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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: Amnesiac on September 19, 2008, 08:50:51 am

Title: Seasonal Adjustment
Post by: Amnesiac on September 19, 2008, 08:50:51 am: Would anyone like to give me a nice and simply run down of how this works?
It's the only topic in CORE that i don't completely understand, but have noticed that it is on a lot of past exam papers.

Any help would be appreciated. Thanks.
Title: Re: Seasonal Adjustment
Post by: *Roxxii* on September 19, 2008, 11:35:03 pm: Seasonal Trend:
When data changes or fluctuates at given intervals, have a fixed or regular period of time between peaks. eg, Temp is high every summer.

When a seasonal trend is present, it is difficult to determine if there are any other trends within the data, eg upwards trend or downwards trend.

To remove the effect of the peaks during seasons, we can seasonally adjust (deseasonalise) the original time series to remove the seasonal variation, therefore exposing any underlying trends.

Example:
Temperatures have been measured each season for the years 2004-2008. It is difficult to recognise any trends, other than a seasonal trend. Deseasonalise the data and comment on the result.

The basic formula to desonalise data is:
Deasonalised figure = original figure / seasonal index

If you are given only the original data, you will need to work out the seasonal index first.
So this is the basic process.

1. Find the yearly average.
eg. (Summer-04 + Autumn-04 + Winter-04 + Spring-04) / 4

2. Divide each number in the original time series by its yearly average found in step 1.
eg. Summer-04 / 2004 Average

3. Find the seasonal averages (also known as seasonal indices)
eg. (Summer-04 + Summer-05 + Summer-06 + Summer-07 + Summer-08) / 5

4. Divide each of the numbers from the original data by the corresponding seasonal index
eg. Summer-04/Summer Seasonal Index

Yayy you will now have the new seasonally adjusted or deseasonalised time series :D

5. Now, you can graph the new seasonal adjusted data against alone or with the original data if you want to compare. Most of the time, some or most of the seasonal variation will be removed.
You might then be able to see a slight upward trend, or a downwards trend, or maybe no trend at all :P
Title: Re: Seasonal Adjustment
Post by: excal on September 20, 2008, 03:16:26 pm: This post is not advice, just a musing.

I remember having to do this last semester. We were taught that:

$\hat{Y}_{t+n} = E_{t} + S_{t+n-p}$

where

$E_{t} = \alpha(Y_{t} - S_{t-p}) + (1 - \alpha) E_{t-1}$

$S_{t} = \beta(Y_{t} - E_{t}) + (1 - \beta) S_{t-p$

$0 \leq \alpha \leq 1$

$0 \leq \beta \leq 1$

and

$E_{t}$ is the expected level at time period $t$
$S_{t}$ is the seasonal factor for time period $t$
$p$ represents the number of seasonal periods

...That was fun maths.
Title: Re: Seasonal Adjustment
Post by: ReVeL on September 20, 2008, 09:48:40 pm: Nice summary Roxxi you helped me understand it better as well.
Title: Re: Seasonal Adjustment
Post by: *Roxxii* on September 20, 2008, 11:00:25 pm: Hehe no probs :) I'm always here if you guys ever need any help ;D
Title: Re: Seasonal Adjustment
Post by: RD on September 22, 2008, 03:11:21 am: Nearly forgot how to do this again! good reminder.
Title: Re: Seasonal Adjustment
Post by: Amnesiac on September 22, 2008, 08:14:04 am: thanks heaps roxxi.. you've given me a great summery of how it works.. now i should be able to answer any question they throw at me for this years exam :)

thanks again.