effect. These are averaged to calculate the average seasonal effects.

Learn more about seasonal effect

Abel Tasman Average Seasonal Effects

AIS p12
AIS p13
AIS p14

pg12 Permanent Arrivals Chch
pg14 Building Consents

12) How do we use Excel to predict the next seasons values?

To predict future data values continue the linear trend line and add the average seasonal effects.

Learn more about predicting future values

Abel Tasman Predictions

Using Excel to pedict values
Ex 2.04 p33
Data sets Q: 1 2 3 4 5 6

AIS p15
AIS p16
AIS p17

pg15 Wholesale Trade
pg17 Car Registrations Chch

13) How do we seasonally adjust the moving average?

By subtracting the average seasonal effect off each data value we obtain a seasonally adjusted value for the moving mean. This can be used to comment on the nature of the data value (above or below average?)

Learn more about seasonal adjustments

Abel Tasman Seasonal Adjusted moving average

AIS p18
AIS p19
AIS p20

14) What if the long term trend line is non-linear?

Non-linear time series analysis can involve an exponential or power model for the trend line

Learn more about non-linear time series

What about a multiplicative model? - you can research this...

Using Excel for non-linear analysis

Ex 2.06 p47
Data sets Q: 1 2 3 4 5

Multiplicatitive model | Hotel tourist numbers

AIS p21

pg22 Energy Statistics
pg23 Department Stores Sales

15) How do we put it all together?

Practice assessments

Time series data library or data excel data sets

Forestry instruction sheet
Forest Production Raw Data | And Solutions
Forestry Discusson

Aussie Motel Numbers
Canadian Traffic Fatalities
Red Wine Sales
Aussie Beer Sales
Purse snatches
Blowfly Data

Practice test pg 24 Data set

Abel Tasman Seasonal Excellence!!!

AIS p24
AIS p25

pg24 Food Outlets Retail Trade

Achieve: You MUST correctly complete ALL of the following.... 1) Produce an Excel table of the Raw and Smoothed the time series data.
2) Graph correctly the Raw and Smoothed time series data.
3) Determine the equation for the long term trend line, and fully describe the trend. (The GRADIENT of the trend line)
4) Calculate the individual seasonal affects for the time series data.

Merit: You MUST correctly complete ALL of the following.... 1) Calculate the average seasonal affects for the time series data. 2) Calculate (with working) predicted future values. (with correct units and scaling)

Good luck in the assessment. Use the force...