{"id":563,"date":"2025-03-22T00:24:31","date_gmt":"2025-03-21T21:24:31","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/caglart\/?p=563"},"modified":"2025-04-05T22:32:03","modified_gmt":"2025-04-05T19:32:03","slug":"563","status":"publish","type":"post","link":"https:\/\/blog.metu.edu.tr\/caglart\/2025\/03\/22\/563\/","title":{"rendered":"F\u0130NANS F\u0130Z\u0130\u011e\u0130\u2019nde NEWTON\u2019un \u00dc\u00c7\u00dcNC\u00dc YASASI"},"content":{"rendered":"

F\u0130NANS F\u0130Z\u0130\u011e\u0130 -16-<\/p>\n

Ge\u00e7mi\u015fdeki yaz\u0131lar\u0131m\u0131zda, Galilei Denklemi\u2019nin, i\u00e7inde ya\u015fad\u0131\u011f\u0131m\u0131z evrenin uzay_zaman\u0131n\u0131n s\u00fcrekli olu\u015fundan, nam-\u0131 di\u011fer, geometrisinden kaynakland\u0131\u011f\u0131n\u0131 yani k\u0131saca, konum de\u011fi\u015fikli\u011fini zaman cinsinden veren s\u0131radan bir Kuvvet Serisi (\u2018Power Series\u2019 ve \u2018Taylor Series\u2019) oldu\u011fundan s\u00f6z etmi\u015f idik. B\u00f6ylesi seriler, kuvvet sabit ise, yani konum de\u011fi\u015fikli\u011finin zamana g\u00f6re ikinci dereceden t\u00fcrevi sabit ise, (daha y\u00fcksek dereceden t\u00fcrevler otomatikman s\u0131f\u0131r olaca\u011f\u0131ndan) Galilei Denklemi\u2019ni t\u0131pat\u0131p vermekteydi.
\n\u0130kinci dereceden t\u00fcrev de yani kuvvet de s\u0131f\u0131r ise, Newton Yasalar\u0131\u2019n\u0131n birincisi, nam-\u0131 di\u011fer Galilei De\u011fi\u015fmezlik (\u2018Invariance\u2019) \u0130lkesi t\u0131pat\u0131p elde edilmekteydi.
\n\u00d6zellkle bu Galilei De\u011fi\u015fmezlik (\u2018Invariance\u2019) \u0130lkesi, Finans Fizi\u011fi\u2019nde d\u00fcz \u00e7izgilerden olu\u015fan destek veya diren\u00e7 d\u00fczeyleri olarak belirmektedir. Bu resmin pek \u00e7ok \u00f6rne\u011fine yine ge\u00e7mi\u015fteki pek \u00e7ok yaz\u0131m\u0131zda yer vermi\u015ftik.
\n\u015eimdi ise, Newton\u2019un \u00dc\u00e7\u00fcnc\u00fc Yasas\u0131 olarak da bilinen Etki=Tepki yasas\u0131n\u0131n Finans Fizi\u011fi\u2019ndeki uygulamalar\u0131na de\u011finece\u011fiz.
\nBu ama\u00e7la, g\u00fcnl\u00fck kapan\u0131\u015f de\u011ferlerinden olu\u015fan bir P(n) zaman serisi elde edelim. Burada n harfi, ba\u015flang\u0131\u00e7 olarak se\u00e7ti\u011fimiz n=1 g\u00fcn\u00fcnden sonraki i\u015f g\u00fcnlerini g\u00f6steriyor olsun.
\nBu durumda, g\u00fcnl\u00fck ba\u011f\u0131l de\u011fi\u015fiklikleri B(n) (oransal de\u011fi\u015fiklikler, logaritmik de\u011fi\u015fiklikler, \u2018log-returns\u2019) \u015f\u00f6ylece hesaplayabiliriz.
\n\"\"<\/a>
\nG\u00fcnl\u00fck ba\u011f\u0131l de\u011fi\u015fim de\u011ferler G s\u00fctununda ve ikinci sat\u0131rdan itibaren a\u015fa\u011f\u0131 do\u011fru b\u00fcy\u00fcyen n de\u011ferleri i\u00e7in s\u0131ralanm\u0131\u015f olsun. \u0130lgili Excel komutlar\u0131 \u015fu \u015fekilde olur:
\n=E\u011eER(G3>0;G3;0)
\nve
\n=E\u011eER(G3<0;G3;0) .
\nSonra da, mesela, g\u00fcnl\u00fck ba\u011f\u0131l de\u011fi\u015fim de\u011ferlerinin N g\u00fcn i\u00e7inde ka\u00e7 kez art\u0131l\u0131 ve eksili oldu\u011fu say\u0131labilir. Hatta daha rafine nice istatistik y\u00f6ntemler de uygulanabilir.
\nHemen alttaki grafikte BIST30 (XU030) endeksine ait 10.04.2002 tarihli kapan\u0131\u015f\u0131ndan d\u00fcnk\u00fc 22.03.2025 dahil kapan\u0131\u015f\u0131 aras\u0131ndaki veriden olu\u015fturulmu\u015f k\u0131rm\u0131z\u0131 renkli zaman serisi \u00e7izgisini ve bundan t\u00fcretilmi\u015f olan B+(m) ve B-(k) adl\u0131 zaman serileri incelenebilir. Fiyat P(n) birimi \u20ba\u2019dir ama B+(m) ve B-(k) boyutsuz ve birimsizdirler. BIST30 i\u00e7in N=5755 olup B+(m) ve B-(k) adl\u0131 zaman serilerinin de\u011fer toplamlar\u0131, s\u0131ras\u0131yla ve yakla\u015f\u0131k olarak 41.62 ve -36.44 de\u011ferlerine e\u015fittir. Ayn\u0131 s\u00fcre i\u00e7inde BIST30 endeksi 3030 g\u00fcn ba\u011f\u0131l art\u0131\u015f ve 2722 g\u00fcn ba\u011f\u0131l azal\u0131\u015f sergilemi\u015ftir. 3030+2722=5752 oldu\u011funa g\u00f6re de (5755-5722=) 3 g\u00fcn ba\u011f\u0131l olarak ayn\u0131 kalm\u0131\u015ft\u0131r.
\nAma, \u00e7ok daha ilginci, ilgili grafik incelendi\u011finde g\u00f6r\u00fclece\u011fi gibi, art\u0131\u015f ve azal\u0131\u015flar\u0131n hemen hemen bak\u0131\u015f\u0131k (simetrik) olu\u015fudur. Yani, yakla\u015f\u0131k olarak her art\u0131\u015f\u0131 (azal\u0131\u015f\u0131) yakla\u015f\u0131k olarak ayn\u0131 miktar azal\u0131\u015f (art\u0131\u015f) izlemi\u015ftir. Tam de\u011ferlerin aras\u0131ndaki farkl\u0131l\u0131klar da endeksin evrili\u015f grafi\u011fini tan\u0131mlam\u0131\u015ft\u0131r.<\/p>\n

\"\"<\/a><\/p>\n

S\u00f6z konusu bak\u0131\u015f\u0131m WTIUSD (ve BRENT) de\u011ferlerinde daha belirgindir. Hemen alttaki grafikte WTIUSD zaman serisi 17.10.2001 tarihli kapan\u0131\u015f\u0131ndan d\u00fcnk\u00fc 22.03.2025 dahil kapan\u0131\u015f\u0131 aras\u0131ndaki veriden olu\u015fturulmu\u015f k\u0131rm\u0131z\u0131 renkli zaman serisi \u00e7izgisini ve bundan t\u00fcretilmi\u015f olan B+(m) ve B-(k) adl\u0131 zaman serileri sergilenmi\u015ftir. Fiyatlar\u0131n birim (USD) $\u2019dir ve WTIUSD i\u00e7in N=5867 olup B+(m) ve B-(k) adl\u0131 zaman serilerinin de\u011fer toplamlar\u0131, s\u0131ras\u0131yla ve yakla\u015f\u0131k olarak 52.49 ve -49.48 de\u011ferlerine e\u015fittir.<\/p>\n

\"\"<\/a><\/p>\n

Ayn\u0131 s\u00fcre i\u00e7inde WTIUSD fiyatlar\u0131 3036 g\u00fcn ba\u011f\u0131l art\u0131\u015f ve 2808 g\u00fcn ba\u011f\u0131l azal\u0131\u015f sergilemi\u015ftir. 3036+2808=5844 oldu\u011funa g\u00f6re de (5867 -5844=) 23 g\u00fcn ba\u011f\u0131l olarak ayn\u0131 kalm\u0131\u015ft\u0131r.<\/p>\n

\u015eu notu d\u00fc\u015fmeksizin bu yaz\u0131y\u0131 bitirmek m\u00fchim bir eksikli\u011fe yol a\u00e7ard\u0131: Yukar\u0131da anlat\u0131lan yakla\u015f\u0131m\u0131 kullanarak ba\u015fka finans ara\u00e7lar\u0131na ve ba\u015fka zaman periyotlar\u0131 ile ve biraz daha ileri d\u00fczey istatiksel analizle destekleyerek ve hele kar\u015f\u0131la\u015ft\u0131rmal\u0131 da olursa \u00e7ok ho\u015f olur, gayet iyi dergilerde bas\u0131labilecek makaleler yapabilirsiniz. S\u00f6z, ben yapmayaca\u011f\u0131m. Ama, ihtimaldir ki, o makale(ler ?) hakemli\u011fe bana gelir (!)<\/p>\n

Grafiklerin PDF’si i\u00e7in:
\nBel1<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

F\u0130NANS F\u0130Z\u0130\u011e\u0130 -16- Ge\u00e7mi\u015fdeki yaz\u0131lar\u0131m\u0131zda, Galilei Denklemi\u2019nin, i\u00e7inde ya\u015fad\u0131\u011f\u0131m\u0131z evrenin uzay_zaman\u0131n\u0131n s\u00fcrekli olu\u015fundan, nam-\u0131 di\u011fer, geometrisinden kaynakland\u0131\u011f\u0131n\u0131 yani k\u0131saca, konum de\u011fi\u015fikli\u011fini zaman cinsinden veren s\u0131radan bir Kuvvet Serisi (\u2018Power Series\u2019 ve \u2018Taylor Series\u2019) oldu\u011fundan s\u00f6z etmi\u015f idik. B\u00f6ylesi seriler, kuvvet sabit ise, yani konum de\u011fi\u015fikli\u011finin zamana g\u00f6re ikinci dereceden t\u00fcrevi sabit ise, (daha y\u00fcksek dereceden […]<\/p>\n","protected":false},"author":1425,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[1],"tags":[],"class_list":["post-563","post","type-post","status-publish","format-standard","hentry","category-genel"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/563","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/users\/1425"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/comments?post=563"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/563\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/media?parent=563"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/categories?post=563"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/tags?post=563"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}