My drawing of the old town on the way to go to the castle, Stirling, Scotland 25-27 March 2024

 

My drawing of the old town on the way to go to the castle, Stirling, Scotland 25-27 March 2024

One scene of Marisa and Alice in Touhou 10 Imperishable Night

 

 

One scene of Marisa and Alice dispatching in Touhou 10 Imperishable Night shown in an anime Touhou, The Memories Of Phantasm.

Tool used: CLIP STUDIO PAINT

These illustrations are posted in my Pixiv page so please visit https://www.pixiv.net/en/users/32334195!

A triangle formation of the crow Tengu clan in Touhou Project.

 

A triangle formation of the crow Tengu clan in Touhou Project: Megumu Iizunamaru, Aya Shameimaru, and Hatate Himekaidou 

These illustrations are posted in my Pixiv page so please visit https://www.pixiv.net/en/users/32334195! 

Three protagonists in Touhou Project

 

Tool used: CLIP STUDIO PAINT

These illustrations are posted in my Pixiv page so please visit https://www.pixiv.net/en/users/32334195! 

 

Satori Komeiji in Touhou Chireiden ~ Subterranean Animism (Touhou11)

 

These illustrations are posted in my Pixiv page so please visit https://www.pixiv.net/en/users/32334195!

Megumu Iizunamaru and Byakuren Hijiri

 

 

Megumu Iizunamaru and Byakuren Hijiri. It has been inspired by the opinion poll of selecting which Touhou character will be your ideal boss (supervisor/manager). 

Tool used: CLIP STUDIO PAINT

 

These illustrations are posted in my Pixiv page so please visit https://www.pixiv.net/en/users/32334195! 

 

I have also written an essay about ethics and political philosophy based on the analysis of these two ladies:

Megumu Iizunamaru (Utilitarian) VS Byakuren Hijiri (Deontologist): 東方利維坦~Leviathan~

 

The mysterious Japanese macroeconomic factor: The national debt per GDP is 251.93%!

 

... well, Japanese national debt percentage of GDP is over 200%! This is one of the mysterious Japanese macroeconomic factors.

One of the reason is that approximately 90% or more of Japanese national bond holders are Japanese nationals. This is why the government can keep these bond holders even with a substantially low interest rate. The hidden cost of this policy is incurred upon Japanese economy because the government is hardly able to raise the interest rate even during the inflationary period.

 

Furthermore, the value of Japanese national bond is so stable that the capital loss risk is low. Because there is still a regular coupon payment (the income gain) with the low capital loss risk at the moment, the majority private banks in Japan keep holding the national bond as the secure asset. The majority Japanese citizens are so risk-averse that they hardly split their saving to private investment: Then, the private bank simply shift their saving account money to the national bond purchase. Although the coupon payment is not so high, the risk premium is still lower than any private bond for the moment. Their risk-averse personality is one of the strong drive of stabilising the national bond price. 

Nevertheless, it is sceptical to assume this mechanism can keep going on. Japanese economy has been stagnated for multiple decades since the last economic bubble burst in 1990s. Nowadays, Japanese economic indices show that Japanese economic strength is even weaker than before. In addition, the entire macroeconomic strength will keep going down due to the ongoing ageing population combined with the constant substantial population decline.

 

Python: Combination of Singular Spectrum Analysis (SSA) and Fast Fourier Transform (FFT)

 

 

This is my non-linear time series analysis combining Singular Spectrum Analysis (SSA) and Fast Fourier Transform (FFT). 

The dataset is the foreign exchange (FX) rate of Euro (EUR) based on US-Dollar (USD) obtained from Frankfurter App provided by the European Central Bank (ECB).

Implementing FFT for each reconstruction component (RC) of SSA gives us much more precise insights of the periodicity of the time series fluctuation. 

# Execute this cell to have access to the API of Frankfurter App

import requests

import json

# importing necessary tools

import networkx as nx

import numpy as np

import pandas as pd

import random

import statistics

import scipy.linalg

from numpy import linalg as LA

from scipy.stats import qmc

from scipy import stats

import statsmodels.formula.api as sm

import math

import cmath

from scipy.linalg import hankel

import scipy.odr

from scipy import odr

# For using Frankfurter app

import ast

# For graphing

import matplotlib.pyplot as plt

import matplotlib.gridspec as gridspec

import seaborn as sns

# Fast Fourier Transform (FFT) https://docs.scipy.org/doc/scipy/tutorial/fft.html

from scipy.fft import fft, ifft, fftfreq

# Showing the plots bigger

plt.rcParams["figure.figsize"] = (20,10)

# defining imaginary number

i=complex(0,1)

i

## Downloading the time series data from Frankfurter App

# Connecting to the API https://www.frankfurter.app/docs/ to get the EUR/USD rates

url = "http://api.frankfurter.app/1999-01-01.."

resp = requests.get(url,{'to':'USD'})

#print(resp.url)

#print(resp.status_code)

#print("Type:", type(resp.content))

#print(resp.content)

print("Type:", type(resp))

# Preparing for the right encoding

import ast

byte_str = resp.content

dict_str = byte_str.decode("UTF-8")

mydata = ast.literal_eval(dict_str)

print("Type:", type(mydata))

#mydata #show the accessed data

EURUSD=(mydata["rates"])

#EURUSD

#mydata #show the accessed data

EURUSD=(mydata["rates"])

#EURUSD

# Sorting the data into the Python dictionary form

Dates_EURUSD=[]

Rates_EURUSD=[]

for key, value in EURUSD.items():

    Dates_EURUSD.append(key)

    for ky,vl in value.items():

        Rates_EURUSD.append(vl)

EURUSD=dict(zip(Dates_EURUSD,Rates_EURUSD))

print('First week:',list(EURUSD.keys())[0],',  Last week:',list(EURUSD.keys())[-1])

#Rates_EURUSD

### Graph output (1) ###

NW=6 # Number of windows to slice this time series dataset

LI=math.floor(len(EURUSD)/NW) # The length of interval

fig, axs = plt.subplots(NW)

for k in range(NW):

    axs[k].plot(Dates_EURUSD[k*LI:(k+1)*LI], Rates_EURUSD[k*LI:(k+1)*LI])

print("Length of data:",len(Rates_EURUSD))

## Singular Spectrum Analysis (SSA)

print("The following refers to https://stats.stackexchange.com/questions/544105/singular-spectrum-analysis-and-their-eigentriplets")

print('This SSA method is almost identical to the one based on MATLAB "Singular Spectrum Analysis - Beginners guide" (MathWorks)')

print(' https://uk.mathworks.com/matlabcentral/fileexchange/58967-singular-spectrum-analysis-beginners-guide which I attempted to duplicate with Python. ')

# Re-defining the time series and its length

s=Rates_EURUSD;

N=len(Rates_EURUSD)

# Getting window length L and lagged length K

#L = 500-1

L = 100

K = N - L + 1

# Constructing the time lagged Hankel matrix

X=np.zeros((K,L))

for m in range (0, L):

    X[:,m] = s[m:K+m]

   

# Trajectory matrix

Cemb = np.dot(X.T,X)/K

# Eigen decomposition

eigenValues, eigenVectors = np.linalg.eig(Cemb)

idx = eigenValues.argsort()[::-1]  

eigenValues = eigenValues[idx]

eigenVectors = eigenVectors[:,idx]

# Vectors of Principal Components

PC = np.dot(X,eigenVectors)

# Pre-allocating Reconstructed Component Matrix

RC = np.zeros((N, L))

# Reconstruct the elementary matrices without storing them

for k in range(L):

    myBuf = np.outer(PC[:,k], eigenVectors[:,k].T)

    myBuf = myBuf[::-1]

    RC[:,k] = [myBuf.diagonal(j).mean()\

               for j in range(-myBuf.shape[0]+1, myBuf.shape[1])]

       

### Graph output (2) ###

# First 6 RC

fig, ax = plt.subplots(3,2)

ax = ax.flatten()

for k in range (0, 6):

    ax[k].plot(RC[:,k])

    ax[k].set_title(str(i))

plt.tight_layout()

### Graph output (3) ###

# Plotting a graph comparison

RawSSA=RC[:,0]

for k in range(L-1):

    RawSSA=np.add(RawSSA,RC[:,k+1])

SCs=10 # Smoothed cycle components

SmoothedSSA=RC[:,0]

for k in range(SCs-1):

    SmoothedSSA=np.add(SmoothedSSA,RC[:,k+1])

plt.subplot(2,1,1)

plt.title("Original vs. Reconstructed time series")

plt.plot(s[:])

plt.plot(RawSSA)

plt.subplot(2,1,2)

plt.title("Reconstructed raw vs. smoothed time series")

plt.plot(RawSSA)

plt.plot(SmoothedSSA)

# sample spacing

Days=N*7 # Number of days

Months=N*7//30 # Number of months

Years=N*7//360 # Number of years

T=1/Months # Defining the sample spacing step-size

yf = fft(s)

xf = fftfreq(N, T) #[:N//2]

# FFT for each RC

RC_fft=[]

RC_fft_power=[]

for l in range(L):

    RC_fft.append(fft(RC[:,l])) #[0:N//2])

    RC_fft_power.append(np.abs(RC_fft[l]))

# Denoise FFT of RC

dn_RC_fft=RC_fft.copy()

dn_RC_fft_power=RC_fft_power.copy()

for j in range(len(RC_fft)):

    for k in range(len(RC_fft[0])):

        DenoisingThreshhold=(sum(RC_fft_power[j])/len(RC_fft_power[j]))

        #DenoisingThreshhold=(max(RC_fft_power[j]))*0.90

        if RC_fft_power[j][k]<DenoisingThreshhold:

            dn_RC_fft_power[j][k]=0

            dn_RC_fft[j][k]=0

        else:

            continue

# Defining the cycle length

CycLen=(xf[0:N//2]) # Cycle length

#CycLen=CycLen[::-1]

CycLen

### Graph output (4) ###

# Showing some examples of the cycle lengths of the frequencies

fig, axs = plt.subplots(7)

for k in range(1,8):

    axs[k-1].stem(CycLen,dn_RC_fft_power[-k*10][N//2-1:-1]) #[0:N//2])

# Summing all the frequencies of RCs for the inverse FFT

tp_dn_RC_fft=list(map(list, zip(*dn_RC_fft)))

tp_dn_RC_fft_power=list(map(list, zip(*dn_RC_fft_power)))

sum_dn_RC_fft=[]

sum_dn_RC_fft_power=[]

for k in range(len(tp_dn_RC_fft)):

    sum_dn_RC_fft.append(sum(tp_dn_RC_fft[k]))

    sum_dn_RC_fft_power.append(sum(tp_dn_RC_fft_power[k]))

# ### Graph output (5) ### Uncomment the following to display

#plt.stem of the denoised power stemplot

plt.stem(CycLen, sum_dn_RC_fft_power[N//2-1:-1])

plt.grid()

plt.show()

### Graph output (6) ### Uncomment the following to display

# Inverse FFT to reconstruct the time series

plt.plot(s)

plt.plot(ifft(sum_dn_RC_fft).real)

Reception at Hakugyokurou: Eiki Shiki Yamaxanadu visiting Hakugyokurou, Yuyuko Saigyouji welcoming

 

Tool used: CLIP STUDIO PAINT

 

These illustrations are posted in my Pixiv page so please visit https://www.pixiv.net/en/users/32334195!