Sake Gina Tsarin Kuɗin Dijital ta Hanyar Sarƙoƙin Markov

Teburin Abubuwan Ciki

1 Gabatarwa

Tun lokacin da Nakamoto (2008) ya gabatar da Bitcoin, kuɗaɗen dijital sun sami kulawa sosai daga hukumomin kuɗi, kamfanoni, da masu saka hannun jari. Ƙaruwar sha'awar ta samo asali ne daga yuwuwar su na rage sarrafa haɗari, inganta fayiloli, da nazarin ra'ayin masu amfani. Wannan binciken yana amfani da hanyoyin sarƙoƙin Markov don sake ginawa da hasashen hanyoyin kasuwar kuɗin dijital, musamman yana binciken Bitcoin (BTC), Ethereum (ETH), da Ripple (XRP).

Nazarin da suka gabata sun gano cewa kuɗaɗen dijital suna nuna gaskiyar da aka tsara kamar kayan ajiyar kuɗi na al'ada, gami da rarraba mai kauri, taruwar saurin canzawa, da kyakkyawar alaƙa tsakanin girma da saurin canzawa. Bariviera (2017) ya nuna kaddarorin ƙwaƙwalwar ajiya na Bitcoin, yayin da Cheah et al. (2018) suka gano sassa na ƙwaƙwalwar ajiya a cikin manyan kuɗaɗen dijital.

2 Hanyar Bincike

2.1 Tsarin Sarƙoƙin Markov

Binciken yana amfani da sarƙoƙin Markov na oda ɗaya zuwa takwas don ƙirƙirar yanayin farashin kuɗin dijital. Hanyar tana amfani da bayanan dawowa na cikin rana don gina matrices na yuwuwar canzawa waɗanda ke ɗaukar yanayin bazuwar na saurin kasuwa. Kowane odar sarƙoƙin Markov yana wakiltar matakan dogaro na tarihi daban-daban a cikin motsin farashi.

2.2 Tattara da Sarrafa Bayanai

An tattara bayanan farashin cikin rana na Bitcoin, Ethereum, da Ripple daga manyan musayar kuɗin dijital. An ƙididdige dawowa a matsayin bambance-bambancen lissafi, kuma an ayyana jihohi masu hankali dangane da ƙofofin dawowa don sauƙaƙe ƙirar sarƙoƙin Markov.

3 Aiwarta ta Fasaha

3.1 Tsarin Lissafi

An ayyana sarƙoƙin Markov na oda-n ta hanyar yuwuwar sharadi:

$P(X_t = x_t | X_{t-1} = x_{t-1}, X_{t-2} = x_{t-2}, \ldots, X_{t-n} = x_{t-n})$

inda $X_t$ ke wakiltar yanayin dawowar kuɗin dijital a lokacin t. Ana ƙididdige yuwuwar canzawa ta hanyar gwaji daga bayanan tarihi ta amfani da ƙididdigar mafi yuwuwa:

$P_{ij} = \frac{N_{ij}}{\sum_k N_{ik}}$

inda $N_{ij}$ ke ƙidaya canje-canje daga jiha i zuwa jiha j.

3.2 Aiwartar Lambar

import numpy as np
import pandas as pd

class MarkovChainForecaster:
    def __init__(self, order=1):
        self.order = order
        self.transition_matrix = None
        self.states = None
    
    def fit(self, returns, n_states=3):
        # Rarraba dawowa zuwa jihohi
        quantiles = pd.qcut(returns, n_states, labels=False)
        self.states = quantiles.unique()
        
        # Gina matrix ɗin canzawa
        n = len(self.states)**self.order
        self.transition_matrix = np.zeros((n, len(self.states)))
        
        for i in range(self.order, len(quantiles)):
            history = tuple(quantiles[i-self.order:i])
            current = quantiles[i]
            hist_idx = self._state_to_index(history)
            self.transition_matrix[hist_idx, current] += 1
        
        # Daidaita layuka
        row_sums = self.transition_matrix.sum(axis=1)
        self.transition_matrix = self.transition_matrix / row_sums[:, np.newaxis]
    
    def forecast(self, current_state):
        idx = self._state_to_index(current_state)
        return np.random.choice(
            self.states, 
            p=self.transition_matrix[idx]
        )

4 Sakamakon Gwaji

4.1 Aikin Hasashe

Sakamakon gwaji ya nuna cewa hasashe ta amfani da yuwuwar sarƙoƙin Markov ya fi zaɓin bazuwar gaba ɗaya. Sarƙoƙi mafi girma (oda 4-8) sun nuna ingantaccen daidaito a ɗaukar rikitattun tsarin kasuwa, musamman ga Bitcoin wanda ya nuna tsarin da ake iya hasashe fiye da Ethereum da Ripple.

4.2 Nazarin Ƙwaƙwalwar Ajiya

Binciken ya binciki sassan ƙwaƙwalwar ajiya ta amfani da lissafin ma'aunin Hurst. Sakamakon ya nuna cewa yayin da Bitcoin ya nuna halin tafiya mara tsari (ma'aunin Hurst ≈ 0.5) bayan 2014, Ethereum da Ripple sun nuna halin dagewa tare da ma'aunin Hurst da ya fi 0.5 gaba ɗaya, wanda ke nuna kasancewar tasirin ƙwaƙwalwar ajiya.

5 Nazari na Asali

Binciken da Araújo da Barbosa suka yi ya ba da gudummawa mai mahimmanci ga nazarin kasuwar kuɗin dijital ta hanyar aiwatar da hanyoyin sarƙoƙin Markov a cikin oda da kuɗaɗen dijital da yawa. Hanyarsu ta nuna cewa sarƙoƙin Markov mafi girma (har zuwa oda 8) na iya ɗaukar rikitattun abubuwan dogaro a cikin dawowar kuɗin dijital yadda ya kamata, suna ƙalubalantar hasashen kasuwa mai inganci wanda ke nuna cewa farashin kadari yana bin tafiya mara tsari.

Wannan aikin ya yi daidai da binciken da aka samu daga kasuwannin kuɗi na al'ada inda ƙirar Markov suka nuna nasara a ɗaukar ƙananan tsarin kasuwa. Kama da takardar CycleGAN (Zhu et al., 2017) wanda ya nuna cewa fassarar hoto-zuwa-hoto mara biyu na iya koyon rikitattun taswira ba tare da haɗin kai ba, wannan binciken ya nuna cewa sarƙoƙin Markov na iya koyon rikitattun abubuwan dogaro na lokaci a cikin jerin lokutan kuɗi ba tare da zato na tsari ba.

Gano sassan ƙwaƙwalwar ajiya daban-daban a cikin kuɗaɗen dijital yana da muhimman tasiri ga sarrafa haɗari da gina fayiloli. Kamar yadda aka lura a cikin nazari daga Bankin Ƙasashen Duniya (BIS, 2021), kuɗaɗen dijital suna nuna bayanan haɗari daban-daban waɗanda ke buƙatar ingantattun hanyoyin ƙira. Tsarin Markov yana ba da kayan aiki mai sassauƙa don ɗaukar waɗannan bambance-bambance.

Idan aka kwatanta da ƙirar GARCH na al'ada da ake amfani da su a cikin lissafin tattalin arziki, sarƙoƙin Markov suna ba da fa'idodi da yawa: suna buƙatar ƙididdiga kaɗan, suna iya ɗaukar abubuwan dogaro marasa layi, kuma suna ba da fassarori masu yuwuwa. Duk da haka, suna iya fuskantar matsaloli tare da matsanancin al'amuran da ba a wakilta a cikin bayanan tarihi ba, kama da iyakoki da aka lura a cikin aikace-aikacen koyon inji ga kuɗi (Journal of Financial Economics, 2020).

Binciken yana ba da gudummawa ga ƙarar littattafai kan ingancin kasuwar kuɗin dijital. Yayin da kayan ajiya na al'ada sukan nuna raguwar hasashe tare da ƙaruwar lokutan gani, binciken ya nuna cewa kuɗaɗen dijital na iya kiyaye sassan da ake iya hasashe ko da a cikin mafi girman odar Markov, watakila saboda rashin balagaggen kasuwa ko abubuwan ɗabi'a da ke tasiri yanke shawarar 'yan kasuwa.

6 Aiwatarwa na Gaba

Tsarin sarƙoƙin Markov da aka haɓaka a cikin wannan binciken yana da aiwatarwa masu ban sha'awa da yawa:

• Cinikin Algorithm: Haɗawa tare da tsarin ciniki mai sauri don kasuwannin kuɗin dijital
• Gudanar da Haɗari: Ingantaccen ƙididdigar ƙimar Haɗari (VaR) ta amfani da yuwuwar canjin jiha
• Saka Idanu na Tsari: Gano tsarin magudi na kasuwa ta hanyar canjin jiha mara kyau
• Inganta Fayiloli: Rarraba kadari mai ƙarfi dangane da jihohin kasuwa da aka hasashe
• Nazarin Kaya-Kaya: Ƙaddamarwa don ƙirar alaƙa tsakanin kuɗaɗen dijital da kayan ajiya na al'ada

Hanyoyin bincike na gaba sun haɗa da haɗa gine-ginen koyon zurfi tare da ƙirar Markov, haɓaka sarƙoƙin Markov masu yawa don hulɗar kuɗin dijital da yawa, da aiwatar da tsarin ga ka'idojin kuɗi na gama gari (DeFi) da tambarin musamman (NFTs).

7 Nassoshi

1. Nakamoto, S. (2008). Bitcoin: Tsarin kuɗin lantarki mai amfani da tsarin abokan karɓa
2. Dyhrberg, A. H. (2016). Ikon kariya na bitcoin. Takaddun Bincike na Kuɗi, 16, 139-144
3. Bariviera, A. F. (2017). Rashin ingancin Bitcoin an sake duba shi: Hanyar da ta dace. Takaddun Tattalin Arziki, 161, 1-4
4. Cheah, E. T., et al. (2018). Dogon lokaci na haɗin kai da rashin inganci a kasuwannin Bitcoin. Takaddun Tattalin Arziki, 167, 18-25
5. Urquhart, A. (2017). Rashin ingancin Bitcoin. Takaddun Tattalin Arziki, 148, 80-82
6. Zhu, J. Y., et al. (2017). Fassarar hoto-zuwa-hoto mara biyu ta amfani da hanyoyin sadarwar adawa. ICCV
7. Bankin Ƙasashen Duniya (2021). Rahoton Tattalin Arziki na Shekara
8. Journal of Financial Economics (2020). Koyon Injini a Kuɗi: Tushe da Ci gaba na Kwanan nan