1. 5 June 2013 SDMX Technical Working Group Luxembourg 1 5 June 2013 SDMX Technical Working Group Luxembourg 1 WP Item 6 The Expressions Language of Banca d’Italia (EXL)

2. 5 June 2013 SDMX Technical Working Group Luxembourg 2 5 June 2013 SDMX Technical Working Group Luxembourg 2 History Mid nineties: Banca d’Italia designed a Language for validations and calculations 2009: A new version of the EXL was released as part of the new Infostat software platform, containing the operators needed for validation and basic calculation On-going: progressive upgrade of the EXL for supporting the data compilation, for example: –Operators for time series manipulation –Operators for data analysis –Operators’ syntax upgrade

3. 5 June 2013 SDMX Technical Working Group Luxembourg 3 5 June 2013 SDMX Technical Working Group Luxembourg 3 Basic example of validation rule Check ()special operator for checks - subtract the multidimensional data <=comparison operator EXPRESSIONS: C3 = get ( C1, keep (DATE, ENTITY, AMOUNT), sum (AMOUNT)) C4 = get ( C2, keep (DATE, ENTITY, AMOUNT), sum (AMOUNT)) C5 = check ( C3 – C4 <= given_threshold ) Two collected data: C1: Loans - Date, Entity, Sector, Amount C2: Loans - Date, Entity, Geo_Area, Amount Check rule: C1 and C2 should be equal if aggregated on their common dimensions (for less than a small amount) EXL operators:

4. 5 June 2013 SDMX Technical Working Group Luxembourg 4 5 June 2013 SDMX Technical Working Group Luxembourg 4 Example of sum Get ()read the specified data Keep ()keep the specified dimensions Sum ()sum the specified measure (if quantitative) + sum the multidimensional data EXPRESSIONS: C3 = get ( C1, keep (DATE, ENTITY, AMOUNT), sum (AMOUNT)) C4 = get ( C2, keep (DATE, ENTITY, AMOUNT), sum (AMOUNT)) C5 = C3 + C4 Two collected data: C1 (Current Accounts): Date, Entity, Sector, Amount C2 (Mortgages):Date, Entity, Geo_Area, Amount The desired result is Loans (= Current Accounts + Mortgages): C5 (Loans):Date, Entity, Amount EXL operators:

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16. 5 June 2013 SDMX Technical Working Group Luxembourg 16 5 June 2013 SDMX Technical Working Group Luxembourg 16 Validation Formal (Structural) –assurance that the formal structure of the data observations matches the Data Structure Definition, in term of concepts, their roles and their admissible values; the formal validation is not treated as a calculation and is not defined through an expression; Of the Information Content (Plausibility) –Assurance that the data content gives right information about the real world (as much as possible); to this end, it is possible to use the a-priori information about the real world and the possible redundancies of the data (e.g. the integrity rules, coherence rules, plausibility rules); this kind of validation rules is normally performed through calculations,

17. 5 June 2013 SDMX Technical Working Group Luxembourg 17 5 June 2013 SDMX Technical Working Group Luxembourg 17 Validations as calculations Use of the same language of the calculations Validations possible in any phase of the process Results of the Validations like any other data are defined and stored can be inquired and disseminated can be further processed

18. 5 June 2013 SDMX Technical Working Group Luxembourg 18 5 June 2013 SDMX Technical Working Group Luxembourg 18 SDMX Compliance The SDMX 2.0 and 2.1 versions already envisaged the introduction of a standard language for validations and calculations The SDMX 2.1 package n. 13 (Transformations and Expressions) is a generic model aimed to track the validation and the calculation of data, derived from the CWM (Common Warehouse Metamodel), a OMG standard (Object Management Group) However this model is not operational in-itself, because it requires a language to specify the validation and calculation expressions The EXL is designed according with the SDMX package n. 13 – Transformations and Expressions

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20. 5 June 2013 SDMX Technical Working Group Luxembourg 20 5 June 2013 SDMX Technical Working Group Luxembourg 20 Transformations; internal view Einstein equation E = MC 2  E = M*(C**2) Operator: ** b p Operand: 2 Operand: C Result: E Operator: * f f Operand: M Constant node Reference nodes Operator nodes Expression nodes 0..*

21. 5 June 2013 SDMX Technical Working Group Luxembourg 21 5 June 2013 SDMX Technical Working Group Luxembourg 21 Transformations: User view Einstein equation E = MC 2  E = M*(C**2) Operand: 2 Operand: C Result: E Expression: E = M*(C**2) Operand: M

22. 5 June 2013 SDMX Technical Working Group Luxembourg 22 5 June 2013 SDMX Technical Working Group Luxembourg 22 Notes on Transformations The Operands may be: Artefacts of the model (e.g. Statistical Data) Constants Operator nodes The property of “Closure” The result is an artefact of the model (e.g. Statistical Data) The result may be operand of other calculations

23. 5 June 2013 SDMX Technical Working Group Luxembourg 23 5 June 2013 SDMX Technical Working Group Luxembourg 23 Graph of the calculations External Institutions C1C1 C2C2 C3C3 C4C4 C5C5 T1T1 T3T3 T2T2 C10C10 C 12 C 13 C 15 C 17 C 16 T 13 T 12 T14T14 Banks & OFI’s reports C.C.R. C 21 C 22 C 23 C 24 T 22 T 21 C 51 C 52 T 53 T 52 T 51 Economic research models C 54 C 53 T 54 C 60 C 61 Statistical bulletin T 60 T 61 Statistical products C 70 T 71 T 70 T 72 C 71 C 72 C 41 T 42 T 41 C 42 Supervision models

24. 5 June 2013 SDMX Technical Working Group Luxembourg 24 5 June 2013 SDMX Technical Working Group Luxembourg 24 Software Tools Dictionary, that is a data base containing all the definitions Warehouse, that is the complex of data archives containing the data, logically unique but also physically heterogeneous and distributed Tool for the administration of the metadata (create, modify, etc.), including the expressions for calculations and controls (this package is built in-house) Tool for validation of the expressions syntax and consistency and for translation of the expressions in the language of the calculation tools (based on the open source ANTLR under the control of a software built in-house) Execution of the expressions, that is the calculation engine of the software platform, based on a software layer developed in-house that interfaces and controls the calculation software, which in turn can be various: currently it is used the open-source R, the SQL, some software built in-house and optimized for specific purposes.

25. 5 June 2013 SDMX Technical Working Group Luxembourg 25 5 June 2013 SDMX Technical Working Group Luxembourg 25 Allowed Data The EXL is applied to any kind of data of interest in the Bank of Italy statistical environment, like –Dimensional data, including as particular cases time series cross sections –Questionnaires –Registers the Bank of Italy is gradual extending the use of EXL to the whole statistical information system to support its industrial processing

26. 5 June 2013 SDMX Technical Working Group Luxembourg 26 End to End processing 1.Data are integrated with information relevant to the collected security codes 2.Missing observations are estimated 3.data are aggregated Use case: production of the information for the ECB concerning the balance sheet of the monetary and financial institutions sector Collect data on securities from MFI on a security by security basis. securities register data Dataflow to ECB Structural and integrity checks Disseminate Process CollectBuild Design check Collect process disseminate check

27. 5 June 2013 SDMX Technical Working Group Luxembourg 27 5 June 2013 SDMX Technical Working Group Luxembourg 27 Some other characteristics Formal – expressed in Backus-Naur form Deals with historicity: –Takes into account the time validity of the artefacts –Allows defining changes of the algorithm with reference to the time May deal with –Mono and multi-measure data –Data attributes having a definable behaviour –Operands having different dimensionality –Subsets of dimensional cubes –Implicit / explicit zeros Allows –Persistent and non persistent results –Expressions as operands of other expressions –Invocation of external routines

28. 5 June 2013 SDMX Technical Working Group Luxembourg 28 Operators used in the validation (1) Data retrieval / storage (Get, Put) Projection (drop, keep …) Filter (=,, >=, <>, like, between …) Aggregation (sum, avg, min, max, first, last …) Other manipulators of the data structure (rename, calc) Join (merge) Algebraic and string manipulation ( +, -, *, /) Comparison (=,, >=, <>)

29. 5 June 2013 SDMX Technical Working Group Luxembourg 29 Operations used for validation (2) Logical (and, or, not) Tailored for Validation: –Check of a generic condition –Existence and referential integrity check –Completeness check –Imbalance –Error severity level Conditional execution (case) Currency conversion Date-time (year, month, day, time shift)

30. 305 June 2013 SDMX Technical Working Group Luxembourg 305 June 2013 SDMX Technical Working Group Luxembourg WP Item 6 Expressions and Calculations