Procesy dwuliniowe i procesy GARCH w modelowaniu finansowych szeregów czasowych

• Autorzy: Joanna Bruzda

Warianty tytułu

Bilinear and Garch Processes in Modelling of Financial Time Series

• Języki publikacji: PL

Abstrakty

Celem niniejszego artykułu jest porównanie dwóch rodzajów modeli nieliniowych: podstawowego modelu z rodziny GARCH oraz modelu liniowego, pod względem ich statystycznych własności oraz użyteczności w opisywaniu i prognozowaniu szeregów finansowych. W konsekwencji tego porównania proponuje się wykorzystać do opisu procesów finansowych, jako jedną z możliwych alternatyw, ogólne modele BL-GARCH. Ilustrację empiryczną oparto na analizie 5 szeregów z polskiego rynku finansowego: dzienne logarytmiczne stopy zwrotu z trzech indeksów giełdowych - WIG, WIG20 i WIRR oraz z dwóch kursów średnich walut w NBP.

EN

In the paper we compare characteristics of two kinds of non-linear processes, namely bilinear and GARCH processes. Although the two processes describe different types of a non-linear dynamic - a non-linearity in the conditional mean value of a process (bilinear processes) and a non-linearity in the conditional variance of a process (GARCH processes)- structures of their unconditional moments are similar, so as, for example, one can take a bilinear process as a process of a GARCH type. We pay attention to a possibility of the correct distinction between the two processes on a basis of linearity tests. We do not treat bilinear and GARCH processes as mutually exclusive alternatives, but rather as two complementary constructions. As a result we propose to join these processes in the form of a BL-GARCH process. The BL-GARCH process can be useful not only as a basis for specification testing, but also for a join expression of two types of a non-linearity, which - as is pointed at by linearity tests - can occur together. An empirical illustration concerns modelling of logarithmic returns of indices at the Warsaw Stock Exchange and exchange rates in the National Bank of Poland. Results of the investigation indicate that popular AR-GARCH models are better fitted than proposed BL-GARCH models in the light of information criteria. However BL-GARCH model have better forecasting properties and give better short-term prognosis.

Słowa kluczowe

PL

Model GARCH; Modele ekonometryczne; Analiza szeregów czasowych; Matematyka finansowa

EN

GARCH model; Econometric models; Time-series analysis; Financial mathematics

• Czasopismo: Przegląd Statystyczny
• Rocznik: 2003
• Tom: 50
• Numer: z. 2
• Strony: 73--95

Twórcy

autor

Joanna Bruzda

Bibliografia

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