On seasonal adjustment of the Quarterly Sector Accounts (QSA): Income, expenditure and savings for households and the NPISH sector

Monthly and quarterly time series are often characterised by considerable seasonal variations that might complicate their inter-period comparability. Therefore, such time series are subjected to a process of seasonal adjustment in order to remove the effects of these seasonal fluctuations. Once data have been adjusted for seasonal effects by X-12-ARIMA or some other seasonal adjustment tool, a clearer picture of the time series emerges.

For more information on seasonal adjustment: http://www.ssb.no/english/metadata/methods/seasonal_adjustment.html

1.2 Why do we seasonally adjust QSA ?

The quarterly institutional sector accounts (QSA) consist of a set of incomes and expenditures from which the items net savings and net lending/net borrowing are derived.

The balancing items, savings and net lending/net borrowing are shown in the accounts for incomes and expenditures for one sector. The saving ratio (the ratio between saving and disposable income) indicates how the sector has been financed. If savings are denoted by a negative sign, it means that a sector has used more resources than it had and had to finance its expenses through borrowing.

Only the full set of accounts for the sector “Households and non-profit institutions serving households (NPISH)” are published on a quarterly basis for the time being.

The table below shows the components and their weights for the Norwegian QSA during the period of 2009-2012. These weights stay almost the same during the whole period.

Income and Expenditure. The shares of the components for the period 2009-2012
Income	weights


+ Compensations of employees	52.7
+ Output producers' price	19.2
+ Pensjons and benefits from general government	16.0
+ Property income received	4.0
+ Correction for FISIM	2.1
+ Benefits from pension funds	2.0
+ Net current transfers for NPISH	1.7
+ Adjustments for households' pension funds	1.6
+ Subsidies on production	0.8
+ Capital transfers, net	-0.1

Expenditure	weights


- Total consumption by households and NPISHs	50.0
- Current taxes on income, wealth, etc.	24.3
- Intermediate consumption	9.0
- Property income paid	4.4
- Investment in non-financial capital	2.9
- Contributions to pension funds	3.6
- Consumption of fixed capital	3.2
- Compensation of employees paid	2.2
- Taxes on production	0.2
- Other current transfers paid, net	0.2

Since the weights for the main components are quite similar on both sides of the table, we can conclude that the value of the savings ratio is influenced by the values of the other small components. A clear example is the level shift in the saving ratio since 2006 as a result of a change in tax rules concerning the payments of dividends

Some of the most relevant series in the QSA show clear evidence of seasonality, for example gross value added and for total consumption. Most of the other series show seasonality in quite different ways. It seems to be that series for income and expenditure do not have identical seasonality.

Therefore, in order to evaluate the current saving rate in an appropriate way, the seasonality must be removed from its components. Series for the QSA are now extensive enough to identify their seasonality.

Series are long enough to run X-12-ARIMA but still remain quite short and therefore some problems of instability can arise. For different reasons as mentioned above, some of the aggregate series show non-identical seasonal patterns before and after 2006.

1.3 Seasonally adjusted series

All series included in the QSA have been seasonally adjusted. The indirect approach has been used for the main aggregates. This means that consistency is maintained for aggregation and definitions in the released tables for the seasonally-adjusted figures. We get better results for the main components when adjusting in this way (indirectly) in place to adjust directly. To arrive to such conclusion we use the results of the table enclosed in chapter 5 as well as other analysis using figures and output from the X-12-ARIMA.

It seems that the indirect adjustment of the main components leads to more stable series (lower irregular components) and therefore less revisions in the future. This is particularly relevant for the saving ratio and net lending/borrowing.

The following tables give an indication for the seasonal patterns for the most important aggregates.

The first table shows the estimated correction factors for 2013 based on prior data by direct adjustment with X-12-ARIMA. The actual factors however will not be identical since they are estimates again when new data are available. The second table shows the means of the actual seasonal factors for the period of 2006-2012 as a result of indirect adjustments of the individual series.

Expected seasonal factors for 2013
Main series	method	Q1	Q2	Q3	Q4


Gross value added	MUL	101.6	90.8	104.9	102.8
Mixed income	MUL	102.3	83.7	108.3	104.7
Primary income	MUL	100.9	99.8	99.6	99.7
Consumption	MUL	96.4	99.5	100.9	102.1
Disposable Income	ADT	-2912	-936	603	1901
Saving	ADT	10190	48	-2758	-7613
Net lending (+) / net borrowing (-)	ADT	10476	-536	-2268	-7802
Savings ratio	ADT	3.4	0.0	-1.0	-2.7
Savings ratio excluding dividends	ADT	4.2	-1.6	0.1	-2.7
Disposable real income in 2000 prices	ADT	-2461	-1656	1162	2438
Saving in 2000 prices	ADT	9167.0	-124.0	-2439.0	-6718.0

Average seasonal factors for the period 2006-2012
Main series		Q1	Q2	Q3	Q4


Gross value added	MUL	100.7	90.7	105.6	102.8
Mixed income	MUL	102.3	83.5	109.4	104.5
Primary income	MUL	100.4	99.5	100.0	100.1
Consumption	MUL	95.5	99.6	101.2	103.6
Disposable Income	ADT	-1154	-1438	-252	3059
Saving	ADT	10533	-266	-3488	-6921
Net lending (+) / net borrowing (-)	ADT	10769	-698	-2850	-7401
Savings ratio	ADT	4.3	-0.1	-1.3	-2.6
Savings ratio excluding dividends	ADT	4.6	-1.7	-0.4	-2.5
Disposable real income in 2000 prices	ADT	-1019	-1364	-234	2792
Saving in 2000 prices	ADT	9875	-318	-3621	-6338

Multiplicative method (MUL) means that seasonally adjusted figures are presented by dividing raw data by the factors showed in the tables. In the case of additive decomposition (ADT), seasonally adjusted is the difference between raw data and the factors.

Another important feature is that the tables show that the expected seasonal correction factors for 2013 match the actual seasonal factors in the previous years quite well. This implies that applying a direct or an indirect method for adjusting the main aggregates does not influence the results considerably.

For more information on the properties of the series please refer to "Analyzing the series of Quarterly Sector Accounts. doc “

http://www.ssb.no/english/subjects/09/90/doc_200907_en/doc_200907_en.pd

2. PRE-TREATMENT

2.1 Pre-treatment routines/schemes

Pre-treatment is an adjustment for variations caused by calendar effects and outliers

Running an automatic pre-treatment of the raw data based on standard options in the seasonal adjustment tools. The method used to calculate raw data for some of the series allows to remove both seasonal and outlier effects. This is especially true for the compensation of employees and for taxes and subsidies on production.

2.2 Calendar adjustment

Calendar adjustment involves adjusting for the effects of working days/trading days and for moving holidays. Working days/trading days are adjustment for both the number of working days/trading days and for that the composition of days can vary from one month to another

The series tested on the number of working days in a quarter can affect the results. For quarterly series, these effects are rarely identified. This is the case for the Norwegian QSAs. None of the series have been pre-treated for trading-day effects.
More relevant is the Easter effect. Four series have been corrected for Easter effects: production, compensation of employees, benefits from pension funds and consumption.

2.2.1 Methods for trading/working day adjustment

RegARIMA correction – in this case, the effect of trading days is estimated in a RegArima framework. The effect of trading days can be estimated by using a correction for the length of the month or leap year, regressing the series on the number of working days, etc. In this case, the residuals will have an ARIMA structure.

2.2.2 Correction for moving holidays

Use of standard options X-12-ARIMA, RegARIMA modeling, to identify and remove Easter effects.
Consumption: Correction based on an estimation of the duration of the moving holidays effects, specifically adjusted to Norwegian circumstances.

2.2.3 National and EU/euro area calendars

Use of default calendars. The default in X-12-ARIMA is the US calendar.

Comments: Final consumption expenditure for households uses the Norwegian calendar.

2.3 Treatment of outliers

Outliers or extreme values are abnormal values of the series

Outliers are detected automatically by the seasonal adjustment tool. The outliers are removed before seasonal adjustment is carried out, and then re-introduced into the seasonally adjusted data.

2.4 Model selection

Pre-treatment requires choosing an ARIMA model, as well as deciding whether the data should be log-transformed or not.

X-12-ARIMA automatically identifies one model if the average of the forecast errors is less than a previously established value. If all the models are refused one of them is manually selected (i.e. a default option). Under these premises the automatic selection must be synonymous with better quality of the results.
The model (0, 1, 1) (0, 1, 1), often referred to as the airline model, is generally the best one. This model has only 2 parameters and is easy to interpret.

2.5 Decomposition scheme

The decomposition scheme specifies how the various components – basically trend-cycle, seasonal and irregular – combine to form the original series. Most frequently used decomposition schemes are the multiplicative, additive or log additive.

It has been taken manual selection after graphical inspection of time series.
For stationary series (constant mean and variance) additive decomposition has been used

3. SEASONAL ADJUSTMENT

3.1 Choice of seasonal adjustment approach

X-12-ARIMA

3.2 Consistency between raw and seasonally adjusted data

The seasonal adjusted quarterly data will not sum up to the annual unadjusted data. This is in line with international recommendations. For the annual figures the seasonally adjusted and the raw series will be alike. This means that the sum of the seasonally adjusted figures for the 4 quarters in a year do not normally add up to the seasonally adjusted annual numbers.

3.3 Consistency between aggregate/definition of seasonally adjusted data

The chosen method imposes the equality between aggregated series and the component series.
Definitions and relationships also apply for seasonally adjusted figures. This is the main reason for choosing the indirect method for component series.

3.4 Direct versus indirect approach

Direct seasonal adjustment is performed if all time series, including aggregates, are seasonally adjusted on an individual basis. Indirect seasonal adjustment is performed if the seasonally adjusted estimate for a time series is derived by combining the estimates for two or more directly adjusted series
Indirect approach has been used. The seasonal adjustment of components occurs using the same approach and software, and then totals are derived by aggregation of the seasonally adjusted components.

3.5 Horizon for estimating the model and the correction factors

When performing seasonal adjustment of a time series, it is possible to choose the period to be used in estimating the model and the correction factors. Correction factors are the factors used in the pre-treatment and seasonal adjustment of the series.

The whole time series is used to estimate the model and the correction factors.

4. REVISION POLICIES

Seasonally adjusted data may change due to a revision of the unadjusted (raw) data or the addition of new data. Such changes are called revisions, and there are several ways to deal with the problem of revisions when publishing the seasonally adjusted statistics.

Both raw and seasonally adjusted data are revised between two consecutive official releases of the release calendar

4.1 General revision policy

Seasonally adjusted data are revised in accordance with a well-defined and publicly available revision policy and release calendar.

The following table gives an indication of the expected growth rate revisions from the previous period when we compare the initial and final published data. This only applies to revisions caused by seasonal adjustment routines where revisions of raw data are not considered.

How many percentage points are seasonally adjusted growth rates changed for period t when we condition on the last observation in the sample (2010 - 2012)
Main series	method	mean	min	med	max	Q1	Q2	Q3	Q4


Gross value added	MUL	0,3	0,0	0,3	0,5	0,3	0,3	0,2	0,3
Mixed income	MUL	0,3	0,0	0,3	0,8	0,3	0,3	0,2	0,6
Primary income	MUL	0,3	0,1	0,3	0,7	0,4	0,2	0,3	0,2
Disposable Income	ADT	634	117	631	1337	780	705	410	644
Consumption	MUL	0,3	0,0	0,3	0,8	0,6	0,1	0,2	0,3
Saving	ADT	789	84	567	1619	963	1053	373	758
Net lending (+) / net borrowing (-)	ADT	987	325	587	2571	1513	1160	483	693
Savings ratio	ADT	0,2	0,0	0,2	0,3	0,1	0,3	0,3	0,2
Savings ratio excluding dividends	ADT	0,2	0,1	0,2	0,4	0,2	0,3	0,2	0,2
Disposable real income in 2000 prices	ADT	732	112	856	1498	604	756	599	1089
Saving in 2000 prices	ADT	738	120	701	1377	798	948	536	638

The figures for the savings rate show that the growth rate from the previous period are exposed to a revision of 0.2 (the median in the period 2010-2012) points when new observations are available. Major revisions for the savings ratio are in Q2 and minor in Q1.

4.2 Concurrent versus current adjustment

Partial concurrent adjustment: the model is identified and estimated yearly, while filters, outliers and regression parameters are re-identified and estimated continuously as new or revised data become available.

4.3 Horizon for published revisions

The revision period for the seasonally adjusted results is limited to 3-4 years (preferably 4) prior to the revision period of the unadjusted data, while older data are frozen.

5. QUALITY OF SEASONAL ADJUSTMENT

5.1 Evaluation of seasonally adjustment data

evaluation using standard measures proposed by different seasonal adjustment tools.

5.2 Quality measures for seasonal adjustment

For most of the series, a selected set of diagnostics and graphical facilities for bulk treatment of data is used.

Table of quality measurement for this statistics is as follows:

QSA : Quarterly sector accounts
SUMMARY OF QUALITATIVE INDICATORS
(Calculated for the period 2002 - 2012) SERIES	Main options		Anova*				Revisions**		Qualitative indicatorer x12-ARIMA

(Calculated for the period 2002 - 2012) SERIES	METHOD	ARIMA MDL	IRREG	TREND	SESONG	TDDAY	ASA***	ACH	M2	M7	M10	M11	Q-verdi

Gross value added	MUL	(0 1 1 ) ( 0 1 1)	0,3	1,8	97,9	0,0	0,2	0,3	0,0	0,1	0,3	0,2	0,2
Mixed income	MUL	(0 1 1 ) ( 0 1 1)	0,2	0,9	98,9	0,0	0,2	0,3	0,0	0,1	0,3	0,3	0,2
Primary income	MUL	(0 1 1 ) ( 0 1 1)	17,7	67,4	14,9	0,0	0,2	0,3	0,4	3,0	1,6	1,0	1,4
Consumption	MUL	(0 1 2 ) ( 0 1 1)	0,7	9,6	89,6	0,0	0,2	0,3	0,1	0,2	0,4	0,3	0,2
Disposable Income	ADT	(0 1 1 ) ( 0 1 1)	22,6	41,0	36,5	0,0	634	634	0,3	1,1	0,8	0,4	0,7
Saving	ADT	(1 1 0 ) ( 0 1 1)	12,0	7,8	80,2	0,0	789	789	0,3	0,4	0,5	0,3	0,7
Net lending (+) / net borrowing (-)	ADT	(0 1 1 ) ( 0 1 1)	11,2	9,1	79,7	0,0	987	987	0,3	0,4	0,6	0,4	0,7
>Savings ratio	ADT	(0 1 1 ) ( 0 1 1)	10,2	6,6	83,3	0,0	0,2	0,2	0,3	0,4	0,6	0,3	0,7
Savings ratio excluding dividends	ADT	(0 1 1 ) ( 0 1 1)	3,1	2,3	94,7	0,0	0,2	0,2	0,2	0,2	0,3	0,3	0,5
Disposable real income in 2000 price	ADT	(0 1 1 ) ( 0 1 1)	20,8	31,0	36,6	11,6	732	732	0,6	1,3	0,7	0,3	1,0
Saving in 2000 prices	ADT	(0 1 1 ) ( 0 1 1)	12,0	8,0	8,0	0,0	738	738	0,3	0,4	0,5	0,2	0,7

	* ANOVA shows the relative contribution to the variance of the per cent change in the components of the original series.
	** ASA : average absolute revisions of the seasonally adjusted series.
	** ACH : average absolute revisions of the quarter to quarter chamged in the seasonally adjusted series.
	*** when method ADT are revisions for ASA og ACH presented as differances and not as percentage.

Comments to the table of qualitative indicators

The series were adjusted with both additive and the multiplicative method. The results of main aggregates are calculated via direct adjustment with X12-ARIMA. Although these series in practice are indirectly adjusted, we may claim that the results are still valid (see chapter 1.3)

X12-ARIMA chooses automatically the most appropriate model for the individual series.

ANOVA shows that the rates of change for the original series are primarily due to seasonal effects.

The contribution from trend and the irregular component is particularly relevant for primary income, saving and net lending/borrowing. For savings rate 83,3 per cent of the change in the raw data is explained by season. The rest is explained 6,6 per cent by trend and 10,2 per cent by the irregular component.

ASA and ACH were calculated for the period 2010-2012.

M- and Q-values for the main aggregates indicate that some of the series (gross value, mixed income and consumption expenditure) are adjusted with satisfactory results. Nevertheless both levels and rates of change for the latest periods are exposed to revisions. The series may have some irregular fluctuations.

The remaining series are adjusted with questionable results. Levels and rates of change may have a great deal of variation in the most recent figures. The results should be interpreted with caution

6. SPECIFIC ISSUES ON SEASONAL ADJUSTMENT

6.1 Seasonal adjustment of short time series

All series are sufficiently long to perform an optimal seasonal adjustment.

6.2 Treatment of problematic series

Problematic series are treated in a special way only when they are relevant. The remaining series are treated according to normal procedures.

7. DATA PRESENTATION ISSUES

7.1 Data availability

Options:

Raw and seasonally adjusted data are available.
All metadata information associated with an individual time series is available.
Historical data are available to enable revision analysis.

7.2 Press releases

In addition to raw data, at least one of the following series is released: pre-treated, seasonally adjusted, seasonally plus working day adjusted, trend-cycle series.
Only levels or different forms of growth rates are presented.
For each series, some quality measures of the seasonal adjustment are presented.

8. REFERENCES:

http://www.ssb.no/english/subjects/09/90/doc_200907_en/doc_200907_en.pdf

ESS Guidelines on Seasonal Adjustment.

Eurostat. (2008). TF-QSA-MAY08-07B: Seasonal Adjustment of key indicators and components – Quarterly (non-financial) sector accounts of the euro area and the European Union-

Hungarian Central Statistical Office (2007): Seasonal adjustment methods and practices (European Commission Grant 10300.2005.021- 2005.709) U.S.

EUROSTAT: Seasonal Adjustment. Methods and Practices

US census: X-12-ARIMA-manual