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Direct vs. Indirect Approach in Seasonal Adjustment:

Proposal for a new tool

Necmettin Alpay KOÇAK[1] Akın ÖZTÜRK[2]

Abstract

In recent years, seasonal adjustment methods have been discussed in the literature, but another topic for consideration is whether to use the direct or indirect approach for a group of series. In particular, the lack of a special software tool for comparing the direct and indirect approaches gives statistical offices and researchers a huge work load in deciding which is better. This article tries to make it easier to choose between the direct and indirect methods by introducing a new effective software tool called DISAT into the seasonal adjustment process. The new tool and background methods are introduced and applied to the Turkish National Accounts dataset as an example. Using the graphical and statistical analysis modules of DISAT, some direct and indirect alternatives are supplied for the aggregated domestic product series.

Keywords: Seasonal adjustment, direct approach, indirect approach, aggregated series.

JEL classification: C43, C87

Acknowledgments : The authors wish to thank their colleagues James Macey from Office for National Statistics (ONS) and Dairo BUONO from EUROSTAT for useful comments and helpful suggestions on various drafts of this article.

Introduction

Seasonal and calendar adjustment is the process of modifying an economic time series to remove (1) regularly recurring short term movements (monthly, quarterly and six-monthly) described as seasonal fluctuations, and (2) the effect of weekends, official and religious (moving) holidays which are varied according to calendar. There are many methods in the literature concerning how these effects can be removed from time series[3]. When considering a single economic time series, which method to be used has importance in seasonal adjustment, but when a group of time series (i.e. balance of payments, national accounts, industrial production and sub-items) is of interest, the situation is slightly more complicated than previous. In this case, the discussion is on which approach (aggregated or disaggregated data) is to be used in seasonal adjustment.

There are basically two approaches in the seasonal and calendar adjustment of a particular group of time series. The first is the direct approach which all of the time series in the group are taken into account individually regardless of additive relationship and seasonal adjustment is then performed to each individual series. Although individually seasonal adjustment of each time series can be treated as an advantage in terms of ease of operation, the corruption of additive (weighted/unweighted) relationship between seasonal adjusted aggregated series and sub-items may be evaluated as a major disadvantage of the direct approach. The second approach is the indirect approach which means the aggregation of seasonally and calendar adjusted sub-item series to obtain seasonally and calendar adjusted upper-level items. Additive relationship between the group of series is being preserved in the indirect approach, however there may be a residual seasonal and/or calendar effect in seasonally and calendar adjusted series which is obtained by aggregation of seasonally and calendar adjusted sub-item series (Astolfi, et al., 2001).

Seasonally and calendar adjusted data of short-term statistics which are published by local agencies and international organizations are very important for policy makers. Since the choice between direct and indirect approach directly affects the information that is given to policy makers (Koçak, Mazzi and Moauro, 2010) the decision must be taken efficiently by agencies and organizations.

One of the approaches must be selected in each case since there are differences between the results of them (European Central Bank (ECB), 2010). There are some theoretical contributions on this topic. It is claimed that indirect approach may be preferable according to the smallest mean-squared-error criterion in case of joint distribution of time series components (trend, seasonal and irregular) is known and linear methods are used Geweke (1978). However, first degree of aggregation of time series reveals quite irregular and non-linear structure. Indeed, Ghysels, et al. (1996) detected that the filters with time varying parameters[4] degrade the linearity of seasonal adjustment process. Also, Ghysels and Osborn (2001) shows that Geweke’s results are not consistent in case of stretching the assumption of joint distribution of time series components are known. Finally, European Statistical System Guidelines on Seasonal Adjustment[5] mentions that there is not superiority in terms of theoretical or empirical results between the two approaches.

Since the theory has not addressed a solution for supremacy problem between these two approaches, the proposed pragmatic solutions have gained popularity in practice. Hood and Findley (2001) suggested a few important criteria i.e. a residual seasonal and/or calendar effect test, the comparison of the relative variability of seasonal component and measuring the size of revisions of seasonal adjusted series to select the appropriate approach. Astolfi, et al. (2001) proposed additional criteria i.e. smoothness of trend component, comparisons of cyclical peaks and troughs. Maravall (2006) also focused on size of the revisions and smoothness of the components.

Considering the statistical classifications (i.e. NACE, ISIC, etc.) used in production of data, it is a difficult task to compare direct and indirect approaches for each aggregated series (for each level of classification). Also, it is hard to say that the individual researcher can benefit from codes generated from, in general, SAS or MATLAB used by statistical agencies. Therefore, the motivation of this paper is the lack of an aggregation module to provide the series according to indirect approach and lack of a tool to easily calculate the criteria proposed in literature to compare of these two approaches. Another objective of this study is to develop the criteria previously explained by the literature. In detail, the diagnostics are extended by taking account the forecast functions of derived components i.e. seasonal adjusted series, trend-cycle etc.

About the developments of a tool on that topic, it should be noted that Eurostat and National Bank of Belgium developed a tool called TSTools which is auxiliary tool of the new seasonal adjustment software called Demetra+[6]. It contains many useful time series analysis tools i.e. trend–cycle analysis, benchmarking, temporal disaggregation and logit/probit models which may be used after seasonal adjustment with Demetra+. Also, there is a direct/indirect seasonal adjustment module in TSTools. The user can perform seasonal adjustment with different specifications of either Tramo&Seats or X-12-ARIMA for time series and then, all seasonally adjusted series are aggregated in a default way which is only the summing up all time series. So, the user obtains direct and indirect seasonally adjusted series. Also, it shows two separate graphics which are the difference between those two approaches and spectrum graphic of this difference series. The main disadvantages of TSTools are that the user has no opportunity to define structure of aggregation and there is no possibility to give a weight for each series during aggregation of all series. In that circumstance, TSTools is of very limited practical use for the production.

Comparison of direct and indirect seasonal adjustment can be made in effectively and time-saving manner with enhanced visual tools and theoretical criteria developed in the Direct&Indirect Seasonal Adjustment Tool (DISAT) proposed by this paper. A brief description of this new tool and theoretical and programmatic details will be presented after this introduction. Then, an application and results will be given. In the conclusion, general evaluation of the paper will be done.

2. New Tool : DISAT

DISAT performs aggregation of the series using by the outputs of individually seasonally adjusted series. During the aggregation process, it uses a classification structure defined by user and weights used in the classification to obtain indirectly seasonal adjusted series. Then, it provides to users both graphical views and statistical criteria to compare the directly and indirectly adjusted series.

This tool is designed to analyze the outputs obtained from TRAMO&SEATS for Windows, hereafter TSW (Caporello and Maravall, 2004), or Demetra+ seasonal adjustment softwares. For TSW, there are two outputs file which are in Excel[7] format and they cover the output time series obtained from both TRAMO and SEATS. For instance, TRAMO Excel output file contains original series, linearized series, etc., and SEATS output file contains original series, trend-cycle series, seasonal adjusted series, seasonal component etc. On the other hand, Demetra+ can produce all outputs in one Excel file which covers, for example, original series, trend-cycle series, seasonal adjusted series, seasonal component, irregular series, and calendar adjusted series.

To be read by DISAT, TSW output files need to be slightly modified by the user. One of the points is about the sheets in the files. The numbers and the names of those sheets must be identical with each other. Another point is that the ARIMA forecasts produced by TSW should be present both in the output files, since DISAT takes into account the forecasts during the comparison of the direct and indirect approaches. In Demetra+ side, user should select all components to be exported for Excel output file.

DISAT needs three basic pieces of information as well as output files of TSW or Demetra+. The first is the frequency of group of the time series. It should be unique for all time series in the group. At the moment, DISAT is able to analyze monthly and quarterly series. The second piece of information is the number of forecasts that are in the output files. Outputs files produced by TSW contain 24 months forecasts for monthly time series and 8 quarters forecasts for quarterly series, as a predetermined value. The number of forecasts that the user enters to TSW should be same with that the user enters to DISAT. Finally, if there is a classification system (hierarchy tree) previously created and saved, it is loaded to DISAT by the user.

a. Hierarchy Tree

Once the outputs files are loaded to DISAT, all of the sheets (name of the series) are listed. The user must identify a hierarchical relationship between the series so that DISAT can perform aggregation process. The hierarchical relationship reflects the relationship between the time series in the group. The relationship may vary depending on the type of group of the series. Such classifications, NACE, MIGS, national accounts by production method, may be examples of this relationship. Each classification has its own hierarchical structure and this structure can be easily created by the user in DISAT. The logic of the hierarchy tree is developed in DISAT tool to facilitate pairing process of classification on interest[8]. The series which is hierarchically at the top of the group will be at the top of the hierarchy tree. During the creation process of that tree, the most important issue is weighting and it is possible to give weight by the user for each series in DISAT[9].

When NACE Rev.2 classification up to 4 digits with 400 time series is concerned, the creation of a tree is quite a hard process and that requires attention. However, once the user created hierarchy tree, it is possible to save this tree as an XML file and to use in other applications, subsequently. Finally, it may be desired to use original series in aggregation process, when there is an absence of statistically significant seasonality in the series of interest. In that case, user may choose the original series instead of the seasonal and calendar adjusted series in DISAT.

b. Aggregation

DISAT begins the analysis with aggregation process of the series in the group. Let i = 1,2,...,n shows the number of the series in the group, and those series can be aggregated in equation (1).

[pic] (1 )

Here, At,O is the aggregated original series; K1,O,...,Kn,O, are sub-items of original series; b1,...,bn, are weights of each sub-items. “O” is the abbreviation of the original series. The total of the weights must be equal to one. In case of the aggregation is done without using weight (direct summation or extraction), values of “b” would be either “+1” or “-1”. The aggregation process used in indirect seasonal adjustment can be formulated for different types of component in a time series shown between equation (2) and (7) which are modified version of equation (1).

[pic] (2 )

[pic] (3 )

[pic] (4 )

[pic] (5 )

[pic] (6 )

[pic] (7 )

Here, S represents the seasonally and calendar adjusted series; L represents linearized series; SA represents only seasonal adjusted series; CA represents only calendar adjusted series; TC represents trend-cycle component of the series on interest; I represents irregular component of the series on interest. For instance, seasonally and calendar adjusted sub-items time series are combined using with their own weights to obtain indirectly seasonally and calendar adjusted At,S series as shown in equation (2). However, seasonality of a series may be not statistically significant for some sub-items. Therefore, original values (O) may be required to be used in the equation (2). The weighting structure and separation of O/S can be identified using by DISAT interface. In the stage of irregular component aggregation, if any of the sub-item series has no seasonality, the values of irregular component of the sub-item are taken zero[10].

Aggregation of the specific components of the time series may be seen as a problem in terms of type of decomposition. At this stage, it would be useful to mention the subject of decomposition. Selecting the type of decomposition is the initial step of the seasonal adjustment. In general, additive and multiplicative decomposition are used in the literature.

[pic] (8 )

[pic] (9 )

Equations (8) and (9) show that how a time series can be decomposed in an additive and multiplicative way, respectively. These equations contain TC, trend-cycle component; S, seasonal component; C, calendar effect component and I shows irregular component. The components here are obtained as level value of the series in case of additive decomposition, but in case of multiplicative decomposition, the components are obtained as factors. In this paper, simple mathematical conversation is used to solve the unit inconsistency problem. In the indirect aggregation process, specifically, equation (10) may be used to convert from factors to level of the series components of K1,t series which is assumed that multiplicatively decomposed.

[pic] x = TC, S, C, I (10 )

Lin means that the component is obtained from additive decomposition; Log means it is obtained from multiplicative decomposition. Equation (10) expressed that it is possible to transform a component obtained multiplicatively to additive component by subtracting 100 from multiplicative component and multiplying that result with original series.

c. Analysis

At the end of the aggregation process, each of the aggregated series in the hierarchy tree which are calculated according to both direct and indirect approach is obtained. Then, to make comparisons between the series calculated by direct and indirect approach, statistical criteria for each of component of each aggregated series are reported in the “Analysis” part of DISAT.

[pic] (11 )

[pic] (12 )

[pic] (13 )

[pic] (14 )

Explanations of the difference indicators given (11) to (14) are presented in Astolfi et al. (2001). In formula (11), D1 is defined as the average of absolute differences between growth rates of the series, and are calculated by the direct and indirect. D2 given in formula (12) is defined as the standard deviation of absolute differences between growth rates of the series, and are calculated by the direct and indirect. D3 and D4 are defined as maximum and minimum values of absolute differences between growth rates of the series, and are calculated by the direct and indirect in formulas (13) and (14), respectively.

DISAT presents concordance measurement as given by Astolfi et al. (2001) and ECB (2010) which is defined as directional compatibility between growth rates of the seasonal adjusted series or components of the series which are calculated by direct and indirect approach.

For time “t”, t=1,2,...,n, and let G represents growth rate of series/components on interest. If,

Gt,Direct > 0 and Gt,Indirect > 0 → c=1

Gt,Direct < 0 and Gt,Indirect > 0 → c=0

Gt,Direct < 0 and Gt,Indirect < 0 → c=1

Gt,Direct > 0 and Gt,Indirect < 0 → c=0

Then, total number of c=1 is divided to “n” number of total observations. This ratio, concordance, is between 0 and 1 (ECB, 2010). And if,

0 < Concordance ≤ 0.6 → No discrimination

0.6 < Concordance ≤ 0.7 → Poor

0.7 < Concordance ≤ 0.8 → Acceptable (Fair)

0.8 < Concordance ≤ 0.9 → Excellent (Good)

0.9 < Concordance ≤ 1 → Outstanding

DISAT calculates the concordance index and four difference criteria explained in the equations between (11) and (14) for three different time period. Thus, it can be observed that how the difference between final estimator and preliminary estimators of statistical criteria are changed.

This time periods are:

❖ Last three years (between n-36th and nth observations for monthly series, between n-12th and nth observations for quarterly series)

❖ Full sample (For all observations in sample)

❖ Forecasts (between n+1th and n+24th observations for monthly series, between n+1th and n+12th observations for quarterly series)

Another measure, which assesses the smoothness of adjusted series suggested by Dagum (1979) may reflect the difference between direct and indirect seasonal adjustment approaches. Accordingly, components/adjusted series calculated by direct and indirect approaches whichever is smoother, that approach (direct or indirect) should be preferred. In equation (15), At = Adjusted series and the approach which gives smallest R1 means that the series calculated by one of those approaches are smoother. R1 statistics in DISAT is calculated for 3 different series such as seasonally and calendar adjusted series, seasonally adjusted series and calendar adjusted series. In addition, the measure of smoothness is calculated for the last three years and for full sample in order to monitor changes to these statistics over time.

[pic] (15 )

Finally, an important criterion used in the comparison between direct and indirect approaches is used to test the existence of residual seasonality mentioned by Hood and Findley (2001) and Astolfi et al. (2001) is presented in DISAT. A residual seasonality test is applied to direct final irregular component (Idirect) and indirect final irregular (IIndirect) components obtained by using equation (7).

The Friedman test[11] used in DISAT evaluates the existence of residual seasonal effects in the final irregular component. This test is a non-parametric test for analyzing randomized complete block designs. It is an extension of the sign test when there may be more than two treatments. The Friedman test assumes that there are N experimental treatments. The observations are arranged in k blocks.

Then the Friedman test is:

H0 : The treatment effects have identical effects

Ha : At least one treatment is different from at least one other treatment

Let

Rij = the ranks assigned to the ith treatment in the jth block.

N : Number of observation in each block

k : Number of blocks

And the Friedman test statistics are calculated by using following formulas (16) and (17):

[pic] (16)

[pic] (17 )

If k is small, k ≤ 5, the approximation to chi-square becomes poor and the p-value should be obtained from tables specially prepared for the Friedman test. If the p-value is significant, appropriate post-hoc multiple comparisons tests would be performed (Kendall and Ord, 1990).

The current version of DISAT does not contain the sliding spans and revisions statistics suggested by Hood and Findley (2001) and Maravall (2006). Use of these diagnostics is also advised by the ESS Guideline on Seasonal Adjustment to compare direct and indirect approaches. But, these additional diagnostics will be included in the next release of DISAT.

d. Outputs

DISAT generates two types of output. The first is the group of the series which are calculated according to the direct and indirect approach. These series are presented in Excel format to the user[12]. The second is the graphics to which we can visually compare the series generated by DISAT[13]. Graphical analysis of the seasonally adjusted time series and other components is essential to assess whether direct and indirect approaches lead to similar results. In particular, this analysis makes it possible to verify the turning points of seasonally adjusted monthly growth rates (ECB, 2010). If it is desired, these charts can be obtained in *.png format. The series and graphics reported by DISAT are given in Table 1. Aggregated results for each series group, and each component of them are transferred to the graphical environment. There are level values and also growth rates of each component. Growth rates of linearized series and calendar effect adjusted series are calculated as year-on-year growth. Growth rates of all other series are calculated as period-to-period growth. The differences between the direct and indirect approach in terms of level and growth rates are also portrayed into graphic tool.

Table 1 Series and graphics produced by DISAT

| |Linearized |Trend- |Seasonal |Calendar |Seasonal and |

| | |Cycle |Adjusted |Adjusted |Calendar adjusted |

|a. Direct approach (level) |+ |+ |+ |+ |+ |

|b. Indirect approach (level) |+ |+ |+ |+ |+ |

|c. Difference (level) (a-b) |+ |+ |+ |+ |+ |

|d. Direct approach (growth rates) |+ |- |- |+ |- |

|(year on year) | | | | | |

|e. Indirect approach (growth rates) |+ |- |- |+ |- |

|(year on year) | | | | | |

|f. Difference (growth rates) (d-e) |+ |- |- |+ |- |

|g. Direct approach (growth rates) |- |+ |+ |- |+ |

|(period to period) | | | | | |

|h. Indirect approach (growth rates) |- |+ |+ |- |+ |

|(period to period) | | | | | |

|i. Difference (growth rates) (g-h) |- |+ |+ |- |+ |

Note: “+” means that the interest is available, “-” is non-available.

3. Application and results

In this study, a short application is designed to show functioning and outcomes of DISAT software. We used the gross domestic product (GDP) series published by Turkish Statistical Institute and its sub-items classified according to the approach of the production method. In that group, there is a total of 21 time series and each of the series covers the period between 1988-Q1 and 2009-Q4. GDP series group by production approach are shown in Table 2. In the stage of raw data production, “A. Total of sectors” is primarily obtained by summing the items A1,A2,...,A17. Then, “GDP” is calculated as the sum of A, B and C series. Therefore, two aggregated series (A. Total of sectors and GDP) are obtained. The problem of the choice of the direct and indirect approach in the seasonally and calendar adjusted data production phase is due to this aggregation relationship.

Table 2 GDP and sub-components according to production approach

|Gross Domestic Product (GDP) |

|Sectoral total |

|Agriculture, hunting and forestry |

|Fishing |

|Mining and quarrying |

|Manufacturing |

|Electricity, gas and water supply |

|Construction |

|Wholesale and retail trade |

|Hotels and Restaurants |

|Transport, storage and communication |

|Financial intermediation |

|Ownership and dwelling |

|Real estate, renting and business activities |

|Public administration and defense; compulsory social security |

|Education |

|Health and social work |

|Other community, social and personal service activities |

|Private household with employed persons |

|Financial intermediation services indirectly measured (-) (FISIM) |

|Taxes-Subsidies |

In the direct approach, each series in the Table 2 individually (under the assumption of there is no additive relationship between the series) is subject to seasonal adjustment. Therefore, the seasonally and calendar adjusted “A. Sectoral total” series is obtained using the direct approach. Same situation is also valid for seasonal adjusted GDP. In the indirect approach, after the sub-items A1, A2, A3,..., A17 series have been seasonal adjustment, the seasonally and calendar adjusted “A. Sectoral total” series is obtained by aggregation just like the aggregated raw data producing process. Then, the indirectly seasonally adjusted GDP series is obtained by summing the indirectly calculated “A. Sectoral total” series and individually seasonal and calendar adjusted B and C sub-items.

The reason why the users have to choose one of the approaches is that the results obtained from the two approaches are not the same, given the seasonality cancel–out effect that recurs when summing-up original series. DISAT is designed as tool that can help users to decide in these cases. In this application, all series in the group of GDP series are seasonally and calendar adjusted using by TSW entering the parameters[14] RSA=3 and IREG=1. Using with IREG=1, the model consists the calendar effect which covers the reference and forecast period. As a result of seasonal adjustment of GDP series group, all series have significant seasonal and/or calendar effect, except for the series “A11. Ownership and dwelling”.

Two Excel files (Figure 1) which contains output series (including forecasts) of TSW are obtained, and these two files are loaded to DISAT. Note that the forecast horizon is 8 observations in the files. Then, the hierarchy tree as mentioned before is created. As there is no significant seasonal and calendar effect in the “A.11 Ownership and dwelling” series, it is stated in the tree that the raw data of this series is used when indirect seasonal adjusted series is obtained (Figure 2). Besides, negative (-1) weight is given to FISIM series in the tree because it has negative impact in the additive relationship of series group (Figure 2).

[pic]

Figure 1 Outputs of TSW = Inputs of DISAT

[pic]

Figure 2 Interface of DISAT

After setting up for analysis, DISAT gives graphics (Figures 3 and 4) which represent seasonally adjusted series calculated directly and indirectly for both “A. Sectoral total” and GDP series. The left side of Figure 3 shows the graphic which represents growth rates (period to period) of directly and indirectly calculated seasonally and calendar adjusted series of “A. Sectoral total”, and right side shows difference series between the series given on the left. It can be suggested that the tendency of growth rates of direct and indirect approach is very close to each other, but the differences between growth rates are in the range of +3 to -3 points. It can be said that the growth rate series which is obtained by the direct approach is smoother than the indirectly obtained.

[pic] [pic]

Figure 3 Graphic outputs for “A. Sectoral total” series

Looking at the aggregated GDP series in the graphics (Figure 4), it can be suggested that indirect approach produces smoother growth rates of seasonally and calendar adjusted series than those of direct approach. It may be suggested that size of the differences between calculated directly and indirectly growth rates are smaller than those shown in right side of Figure 4. To make a more precise decision for “A. Sectoral total” and “GDP” series, statistical criteria should be consulted. Summary tables 3, 4, 5 and 6 represents the comparison between statistical criteria produced by DISAT for directly and indirectly calculated seasonally and calendar adjusted series of both aggregates.

[pic] [pic]

Figure 4 Graphic outputs for GDP series

The following remarks may be made for Tables 2 to 5. For the series “A. Sectoral total”, according to Table 3, absolute values of differences between growth rates of seasonally and calendar adjusted series calculated by direct and indirect approach. The average value of last three years is lower than that of full sample. The average of differences between the growth rates of forecasts is lower than those of last year and full sample. The standard deviation of the last three years is lower than that of full sample, as it is in average. Also, this difference is the minimum for the forecasts. The largest deviation is 1.753 (at Q3-2009), but that is 2.343 (at Q1-2001) when full sample is considered. It should be noted that the periods Q1-2001 and Q3-2009 are the time of economic crisis in Turkish economy. On the other hand, it can be said that forecasts are more consistent. The smallest deviation is nearly zero when the last three years and the full sample are considered. So, it can be said that the range between growth rates of direct and indirect seasonally adjusted series is quite narrow. Considering the concordance index of direct and indirect approach for different time period, two growth rates show outstanding compliance with each other by the rate above 90%. According to Table 4, considering the measurement of smoothness (Dagum, 1979), in last three years, indirect approach is smoother, however direct approach is more when full sample is taken account. So, the indirect approach is useful in the period of the last economic crisis.

Table 3

[pic]

Table 4

[pic]

For the series “GDP”; according to Table 5, absolute values of differences between growth rates of seasonally and calendar adjusted series are calculated by the direct and indirect approach, the average value of last three years is lower than that of full sample. The average of differences between the growth rates of forecasts is higher than those of last year and full sample. Note that there is an inconsistency between forecasts of direct and indirect approach. The standard deviation of the last three years is lower than that of full sample, as it is in average. The largest deviation is 0.310 (at Q3-2009) in last three years, but that is 1.373 (at Q1-2001) when the full sample is considered. Also, it can be said that forecasts are more compatible. The smallest deviation is 0.026 in last three years, but that is nearly zero when full sample is considered. So, it may be said that the range between growth rates of direct and indirect seasonally adjusted series is quite narrow. On the other hand, differences between forecasts are larger as supported in D1 statistics. Considering the concordance index of direct and indirect approaches for different time period, the two growth rates show outstanding compliance with each other by the rate above 90%. According to Table 6, considering the measurement of smoothness (Dagum, 1979), In the last three years, direct approach is smoother; however the results are almost equal when full sample is taken account. Considering the indirect approach is selected for the first aggregate “A. Sectoral total” series and equality of Dagum statistics for full sample, using of the indirect approach can be suggested for aggregated GDP series.

As last diagnostic, Friedman residual seasonality test results are evaluated. As can be seen in Table 7, the null hypothesis which suggests there is no residual seasonality cannot be rejected for the irregular components of “A. Sectoral total” and “GDP” series calculated by direct and indirect approaches due to those probabilities (in parenthesis).

Table 5

[pic]

Table 6

[pic]

Table 7 Results of residual seasonality test

| |Direct |Indirect |

|A. Sectoral total |1.14 (0.999) |1.90 (0.996) |

|GDP |1.58 (0.998) |1.58 (0.998) |

Before making an overall assessment of these results, it must be pointed out that the most appropriate seasonal assessment specification was not used for the 21 series in this group, but the automatic procedure was used. This paper does not aim to find the best model specification for seasonal adjustment of group of the specific series of interest. Therefore, differences in the seasonal adjustment process of individual series will affect the results of choices between direct and indirect approach. Also, all remarks are about the seasonally and calendar adjusted data, not about the other component i.e. linearized series, trend-cycle component and etc. Under these conditions, direct approach can be preferred for “A. Sectoral total” series, indirect approach can be preferred for “GDP” series.

4. Conclusion

While there is a debate in the literature about which method to use in the seasonal adjustment process, choice of the direct or indirect approach in seasonal adjustment is the subject of a separate discussion when a group of series are considered. From the studies in the literature, it cannot be reached that there is a clear consensus about which approach is more superior to other. On the other hand, there are a very limited number of tools that can be used in the decision-making process. Despite the fact that the users can compare these two approaches by using program codes in databases, they feel that there is a lack of tool which covers statistical and graphical criteria explained in the literature. Considering the ability of exhibiting the comparisons between direct and indirect seasonal adjustment in the graphical and statistical perspective, DISAT is thought to be a useful tool because it is easy to use. In this study, it may be suggested that a decision for national accounts series is made. As a result of application, indirect approach can be preferred for both “A. Sectoral total” series, and “GDP” series. When making a decision, graphic interface of DISAT is used and statistical criteria calculated by DISAT are considered. Finally, it should be emphasized that the DISAT tool will be a more effective tool when it contains other benchmarking criteria (revisions, sliding spans etc.) explained in the literature.

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Maravall, A., 2006, “An application of the TRAMO-SEATS automatic procedure; direct versus indirect adjustment,” Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2167-2190, May.

Maravall, A. 2007. “Application of Program TSW to a Set of Macroeconomic Time Series”, Mimeo, Bank of Spain, 136 pp. Available at:



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[1] Expert in Department of National Accounts and Economic Indicators at Turkish Statistical Instıtute.

E-mail: alpay.kocak@.tr . Corresponding author.

[2] Expert in Department of Information and Communication Technologies at Turkish Statistical Instıtute.

E-mail: akin.ozturk@.tr

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[3] Fischer (1995) gives detailed information for suggested methods in the literature i.e. TRAMO&SEATS (Gomez and Maravall, 1996) and X-12-ARIMA (Findley et al, 1998).

[4] A filter used in seasonal adjustment process exhibits preliminary and final properties for related time series.

[5] Available on the Eurostat website at



[6] Demetra+ and also TSTools have published officially by Eurostat, the final-release version of Demetra+ is available at .

[7] DISAT is able to read and write the Excel 97/2003 and Excel 2007 files since it uses the Microsoft Excel 11.0 Object Library for reading Excel file.

[8] XML is used to hold tree combination structure for displaying and calculation steps. User can define nodes and bind them tree wherever it is necessary.

[9] In the following part “Application and Results”, there is an example showing how the user can enter the weight for each series.

[10] It is because of the general assumption that irregular component distribution is i.i.d. (0,[pic])

[11] The non-parametric rank test called Friedman test to detect seasonality in a series is firstly suggested by Kendall and Ord (1990) and then Maravall (2007) used this test to detect seasonality in original series, linearized series and seasonally adjusted series.

[12] technology is used when writing data to Excel temporary files.

[13] ZedGraph, which is a charting class library written in C#, for graphic operations is used in DISAT. ZedGraph is licensed under the LGPL, GNU Lesser General Public License.

[14] For the commands and detailed user instructions of TSW, please see Caparello and Maravall (2004).

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