Christian Ullrich

Foreign Exchange Trading with Support Vector Machines

This paper analyzes and examines the general ability of Support Vector Machine (SVM) models to correctly predict and trade daily EUR exchange rate directions. Seven models with varying kernel functions are considered. Each SVM model is benchmarked against traditional forecasting techniques in order to ascertain its potential value as out-of-sample forecasting and quantitative trading tool. It is found that hyperbolic SVMs perform well in terms of forecasting accuracy and trading results via a simulated strategy. This supports the idea that SVMs are promising learning systems for coping with nonlinear classification tasks in the field of financial time series applications.

Real Floating-Point Arithmetic—The Heart of a Scientific Programming Language

This chapter discusses the real floating-point arithmetic. The notation squarecirc is used to distinguish operations on floating-point numbers (type real) from the corresponding real operations o ∈ {+, – , *, / }. Thus, the result of ⊞ has to be a floating-point number. It makes sense to take this to be one of the two floating-point neighbors of the exact real result, perhaps the closer. For the calculation of bounds for a real number, it must be ensured that the computed floating-point number is either smaller or larger than the exact real result and that the nearest smaller or larger neighboring floating-point number is chosen. In each case, it is important that no floating-point numbers lie between the computed floating-point result and the exact real result. Floating-point operations with this property are said to be accurate up to a unit. An operation should result in an error interrupt in case its result is too large in absolute value, that is, it lies in the overflow region.

Functions and Operators with Arbitrary Result Types

This chapter discusses the generalized function and operator concepts of Pascal-SC. The definition of functions in Pascal-SC has been extended to include structured result types, and operator definitions have been introduced. With these, it is possible to write expressions for structured types in the same way as one customarily writes real or integer expressions. In Pascal-SC, arbitrary type identifiers are permitted as function types, with the exception of file structure types (FS TYPE). File structure types are all files and all structured types which include files in some component. The call of a function with an arbitrary result type does not differ syntactically from a function call in standard Pascal. The result of a function call is an expression with the type of the function. Therefore, a function is distinguished by its identifier and the number, type, and sequence of its parameters. A direct reference to a component of the function result is not possible at the call of the function. In Pascal-SC, the declaration of an operator follows the form of a function declaration closely. The operator symbol (or operator identifier) DYADOP or MONOP, respectively, replace the function identifier. Binary (dyadic) operators have exactly two operands, and unary (monadic) operators have exactly one operand; the symbols + and − are the only operator symbols that occur as both monadic and dyadic.

An Introduction to Pascal-SC

This chapter discusses the features of Pascal-SC. Numerical calculations frequently involve complex numbers. In contrast to FORTRAN, standard Pascal does not provide the data type complex. Pascal-SC provides a number of operators, functions, and procedures for computation with complex numbers. The subroutines are organized into an arithmetic module. To use these routines, the standard declaration is assumed. Thus, the standard representation of complex numbers in Pascal-SC is in Cartesian coordinates. In standard Pascal, procedures have to be used for complex arithmetic and function evaluation. In Pascal-SC, operator overloading considerably simplifies notation and, hence, programming. In the Pascal-SC algorithms for complex multiplication and division, overflow does not occur unless the real or imaginary part of the result is greater in absolute value than the largest possible floating-point number. By contrast, overflow can occur in the procedure cdiv during the calculation of the intermediate results denom, u.re, or u.im, even though the final result has real and imaginary parts, which are representable as floating-point numbers.

A Review of Standard Pascal

This chapter discusses the characteristics of standard Pascal. Pascal provides statements for value assignment, input and output, and comparison. In provides three repetition statements while, repeat, and for statements, and also the case statement for better program structuring. In standard Pascal, access to attributes of an array variable (such as the limits of the individual index variables) is not possible by means of standard functions. Thus, if an array is used as a formal parameter of a function or procedure, either the index limits likewise have to be given as parameters or else introduced as global variables. By provision of new standard functions Ibound (lower bound) and ubound (upper bound), the situation is considerably improved. The case statement in standard Pascal requires a complete enumeration of all case selector labels that can be encountered in the execution of the statement within the program. Thus, various implementations provide a notation for an entire range of case selector label and a so-called else-branch to make a complete enumeration of case selector labels unnecessary.

Strings and Text Processing

Standard Pascal offers only limited capabilities for text processing. To be sure, strings can be written as literal constants in the usual form. According to the standard, manipulation of strings is only supported by value assignment of a string constant or variable to a string variable (equality of lengths is required), an output statement for a string constant or variable, and lexicographic comparison of string constants and variables (equality of lengths is required). This defect has been largely removed in Pascal-SC. In the design of the language, the most important features of a sensible way to process strings were taken into consideration: simple declaration of string variables, value assignments of strings of arbitrarily length, input of strings, output of the values of arbitrary string expressions, and standard functions for the manipulation of strings. In addition, the concepts of functions with arbitrary result types and user-defined operators give the programmer the capability of formulating other routines in a meaningful way.

CHAPTER VII – Dynamic Arrays

Publisher Summary nThis chapter discusses the characteristics of dynamic arrays that have been introduced in Pascal-SC. Pascal-SC offers the possibility of dynamic array declaration. This essentially means that the index variables inside of subroutines are not essentially static as in standard Pascal, being declared with fixed dimension and index ranges, but can be specified with different index limits at each subroutine call. The introduction of dynamic arrays and their application to the specification of formal parameters accomplishes the same purpose as the conformant array schemata of standard Pascal, but somewhat different syntax is used. The introduction of dynamic types makes an extension of the of compatibility requirements necessary. Just as in standard Pascal, two array types are compatible only if they are the same type. Therefore, this means that a dynamic array type is not compatible with a static type. The overloading of procedures, functions, and operators is, thus, possible without restriction.

CHAPTER VIII – Modules

Publisher Summary nIt is convenient to prepare a program in several parts, called modules, which can be developed and translated independently of each other. In Pascal-SC, a module concept has been introduced and provides many advantages: a program can be made up of several modules, which contain logically dependent parts and can be developed and translated independently of each other; syntax and semantics will be checked completely across module boundaries; in case of changes in an existing program, the unchanged modules do not need to be retranslated; collections of standard modules can be assembled to extend the scope of the Pascal-SC language (graphics, error handling, complex arithmetic, and so on). In contrast to the languages termed modular, for example, Modula-2, the only language extensions that have been undertaken in Pascal-SC are the ones that are absolutely required to serve a specific purpose. In this way, Pascal-SC stays as close as possible to standard Pascal, so that it is not necessary to learn a whole new language in order to use it.

Solving Problems with Pascal-SC

As with any programming language, Pascal-SC is learned best through the experience of actually writing programs to solve problems of interest. In Pascal-SC, it is possible to write expressions involving these entities which follow ordinary mathematical notation. Packages of pre-translated or source code are provided for the numerical data types most commonly encountered in scientific computation. These give the arithmetic operators and standard functions for the corresponding type, and also the utility routines such as input and output. The chapter describes the packages for complex and interval arithmetic, and vector and matrix arithmetic for real numbers. It also describes the vector and matrix arithmetic for intervals and complex numbers. The examples presented in this chapter suggest ways of organizing such computer programs. They are also useful in their own right for some simple numerical computations. These examples can be translated and executed by what might be termed a level 0 implementation of Pascal-SC.