What Exactly Is Seasonally Adjusted

[classixuk]

I'm going to admit that I haven't a clue what "seasonally adjusted" means, other than it's something to do with the seasons!

Could somebody tell me in plain english what a seaonal adjustment is, why it's done, and how it's worked out.

For the purpose of this example, could you use the figures below so that I can follow the maths? Thanks

Noddyland Non Seasonally adjusted house prices

Year 1

Q1 £10

Q2 £15

Q3 £20

Q4 £25

Year 2

Q1 £30

Q2 £20

Q3 £18

Q4 £20

*incase seasonal adjustment has anything to do with inflation can we say that in year 1 inflation was 3%, and in year 2 inflation was 2%.

Thanks to those who answer this post and educate little old me (I'm sure other readers are in the dark too, but perhaps it takes a brave man like me to hold up the stupid flag and take the flaming from the trolls)!

[karhu]

I'm going to admit that I haven't a clue what "seasonally adjusted" means, other than it's something to do with the seasons!

Could somebody tell me in plain english what a seaonal adjustment is, why it's done, and how it's worked out.

For the purpose of this example, could you use the figures below so that I can follow the maths? Thanks

Noddyland Non Seasonally adjusted house prices

Year 1

Q1 £10

Q2 £15

Q3 £20

Q4 £25

Year 2

Q1 £30

Q2 £20

Q3 £18

Q4 £20

*incase seasonal adjustment has anything to do with inflation can we say that in year 1 inflation was 3%, and in year 2 inflation was 2%.

Thanks to those who answer this post and educate little old me (I'm sure other readers are in the dark too, but perhaps it takes a brave man like me to hold up the stupid flag and take the flaming from the trolls)!

Seasonal adjustment is done so that MONTHLY rises/falls can be extrapolated to YEARLY rises/falls.

House price movements are non-linear with respect to month due to market activity being specifc to particular months.

They should take historical monthly data and average them over a number of years to work out which months typically have the largest rises. When seasonally adjusted all months should have the SAME RISE in theory assuming activity does not change due factors other than those present seasonally, which should be 1/12 of the yearly value.

It has little relevance if you want to look at monthly rises is the absence of yearly rises.

And it may not be very relevant when economic factors are changing on a monthly basis (like interest rates for example) as that may make monthly activity atypical (but this could also be seen as strengthening/weakening of the market). They may also be skewed by other factors such as climate change, which could equate to less rain etc. in certain months.

SO take home message:

If you use SA adjusted figures quote the YOY [extrapolated] values.

If you want to quote the MOM value use non-seasonally adjusted.

Edited November 1, 2005 by karhu

[classixuk]

Seasonal adjustment is done so that MONTHLY rises can be extrapolated to YEARLY rises.

House price rises are non-linear with respect to month due to market activity being specifc to particular months.

They should take historical monthly data and average them over a number of years to work out which months typically have the largest rises. When seasonally adjusted all months should have the SAME RISE in theory assuming activity does not change due factors other than those present seasonally, which should be 1/12 of the yearly value.

It has little relevance if you want to look at monthly rises is the absence of yearly rises.

And it may not be very relevant when economic factors are changing on a monthly basis (like interest rates for example) as that may make monthly activity atypical. They may also be skewed by other factors such as climate change, which could equate to less rain etc. in certain months.

Ok.

So why do we bother with seasonal adjustment at all? Can't the UK just accept that each year one month will always be busier than the other 11 in a given market etc.

We all accept that December will be a busy month for toy sales (recession or not). We don't need to seasonally adjust the figures over the year.

Have I missed the point, or is there actually a point to seasonal adjustment?

Thanks for replying by the way!

[spline]

A technical analysis and reverse engineering of the Nationwide SA shamelessly extracted and reposted from C4

phugoid

Posted 02-04-05 15:57 02-04-05 14:57

Originally posted by Fran Tick:

... have you ever plotted the land registry data? If so you will have seen how prices do vary during the year, basically it's a dip around Xmas and a peak around the spring/summer.

Yes, the house price data does show seasonal variations, and is roughly about 1-2% below trend in Jan/Feb, and about 1-1.5% above trend in Jul/Aug - it is worth trying model the effect, but as the methodology is not published, one has try and reconstruct how it might be done.

There seem to be two essentially different ways to tackle this.

One approach is to argue that as HPI is distributed non-uniformly over the year, one should take the overall annual HPI, and then re-distribute this evenly over each month. The redistribution could be done with a monthly template and scaled on the annual HPI. In this model the corrections vanish if annual HPI vanishes and reverses if HPI reverses.

The other approach is to argue that house prices exhibit a constant amount of seasonal variation (in percentage terms), irrespective of whether HPI is positive, zero, or negative. In this model the seasonal variation is always the same fixed percentage.

If you take the historical data, and take a diff from a non-lagging rolling average, and average into monthly bins (model 2 above), then you do recover a monthly template that is close to SA adjustment applied by Nationwide, Halifax, or whoever published the data.

But there is also considerable scatter, partly down to inherent volatility, but also because one would expect the size of the adjustments to be proportional (at least in some broad way) to the underlying annual HPI (as the SA is simply redistributing this number, model 1 above). Doing this improves the fit, but is not the whole story as there is still a residual seasonal variation even when HPI is roughly zero (as in 1992-95), so it looks more like a blending of the two models is needed.

There is also the awkward question of whether the normal seasonal dynamic applies at the peak of the cycle, or whether volatility driven by uncertainty (and newspaper headlines, IR expectations, elections) swamps it, so that it is no longer particularly relevant and should be ignored. Obviously, the SA at the present time should be treated with some caution, and certainly shouldn’t be the sole basis for calling a dramatic headline (whatever the direction).

Fran Tick

Posted 03-04-05 00:22 02-04-05 23:22

Thanks for the reply phugoid.

From the way I understand it I agree with your method 2.

As for method 1 I really don't agree at all. If June is normally a strong month for house price growth, then it will be a strong month regardless of whether the HPI across the whole year is +50%, +20%, 0%, or -20%. So it seems obvious that we want a negative seasonal adjustment for June even if prices are going down across the year.

I understand you have blended the two methods to reverse engineer the best fit but I am not sure this is possible to do given the lack of precision in the published figures and the overall complexity of their probable method.

As for querying the use of the usual methods at the peak of the cycle, realistically we won't know it was the peak till some time afterwards so I don't see that it's right to throw away the seasonal adjustments now.

Editor's note: Yes it's method 2.

Fran Tick

Posted 03-04-05 14:35 03-04-05 13:35

Hi again phugoid, having looked into it a bit more I think this is how it works...

The Seasonal Adjustment is based on historical data of years gone by, including the actual house price inflation seen by the year end.

When releasing 2004-01's figures, Nationwide have used the SA from 2003-01 as they don't know what HPI will be over 2004. Although they have their own estimate of HPI for 2004, they don't make use of this in applying SA during 2004.

At the end of 2004 the HPI for the year is known and a new set of SA, based on 2004's activity and all the preceding years, can be calculated. Nationwide then go back over 2004's figures, and preceding years, using this new SA.

This is why when you look back at historical data it seems a better fit than examining the monthly reports for the current year as they get released.

Jan Feb Mar

2000 1.712168 1.279981 0.055370

2001 1.709352 1.394377 0.065760

2002 1.743282 1.492831 0.131389

2003 1.820323 1.565923 0.234517

2004 1.871577 1.607901 0.296068

2005 1.871577 1.607901 0.296068 [identical to 2004]

SA% extracted from Nationwide's historical data spreadsheet.

So the seasonal adjustment elements of the historical data in your original link are periodically recalculated and so the figures are different from those in the original press releases which can be found here:

http://www.nationwide.co.uk/hpi/archive.htm

Rent and see!

phugoid

Posted 03-04-05 20:36 03-04-05 19:36 Hi Fran Tick

Excellent, and I think it looks right. You clearly show that the monthly SA factors really are copied from the previous year, and then updated (and frozen) later when there is enough data (on either side) to do a better job with the rolling average and the trend extraction. And that the press releases, and hence newspaper headlines, are based on SA factors recycled from the previous year. But to be fair, we can expect that the SA factors will vary only slowly from year to year, unless, of course, the market is structurally changed somehow – not really sure whether post peak is different or not

This fits nicely with what seems to be a standard(ish) method [X11] for seasonally correcting data – gory details here ...

Assume that the house price series Q can be decomposed multiplicatively into Q = T*S*I, where T is the trend, S is the seasonal variation, and I is the irregular bit. Then the first estimate of the trend T1 is given by averaging Q over a rolling window, so T1 = <Q>, where <> is the rolling average. The trend is removed, so S*I ~ Q/T1, and the first estimate of the seasonal component S1 is done by averaging Q/T1 into monthly bins. This allows a first correction of the series to remove the seasonal component, so Qadj1 = Q/S1. A second iteration can be done if needed, so T2 = <Qadj1>, S2 = bin average of Q/T2, and Qadj2 = Q/S2. Finally, the irregular bit can be extracted as I2 = Qadj2/T2.

The rolling average requires (let’s say) 6-12 month data on either side, and can’t be applied (at least not directly) within the last 6-12 months, leaving a gap - copying the S2 factors forward is the simplest way to fill it. The adjusted figures are temporary until they are 6-12 months old, when they are updated and frozen naturally be the method.

Nationwide's footnote:

Price indices are seasonally adjusted using the

US Bureau of the Census X11 method. Currently the calculations are based on a monthly data starting from January 1991. Figures are recalculated at six month intervals, in June and December.

C4 Source: http://community.channel4.com/groupee/foru.../5930057681/p/1

Edited November 1, 2005 by spline

[karhu]

Ok.

So why do we bother with seasonal adjustment at all? Can't the UK just accept that each year one month will always be busier than the other 11 in a given market etc.

We all accept that December will be a busy month for toy sales (recession or not). We don't need to seasonally adjust the figures over the year.

Have I missed the point, or is there actually a point to seasonal adjustment?

Thanks for replying by the way!

I guess it tries to smooth out the monthly data. For example, if we saw 2% rises in June, we might think oh my goodness HPC has been called off [2*12=24%], when in fact that may imply a yearly fall, being below average [sA figure -0.2, and therefore -0.2*12=-2.4%].

In a way we should only concern ourselves with well averaged data, e.g. YOY averages, but we're too impatient for that, and that impatience leads to the crazy world of seasonal adjustment.

The monthly sampling rate is basically TOO HIGH is this market. Reading anything into the monthly figures is non-scientific and basing any decisions on monthly data is downright stupid.

Edited November 1, 2005 by karhu

[spline]

The monthly sampling rate is basically TOO HIGH is this market. Reading anything into the monthly figures is non-scientific and basing any decisions on monthly data is downright stupid.

In my view the more samples the better , unless they swamp us, and I’m pleased that the raw data is made public so that we have the option of doing our own analysis.

Edited to add:

The point of SA correction is that when something in measured monthly (or quarterly) you usually see seasonal variations – sometimes this is what you are interested in (e.g. shopping at Xmas) but sometimes you want ignore the seasonal part and just focus the underlying trend, i.e. want to split the ‘signal’ into a trend + seasonal component + irregular bit. The SA aims to determine the seasonal component and then remove it from the series.

Edited November 2, 2005 by spline

[karhu]

I’m pleased that the raw data is made public

I wish that I could see the RAW DATA!

unless there is an aliasing problem (there isn’t here)

It's more of a statistical scatter problem.

If you add the errors on the monthly value to those on the SA adjustment that probably leads to an error of +/- 0.5% making the values only slightly less than meaningless and especially for people who are not used to analysing statistics.

Edited November 1, 2005 by karhu

[spline]

I wish that I could see the RAW DATA!

It's more of a statistical scatter problem.

Yikes, that would be something!

But a there has to be some balance here – I don’t mind letting them do the mix-adjust and regional aggregation but am happy that they provide the ‘uncooked’ NSA datasets.

Also they are measuring something that's inherently volatile and it's not really a big deal to simply smooth it over, or even look at the YoY.

But I agree that frontpage newpaper headlines based on monthly rise/falls is just plain stupid.

Edited November 1, 2005 by spline

[karhu]

But I agree that frontpage newpaper headlines based on monthly rise/falls is just plain stupid.

I suppose it keeps someone in a job

[spline]

The current (Oct/05) Nationwide SA profile is:

SA = NSA + Adjust

Month % Adjust

Oct-04 +0.4%

Nov-04 +0.5%

Dec-04 +0.8%

Jan-05 +1.7%

Feb-05 +1.4%

Mar-05 +0.5%

Apr-05 -0.3%

May-05 -0.7%

Jun-05 -1.2%

Jul-05 -1.3%

Aug-05 -0.9%

Sep-05 -0.6%

Oct-05 +0.4%

Edit: extracted from the Nationwide UK Monthly Indices spreadsheet - see explanation below.

Edited November 1, 2005 by spline

[Sledgehead]

The current (Oct/05) Nationwide SA profile is:

SA = NSA + Adjust

Month % Adjust

Oct-04 +0.4%

Nov-04 +0.5%

Dec-04 +0.8%

Jan-05 +1.7%

Feb-05 +1.4%

Mar-05 +0.5%

Apr-05 -0.3%

May-05 -0.7%

Jun-05 -1.2%

Jul-05 -1.3%

Aug-05 -0.9%

Sep-05 -0.6%

Oct-05 +0.4%

Spline, give us a ref for those adjustments please. Cheers, SH

[spline]

Spline, give us a ref for those adjustments please. Cheers, SH

The SA adjustments are not constant and actually drift slightly over time as newer figures come under the rolling average - so probably not worth trying to reference them - but the easiest way to dig them out is from the Price = (Trend * Seasonal * Irregular) decomposition posted above, so for example, if the raw NSA series is given by Pnsa = T*S*I, then removing S gives the SA version Psa = T*I = Pnsa/S and S = Pnsa/Psa. Now because the correction NSA->SA is in the opposite direction we have the percentage correction Adj = 1/S –1 = Psa/Pnsa – 1. This last bit is hugely obvious with hindsight but it *is* useful see how it relates to the underlying methodology.

Edited November 1, 2005 by spline

[spline]

classixuk - Attached spreadsheet with simple example of SA adjustment using Land Registry house prices [excel, zipped]

seasonal_adjust_ex_v1.1.xls.zip

seasonal_adjust_ex_v1.1.xls.zip