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Version 2.6 by Helena K. on 2026/01/27 13:40
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4
5 = 1. Problem Statement =
6
7 Time transformation is defined as a time-related operation performed on a time series, solely involving observations of that time series. Examples of such time transformations are growth rates, cumulative sums over several periods and moving averages.
8
9 To express a time transformation, three elements are required: the type of transformation, the number of periods involved and the length of each period. Even though in theory you could express the base value and the transformation applied, it is much more practical, and in many cases sufficient in statistical data exchange, to transmit the time-transformed values themselves.
10
11 The operation to be coded can be expressed generically as such: For value //V// the transformation //T// was applied over //P// periods with frequency //F//.
12
13 Examples:
14
15 |(% style="width:501px" %)**Statement**|(% style="width:303px" %)**T**|(% style="width:472px" %)**P**|(% style="width:454px" %)**F**
16 |(% style="width:501px" %)Quarter on quarter growth rate|(% style="width:303px" %)Growth rate|(% style="width:472px" %)2|(% style="width:454px" %)Q
17 |(% style="width:501px" %)Contribution to growth over 1 year (quarterly data)|(% style="width:303px" %)Contribution to growth|(% style="width:472px" %)4|(% style="width:454px" %)Q
18 |(% style="width:501px" %)Contribution to growth over 1 year (annual data)|(% style="width:303px" %)Contribution to growth|(% style="width:472px" %)1|(% style="width:454px" %)A
19 |(% style="width:501px" %)3 months moving average|(% style="width:303px" %)Moving average|(% style="width:472px" %)3|(% style="width:454px" %)M
20 |(% style="width:501px" %)Annual index (reference year=100){{footnote}}Note that for the case of an index, it is useful to specify the reference base period in an additional attribute (see concept BASE_PER specified in the SDMX Glossary).{{/footnote}}|(% style="width:303px" %)Index|(% style="width:472px" %)1|(% style="width:454px" %)A
21
22 This guideline describes two methods that may be used to code a time transformation:
23
24 1. A normalised, multi-concept approach that is described in section SDMX CONCEPTS FOR TIME TRANSFORMATIONS. The overall time span involved in the time transformation depends on the number of periods stated and the frequency of a series.
25 1. A denormalised, compound concept approach that is described in section COMPOUND CODING FOR TIME TRANSFORMATIONS. The overall time span involved in the time transformation does not necessarily depend on the number of periods stated and the frequency of a series.
26
27 Both of these methods are included as separate use cases as served by each method. The aim of this document is to demonstrate that guidance and a standard approach is available and promoted for each use case. The use cases are described in the related sections.
28
29 Further recommended code values for expressing general statistical concepts such as "not applicable", etc., can be found in section “Generic codes” of the "Guidelines for the creation and management of SDMX Cross-Domain Code Lists" (to be found under “Guidelines” on the official SDMX website{{footnote}}http://sdmx.org/{{/footnote}}).
30
31 = 2. SDMX Concepts for Time Transformations =
32
33 SDMX defines two cross domain concepts for the purpose of coding time transformations: Time transformation type (ID TIMETRANS_TYPE) and time transformation periods (ID TIMETRANS_PER). The concept TIMETRANS_TYPE is coded with a cross domain code list. The concept TIMETRANS_PER is coded with a coded list of integers.
34
35 == 2.1 Time Transformation Type ==
36
37 Definition: This concept provides coded information about time-related transformation types of time series.
38
39 **Concept ID: **The concept ID is TIMETRANS_TYPE.
40 **Code List Name**: Code list for Time Transformation Type.
41 **Code List ID:** CL_TIMETRANS_TYPE.
42 **Established international standard(s) used as input for the code list**: None.
43
44 **Version**: 1.0, 15 September 2016
45
46 |**Recommended code value**|Recommended code description|Annotation
47 |**N**|Non transformed|TIMETRANS_PER is always 1, since a non-transformed number covers by definition a single period
48 |**A**|Average|Moving average, i.e. an operation that preserves the frequency of the series
49 |**C**|Cumulated sum|
50 |**D**|Difference|
51 |**DD**|Difference, second order|A second order difference is the delta of deltas
52 |**F**|Growth rate, flow over stock|
53 |**FC**|Contribution to growth, flow over stock|
54 |**G**|Growth rate|
55 |**GC**|Contribution to growth|
56 |**I**|Index|In the usual case, the index is fixed to 100 for a specific reference period, in most cases a year. It is recommended that the DSD contains an additional attribute BASE_PER (type ObservationalTimePeriod), which specifies the reference period of the index. In special cases (e.g. National Accounts chain linking), the index is fixed to a value different to 100 in the reference year. In these cases the BASE_PER attribute is even more important.
57 |**LA**|Annualised levels|This relates to stock versus flow series. For example, many countries publish their Quarterly National Accounts (QNA) at quarterly level, which means that annual Gross Domestic Product (GDP) is the sum of the four quarters, whereas some countries publish their QNA at annual level (e.g. US), which means that annual GDP is the average of the four quarters. In order to present quarterly data in comparable levels across countries and to derive zone aggregates, quarterly data expressed at quarterly levels are “transformed” to annual levels (i.e. multiplied by four) and have this code.
58 |**S**|Shifted|The time series was moved back or forth in time. This may for instance be used when non-calendar year series are aligned to the calendar year using certain estimation formulas.
59 |**_O**|Other transformation|This code is taken from the guidelines on generic codes, specifying "Other". In that context it should be used if more complex transformations are applied. An explanation of the transformation or a transformation script should be given in a comment field.
60
61 == 2.2 Time Transformation Periods ==
62
63 Definition: This concept provides information about the number of periods used for a time-related transformation of the time series.
64
65 **Concept ID: **The concept ID is TIMETRANS_PER.
66
67 **Code List Name**: Code list for Time Transformation Periods.
68
69 **Code List ID:** CL_TIMETRANS_PER.
70
71 **Established international standard(s) used as input for the code list**: None.
72
73 **Version**: 1.0, 15 September 2016
74
75 |**Recommended code value**|**Recommended
76 code description**|**Annotation**
77 |**1**|One|
78 |**2**|Two|
79 |**etc.**|etc.|
80
81 == 2.3 Relation of transformation coding to transformation rules ==
82
83 Transformation can also be expressed with transformation rules using a syntax such as the Validation and Transformation Language (VTL). Following the transformation graph model behind VTL, the transformation coding suggested in this guideline can be seen complementary with using transformation rules in VTL. The idea is that a coded non-transformed time series is transformed using a VTL rule and the result is then coded again with transformation codes for further data exchange. This principle is shown in the graph below:
84
85
86 |(((
87 Level series
88 )))
89
90 |(((
91 Transformed series
92 )))
93
94 |(((
95 Transformation rule
96
97 (VTL)
98 )))
99
100 Using the two concepts as suggested above for coding the type of transformation applied and the number of periods covered will additionally ensure that the parameters used for the formula are directly used in the coding of the resulting series. Thus no complex mapping is needed. The transformation applied is linked to the transformation type concept and the number of periods used for the calculation is linked to the transformation periods concept.
101
102 **Example:**
103
104 The formula for a simple annual growth rate can be expressed as follows:{{footnote}}Note: often growth rates are expressed as percentage growth, in which case the value is multiplied with 100%. This is however not relevant for this guideline and is left out for simplicity.{{/footnote}}
105
106 //GT= VT-VT-PVT-P//[[image:file:///C:/Users/axyli/AppData/Local/Temp/msohtmlclip1/01/clip_image001.png]]
107
108 à A growth rate over P years in year T is the difference between the current year value and the value P years ago related to the value P years ago; with G being the growth rate, V being the absolute value, T being the time (year) and P the number of periods.
109
110 The growth rate formula can be expressed in VTL and linked to transformation type G. The year T is linked to the respective year in the time series and the parameter P is linked to the transformation period concept.
111
112 **Example:**
113
114 |**Year à**|**2010**|**2011**|**2012**|**2013**
115 |**GDP Level**|500|505|510|505
116 |**Growth rate,
117 period on period**| |0.0100|0.0099|-0.0098
118 |**Formula**| |//GT= V2011-V2011-1V2011-1//[[image:file:///C:/Users/axyli/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png]]|//GT= V2012-V2012-1V2012-1//[[image:file:///C:/Users/axyli/AppData/Local/Temp/msohtmlclip1/01/clip_image003.png]]|//GT= V2013-V2013-1V2013-1//[[image:file:///C:/Users/axyli/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png]]
119 |**Growth rate,
120 over 2 periods**| | |0.0200|0.0000
121 |**Formula**| | |//GT= V2012-V2012-2V2012-2//[[image:file:///C:/Users/axyli/AppData/Local/Temp/msohtmlclip1/01/clip_image005.png]]|//GT= V2013-V2013-2V2013-2//[[image:file:///C:/Users/axyli/AppData/Local/Temp/msohtmlclip1/01/clip_image006.png]]
122
123 When looking at the formulas, you can see that the same parameters that are used to call a transformation service can be used to code the resulting series, which makes it very easy for data processing systems to ensure consistency between calculations and coding of results:
124
125 |**Year à**|2011|(% rowspan="4" %)(((
126 **Transformed series:**
127
128 REF_YEAR à 2011
129
130 OBS_VALUE à 0.0100
131
132 TRANS_TYPE à G (Formula / VTL function)
133
134 TRANS_PER à 1
135 )))
136 |**GDP Level**|505
137 |**Growth rate,
138 period on period**|0.0100
139 |**Formula**|//GT= V2011-V2011-1V2011-1//[[image:file:///C:/Users/axyli/AppData/Local/Temp/msohtmlclip1/01/clip_image007.png]]
140
141 This is especially useful when only transformed series should be exchanged and level series or transformations are not subject to exchange. An example could be GDP growth rates, where for early estimates often level series are still under embargo, whereas growth rates are publishable.
142
143 == 2.4 Recommendation ==
144
145 Where possible, it is recommended to use the above solution with the two concepts TIMETRANS_TYPE and TIMETRANS_PER to express time transformations because:
146
147 * this method separates the type of transformation and the number of periods involved, therefore the coding of time transformation is simpler with no redundancy;
148 * it is possible to add extra concepts if required without introducing ambiguity;
149 * the coded transformations can be linked directly with transformation formulas.
150
151 = 3. Compound coding for time transformations =
152
153 == 3.1 Known Limitations ==
154
155 The normalised approach as presented above does not support the definition of mixed-frequency time transformations – like monthly series of annual growth rates – since there is only a single frequency dimension available. This also means that when annual growth rates are expressed in a quarterly dataset, the time transformation period would need to be modified (i.e. when frequency changes from A to Q, the number of periods need to be quadrupled).
156
157 A "transformation frequency" might be added to keep the normalised approach also for those cases.
158
159 It also does not allow to directly code complex transformations, like transforming already transformed series (like the period-on-period growth rate of a four-period cumulative sum). For that case it is recommended to use the generic code "_O - Other" to specific that another transformation has been applied and provide the explanation or the transformation script in a comment field.
160
161 However, both of these use cases may lead to a quite complex data structures or issues if various different complex transformations should be coded. Thus an alternative solution is presented in chapter 3 for cases where these use cases need to be covered and additional concepts should not be added to the data structure.
162
163 In case the mixed frequencies or complex transformations as outlined above are needed in a simpler way and normalisation does not need to be strictly enforced, a composite code list CL_TIMETRANS may be created.
164
165 The number of periods in the code follows the frequency of the series unless stated otherwise. Example: code G3Y refers to a three-year growth rate, irrespective of the series frequency. For complex transformations, the codes that would be used for the respective transformations can be concatenated and separated by an underscore{{footnote}}Example:
166 G1_C4 Growth rate, period on period, over 4-period cumulated sum{{/footnote}}.
167
168 Example for composite CL_TIMETRANS:
169
170 |**Recommended code value**|**Recommended
171 code description**|**Annotation**
172 |N|Non transformed data|
173 |A2|2-period moving average|Period on period
174 |A3|3-period moving average|
175 |A4|4-period moving average|
176 |A6|6-period moving average|
177 |A12|12-period moving average|
178 |C3|3-period cumulated sum|
179 |C4|4-period cumulated sum|
180 |C6|6-period cumulated sum|
181 |C12|12-period cumulated sum|
182 |C16|16-period cumulated sum|
183 |D2|Differences, period on period, first order|
184 |DD|Differences, period on period, second order|
185 |D4|Difference, period on 4 periods, first order|
186 |F2|Growth rate, flow over stock, over two periods|Period on period
187 |F3|Growth rate, flow over stock ,over 3 periods|
188 |F4|Growth rate, flow over stock over 4 periods|
189 |F6|Growth rate, flow over stock over 6 periods|
190 |F12|Growth rate, flow over stock over 12 periods|
191 |FO2|Contribution to growth rate, flow over stock, over two periods|Period on period
192 |FO3|Contribution to growth rate, flow over stock, over 3 periods|
193 |FO4|Contribution to growth rate, flow over stock, over 4 periods|
194 |FO6|Contribution to growth rate, flow over stock, over 6 periods|
195 |FO12|Contribution to growth rate, flow over stock, over 12 periods|
196 |FO16|Contribution to growth rate, flow over stock, over 16 periods|
197 |G2|Growth rate, over two periods|Period on period
198 |G3|Growth rate over 3 periods|
199 |**G4**|**Growth rate over 4 periods**|
200 |G6|Growth rate over 6 periods|
201 |G10|Growth rate, over 10 periods|
202 |G12|Growth rate over 12 periods|
203 |GR|Growth rate, over reference year|
204 |GO2|Contribution to growth rate, over 2 periods|Period on period
205 |GO3|Contribution to growth rate, over 3 periods|
206 |GO4|Contribution to growth rate, over 4 periods|
207 |GO6|Contribution to growth rate, over 6 periods|
208 |GO12|Contribution to growth rate, over 12 periods|
209 |LA|Annualised levels|This relates to stock versus flow series. For example, many countries publish their QNA at quarterly level, which means that annual GDP is the sum of the four quarters, whereas some countries publish their QNA at annual level (e.g. US), which means that annual GDP is the average of the four quarters. In order to present quarterly data in comparable levels across countries and to derive zone aggregates, quarterly data expressed at quarterly levels are “transformed” to annual levels (i.e. multiplied by four) and have this code.
210 |G1Y|Growth rate, over 1 year|
211 |F1Y|Growth rate, flow over stock, over 1 year|
212 |D1Y|Difference, over 1 year|
213 |G3Y|Growth rate, over 3 years|
214 |G4Y|Growth rate, over 4 years|
215 |GC5Y|Compound growth rate, over 5 years|
216 |GC10Y|Compound growth rate, over 10 years|
217 |GO1Y|Contribution to growth rate, over 1 year|
218 |C1Y|Cumulated sum, over 1 year|
219
220 The use of codes like G3Y introduces redundancy in the code list. G3Y equals G36 for monthly data, G12 for quarterly data and G3 for annual data. Thus introducing such extensions should be well justified by solid use cases and DSD guidelines should explain which of the two possibilities (GxY or Gx) are preferred and why. Machine-to-machine queries, formulas, validation rules or coding templates may require mappings between those possibilities, taking into account both the frequency of a series and the transformation code.
221
222 = Annex: coded examples =
223
224 The table below shows coding example using all 3 options lined out above.
225
226 |Statement|Normalised{{footnote}}For sake of readability the prefix TIMETRANS_ was not put in the table. The concepts are in fact called TIMETRANS_TYPE and TIMETRANS_PER.{{/footnote}}|Type+Period|Type+Period+Freq
227 |Level series (non transformed data)|(((
228 FREQ=A or Q or M …
229
230 TYPE=N
231
232 PER=1
233 )))|(((
234 FREQ=A or Q or M …
235
236 TIMETRANS=N
237 )))|(((
238 FREQ=A or Q or M …
239
240 TIMETRANS=N
241 )))
242 |Quarter on quarter growth rate|(((
243 FREQ=Q
244
245 TYPE=G
246
247 PER=1
248 )))|(((
249 FREQ=Q
250
251 TIMETRANS=G1
252 )))|(((
253 FREQ=Q or M …
254
255 TIMETRANS=G1Q
256 )))
257 |Contribution to growth over 1 year (quarterly data)|(((
258 FREQ=Q
259
260 TYPE=GC
261
262 PER=4
263 )))|(((
264 FREQ=Q
265
266 TIMETRANS=GC4
267 )))|(((
268 FREQ=Q
269
270 TIMETRANS=GC1Y
271 )))
272 |Contribution to growth over 1 year (annual data)|(((
273 FREQ=A
274
275 TYPE=GC
276
277 PER=1
278 )))|(((
279 FREQ=A
280
281 TIMETRANS=GC1
282 )))|(((
283 FREQ=A
284
285 TIMETRANS=GC1Y
286 )))
287 |3 months moving average|(((
288 FREQ=M
289
290 TYPE=A
291
292 PER=3
293 )))|(((
294 FREQ=M
295
296 TIMETRANS=A3
297 )))|(((
298 FREQ=Q or M …
299
300 TIMETRANS=A3M
301 )))
302 |Annual index|(((
303 FREQ=A
304
305 TYPE=I
306
307 PER=1
308 )))|(((
309 FREQ=A
310
311 TIMETRANS=I1
312 )))|(((
313 FREQ=A or Q or M …
314
315 TIMETRANS=I1Y
316 )))
317
318
319
320 ----
321
322 {{putFootnotes/}}
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