Showing posts with label Statistics. Show all posts
Showing posts with label Statistics. Show all posts

Saturday, September 12, 2026

The trouble some issues encountered while modelling the economic growh together with a new exponential modelling

 

The following text is AI (ChatGPT plus) generated with reference to my current issue in mathematical modelling of the macroeconomic growth theory. 

---  

This week I had an interesting little incident at the boundary between economics and mathematics.

I was checking an exponential model for an economic growth / Total Factor Productivity (TFP) problem. After going back to the mathematical formulation and implementing it carefully in MATLAB, the objective function Q(ϕ)Q(\phi) showed a clear minimum.

At first sight, that sounds encouraging: the optimisation problem has a well-defined solution.

However, when I reconstructed the corresponding TFP trajectory using the parameters associated with that minimum, the result did not reproduce the observed trajectory satisfactorily.

So I found myself in an interesting situation:

the mathematics said, “Here is the optimum,” while the economic data replied, “Not so fast.” 😅

This does not necessarily mean that the exponential approach is mathematically wrong. Rather, it raises a more interesting question: is this particular model structure appropriate for representing the empirical behaviour of TFP?

At the moment, I am therefore also comparing the result with a penalised smoothing spline, which appears to represent the trajectory more naturally.

For me, this has been a useful reminder that finding a mathematically neat optimum is not the same thing as finding a good empirical model. Optimisation, model specification, and interpretation all have to work together.

The investigation is still ongoing, so this is not a final conclusion — just one of those small research episodes where economics and mathematics refuse to cooperate quite as politely as expected.

 

Sunday, July 26, 2026

My codes of financial time series analysis and the AI art used in my Yukkuri Commentary movie posted on YouTube


This video presents our recent research on financial volatility forecasting, comparing classical econometric models, signal-processing techniques, and modern machine-learning approaches.

The study evaluates the forecasting performance, volatility prediction accuracy, computational efficiency, and interpretability of five different methods:

• GARCH
• SARIMA
• Matrix Pencil (MP)
• XGBoost
• Long Short-Term Memory (LSTM)

Using Bitcoin returns as a high-volatility financial asset, we investigate whether modern AI-based methods consistently outperform traditional forecasting techniques when accuracy, explainability, and computational cost are considered simultaneously.

Our results show that:

✓ SARIMA achieves the lowest return forecasting error.
✓ Matrix Pencil delivers comparable forecasting accuracy with extremely low computational cost.
✓ XGBoost provides a strong balance between accuracy and efficiency.
✓ LSTM exhibits relatively strong performance in tracking volatility patterns and market regime changes, despite higher forecasting errors and computational requirements.
✓ No single model dominates across all evaluation criteria.

The findings suggest that the Matrix Pencil method remains a competitive and highly interpretable alternative to black-box machine-learning models for financial forecasting applications. 

NicoNico: https://www.nicovideo.jp/watch/sm46580360 

Sakuya, Youmu, and Marisa challenge a unique cooking competition!
Using Bitcoin market data as ingredients, five dishes — GARCH, SARIMA, Matrix Pencil, XGBoost, and LSTM — to compete to predict future market movements ♬
This video explains the strengths and characteristics of traditional econometric models, signal-processing approaches, and modern AI techniques through a fun Yukkuri-style commentary.
Which model will create the best “forecasting recipe” for the future market?

Artwork including original character illustrations:
https://www.pixiv.net/en/tags/%E5%A6%...

Music, sound effects, and background materials used in this video are credited in the end credits.
#TouhouProject #Touhou #YukkuriCommentary #reimu #marisa #sakuya #youmu #remilia #yuyuko #Finance #Bitcoin #Cryptocurrency #QuantitativeFinance #FinancialEngineering #FinancialForecasting #VolatilityForecasting #Econometrics #ARIMA #SARIMA #GARCH #ArtificialIntelligence #MachineLearning #DeepLearning #DataScience #TimeSeriesAnalysis #ExplainableAI #XGBoost #LSTM #SignalProcessing #MatrixPencil #Prony #PronyMethod #Python #Research


This image is posted on my pixiv page: https://www.pixiv.net/en/artworks/147674029
My attempt is to generate an AI art with free of charge using ChatGPT. Many AI illustration tools charge fee and are not so flexible yet. I have experimented with generating an image based on my rough drawing together with the input script into ChatGPT.
This is an AI-synthetic illustration output by ChatGPT based on my rough drawing. The following is the input script. It is like asking the contemporary popular character designer to illustrate Touhou Project characters in his style. ☆彡



Redraw this illustration in a 1990s Japanese fantasy RPG illustration style with the scene shows three cooks working side by side in a cozy kitchen:
• on the left, a refined silver-haired maid in a blue-and-white uniform with a green ribbon, skillfully slicing vegetables with a kitchen knife
• in the center, a white-haired swordswoman in a green outfit, attentively stirring a pot of simmering food on the stove
• on the right, a blonde witch-like girl wearing an oversized black pointed hat and a black-and-white outfit, energetically stir-frying ingredients in a frying pan.
Please improve the line quality, proportions, and shading while preserving the original composition.
 
 I have got to prepare for a cover image for a video I am currently creating to post YouTube. Furthermore, over here, it is too hot to be concentrated with my usual art works. .... seriously, it's tough enough to make me sleep quite a few hours! In an accommodation where I am currently living, there is no AC! My energy has recently been drained without noticing. Therefore, I just decided to spend my experiment in the AI output while my concentration and energy for my own artwork is sizably limited 

Tuesday, April 08, 2025

Financial time series analysis with Matrix Pencil, the modern Prony's method - Python, Future prediction, Yahoo finance

 Originally Saturday, November 30, 2024

 The misprints of the elements in unitary-matrices in the recipe corrected on Tuesday 8th April 2025





The misprints  the elements in unitary-matrices in the recipe corrected on Tuesday 8th April 2025

 

 


 

Friday, March 28, 2025

Engle's ARCH motion prediction model with the simulation data with Python

 This is introduced in my cartoon video of Yukkuri Kaisetsu (Touhou Project fan-art):




Auto-Regressive Conditional Heteroscedasticity (ARCH)

ARCH was developed by an economist Robert F. Engle III having won the 2003 Nobel Memorial Prize in Economic Sciences for its achievement.

Dependent variable: the variance error terms of the first regression:
The explanatory variable X can be the lagged dependent variables and/or the other variables: 
Then, it find the coefficient γ of the lagged squared error terms with reference to the log-likelihood: 
 

Generalised Auto-Regressive Conditional Heteroscedasticity (GARCH)

GARCH assumes the variance of the error term symmetrically varies depending the average size of the error terms in pervious time steps. It adds the lagged variance on the explanatory variable of the second regression with reference to the log-likelihood for finding the coefficients γ and δ:

 

 Simulation Data with Python

The following exhibits display the simulation data evaluated using ARCH to illustrate how ARCH functions.

To facilitate the visual representation of this simulation, the most basic form of Engle's ARCH, as introduced in the Wikipedia entry below, has been implemented.

Ref: https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity

This simplified simulation demonstrates motion prediction for intercepting incoming flying projectiles with erratic movements, resembling the fluctuations of a stock price.

Following is my Python codes: 

Monday, November 11, 2024

Normal Distribution Random Normal T-test Type I Error







I've edited and published Yukkuri Kaisetsu movie with my original stand picture of Statistical test based on Python programming.

 

Thursday, May 23, 2024

ARCH, GARCH, and ARIMA

 

Auto-Regressive Conditional Heteroscedasticity (ARCH)

ARCH was developed by an economist Robert F. Engle III having won the 2003 Nobel Memorial Prize in Economic Sciences for its achievement.

Dependent variable: the variance error terms of the first regression:
The explanatory variable X can be the lagged dependent variables and/or the other variables: 
Then, it find the coefficient γ of the lagged squared error terms with reference to the log-likelihood: 
 

Generalised Auto-Regressive Conditional Heteroscedasticity (GARCH)

GARCH assumes the variance of the error term symmetrically varies depending the average size of the error terms in pervious time steps. It adds the lagged variance on the explanatory variable of the second regression with reference to the log-likelihood for finding the coefficients γ and δ:

 


Auto-Regressive Integrated Moving-Average (ARIMA)

Another popular auto-regressive method (AR) + Integrated differences (I) + moving-averaging (MA). 


Ref.: https://people.duke.edu/~rnau/411arim.htm 


Integrated (I): Using the differentiating a non-stationary time series to attempt to transform it to a stationary series. 


Moving-Average (MR) model: Using the past forecasted error terms instead of the lags of the dependent variable. 


 Limitation of these AR methods

Ref. Modeling daily realized futures volatility with singular spectrum analysis    Dimitrios D. Thomakosa, Tao Wanga, Luc T. Willeb; ∗ Received 29 November 2001 https://doi.org/10.1016/S0378-4371(02)00845-2

Limited as the forecasting model: Whereas it provides the magnitude of the fluctuations e.g., volatility, their distribution is assumed to be symmetric. The error of the estimation expands for the future estimate


The coefficients of the lagged variable contain non-periodic noise terms, which disrupt the estimation of the important periodicities represented by these coefficients.

SSA and Prony-like methods can extract the cyclical physical components that contain important information about the periodicity and its magnitude by distinguishing them from the noise components.


SSA performs better than various auto-regressive methods and Hodrick-Prescott filter (Noise-filtering method) introduced in "Singular spectrum analysis for real-time financial cycles
measurement   Maximilien Coussin 1 https://doi.org/10.1016/j.jimonfin.2021.102532"

Monday, January 08, 2024

The European Monetary Union is inevitable, but has to be fundamentally revised

Published on 23/07/2011 09:18 British Summer Time

1. Introduction

This Eurozone crisis has been predicted by many economists. These economists put emphasis on the impact of the money supply volume on the stability of economic environments such as the price inflation rate, the unemployment rate, the gross domestic product (GDP), and the speculative trend on financial market. They argued that, when the monetary policy is unified, the common fiscal policy is also required to be established, all the member countries of this monetary union are supposed to have the financial regulation for all these countries, and the labour mobility needs to be flexible for workers in these member countries to move across these countries in order to stabilise the economic environments. In addition, the econometric analysis of the Eurozone average inflation rate indicated that the European Monetary Union (EMU) is beneficial to majority of the member countries owning to the harmonised inflation rate, but it still requires something to control the different inflation rate of each individual member country. The reason of German refusal of issuing Eurobond is assumed to be because of uncooperative attitudes of Greece. Mr. Trichet, the governor of the European Central Bank (ECB) also suggests that the EMU has to fundamentally change its overall structure before allowing any countries to keep incurring their debt. Overall, the solution of the currently ongoing Eurozone crisis is the fundamental improvement on the EMU fiscal, financial, and labour market structure, and getting rid of the common currency will never be a solution.


2. The problem caused by the monetary policy transformation

The disadvantage of abandoning the national monetary policy (to join the common monetary union) is that this country becomes no longer able to set her own interest rate and the volume of her own money supply. Greece used to be heavily relying on her own unique monetary policy, based on the money supply which was remarkably higher than the average of European countries, in order to finance her government expenditure which could not be sufficiently financed by her unsophisticated fiscal policy. However, after Greece joined the EMU, she could no longer use her high money supply. Greece may rely on the tax revenue burdened on her export revenue such as her tourist industry and the growth of her private sectors stimulated by the economic growth of the entire Eurozone economy. Nonetheless, unless she tightens her fiscal policy, when the entire Eurozone economy falls into recession and/or the demand of Greek tourist industry declines, Greece starts struggling to obtain her public finance resource. This problem has been seen in many Southern European Nations such as Italy, Spain, and Portugal. But, Greece seems to be more problematic than these Southern nations. Spanish government shows a strong commitment on tightening Spanish fiscal policy under the European central government’s induction. Italy still has her strong initiative in European economy thanks to her famous industries such as finance, manufacturing, and tourism. Portugal seems to be similar to Greece, but the quantitative data analysis shown in the next chapter indicates Portuguese suffers much less than Greece.




3. The econometric analysis of the Eurozone average inflation rate

This graph (Qualitative method) above shows the different inflation of the Eurozone countries (IMF, 2011). Majority of the Eurozone countries have a synchronised inflation rate trend from 2002 to 2010. The econometric analysis of the Eurozone average inflation rate, whose results are shown by the following figures, indicated that the price inflation of the individual countries joining the European Monetary Union (EMU) is influenced by the price inflation of the other different EMU countries.




This equation is the inflation rate of all individual Eurozone countries (〖Inflation〗_(i,t)) regressed on the inflation rate in the last year 〖Inflation〗_(i,t-1). As the coefficient of 〖Inflation〗_(i,t-1) is less than 1, this variable is stable enough to converge into a particular point in the long run as follows:




So, this proves that the Eurozone inflation rate is converging into 2% which is what the ECB targets to make! The following regression analysis proves that the GDP grows furthermore when the inflation rate becomes closer to 2%:




This result shows the natural log of the GDP in the Eurozone economy, ln⁡(〖GDP〗_(i,t) ) (Footnote 1.) , is significantly negatively correlated with the inflation rate deviating from 2% which is shown as the absolute number of the inflation rate minus 2, |〖Inf〗_(i,t)-2|. The following auxiliary regression shows both the GDP and the inflation are co-integrated each other:



〖 u〗_(i,t) is the residuals from the previous regression. As the lagged residuals 〖 u〗_(i,t-1) is negatively correlated with change in the residuals 〖∆u〗_(i,t), the variables used in the previous regression, ln⁡(〖GDP〗_(i,t) ) and |〖Inf〗_(i,t)-2|, are stable and co-integrated with the EU inflation rate, which means the movement of these variable affects on the other’s. However, the stability test for Greece and Ireland showed a relatively pessimistic result as follows:

Greek inflation on the inflation of the entire Eurozone countries



This analysis suggests that, , not only the percentage of the entire Eurozone inflation's contingency on Greek inflation rate is 47% in average, which is high,(Amended part) but also change Greek inflation is highly contingent to the entire Eurozone (Footnote 2.). Therefore, it is not only Greece suffers more than the other Eurozone countries and but also Greek economy is highly responsible on the entire Eurozone economy. This aspect may suggest both Greece and the entire Eurozone need to cooperate each other very seriously because Greece should not leave the EMU because her business cycle is already tied up with the EMU.

Irish inflation on the inflation of the entire Eurozone countries



On the other hand, Irish inflation rate is neither stable nor co-integrated with the entire Eurozone one. Therefore, Greece seems to suffer from the volatility of the inflation far more than the other Eurozone members so that she needs either the intervention by the European central government or the fiscal restructuration, or both, to calm down her inflation rate. Unlike Greece, Ireland may be benefitted when she leaves the EMU. Irish business cycle is not correlated with the Eurozone economy. But, if Ireland still wants to keep the membership, the Eurozone eventually needs to have a strong fiscal stimulus enough to enable Irish business cycle to harmonise with the entire Eurozone business cycle.

4. German refusal of participating into the Eurobond programme

The concern of Germany on Greece is that Greek catastrophic crisis will be permanent unless Greece tries to reform her fiscal policy fundamentally and cooperates with the EU central governmental policy rather than her own selfish and irrational nationalism. When a person purchases equity, s/he expects its value to be either stable in the long term or predicted to grow significantly. The value of Greek national debt seems to be neither stable in the long term nor predicted to increase its value in the short term. Even if German government is altruistic enough to sustain Greek public finance by purchasing Greek debt in order to rescue the entire Eurozone, there is a risk for Germany to be drawn into the recession or even to be bankrupt.
The Eurobond programme suggests the Eurozone countries to share both the risk and the benefit of issuing the government debts among the entire Eurozone countries rather than burdening the responsibility on each individual country for incurring the government debt. For example, as shown in the graph below, when Germany experiences the economic growth relatively higher than any other nations whilst France falls into the recession, it needs to tune the aggregate demand of both nations.


As there is no national monetary policy available for both France and Germany, one of the optimum solutions would be increasing the tax revenue of Germany to transfer it to subsidise France. The econometric analysis shown in the previous chapter indicates that French and German economies are highly contingent to each other so that French downturn has to be diverted by German contribution to save Germany herself. This is the idea of sharing the risk and benefit of the national debt and its usage under the collective responsibility among the countries.
Nonetheless, this mechanism may work efficiently and effectively because French fiscal policy does not have a problem like Greek. France and Germany have much more similar labour market situation than Greece. In addition, France and Germany are geographically closer each other than Greece. So, the labour mobility is much more flexible between France and Germany than between Greece and them. Furthermore, France and Germany balance their budget without relying on the excess money supply unlike Greece. If this case scenario were Greek instead of France, German tax revenue transfer to subsidise Greece is ineffective and inefficient.
The intervention from the European central government into Greek fiscal policy under the strict guideline of the central government is also emerged. Greece is still resisting against this intervention due to the sentimental irrational populist nationalism. The European central government regards that, in order to make this money transfer to Greece more effective and efficient, Greek fiscal reform lead by the further privatisation of the entire Greek economy are inevitably required. Greek labour market is rigid because of Greek economy’s reliance on the huge public sector, which disrupts the flexibility of the labour mobility. On the top of the inflexible labour mobility, Greek public sectors are not rational enough to balance their budget. They are not used to the market competition and the thread of bankruptcy because they are always protected by the nation unlike the private sectors. By contrast, the private sectors are much more used to balancing their budget under the market competition. As long as Greek public sectors struggle to rationalise their budget to be balanced by their own effort, the enforced privatisation seems to be only the antidote of the fiscal imbalance.
All in all, the responsibility of Greek fiscal policy should be burdened more on European central government to discourage Greek irrational populist nationalism which is notoriously uncooperative to solve this currently ongoing problem for both Greece herself and the entire Eurozone economy. In order to discourage this pathetic nationalism, the privatisation to minimise Greek national government authority can be a key solution before substituting the power of Greek nationalism with the European economic cooperation.


5. The ECB’s point of view and warning from Mr. Trichet

Focusing on the ECB’s point of view on the current Eurozone financial havoc, the ECB executives are suffering from the dilemma between putting priority on saving the Eurozone economy and focusing on calming the inflation by suggesting the fiscal policy of all Eurozone countries to be tightened. In particular, Mr. Trichet, the governor of the ECB, always rejects the optimism on the Eurobond programme without fundamentally reconstructing the fiscal structure in the entire Eurozone. Mr. Trichet has been always suspicious about the stability of the Eurozone economy since the ECB was established. His suspicion is related to the fiscal problem mentioned in the previous chapter.
The ECB has been purchasing a large volume of the national debt of the Eurozone countries by its quantitative easing. In order to keep the value of these bonds to invest to rescue these governments, the ECB has. The ECB cannot survive without an economic activity of these nations so that the ECB needs to save the national governments of the Eurozone. Otherwise, the value of Euro becomes zero so that the ECB itself disappears. However, the expected result still cannot be seen, and the aggregate government bonds incurred has never stopped expanding. This mechanism still enables the Euro exist, but it depreciates the value of Euro further. This phenomenon causes the inflation to hike up, and then the nominal interest rate eventually needs to rise. Overall, rescuing the Eurozone countries damages the private sectors and individual citizens by a high interest rate, and it creates further government deficit which requires the further ECB’s quantitative easing, which again induces a further inflation. Mr. Trichet has already warned this spiral would occur and urged to divert from it since the beginning of the Eurozone crisis (Footnote 3.). Thus, he rejects all the optimism of perpetuating this situation.
The ECB also struggles with negotiating with the private sectors. Although the previous chapter stated the positive aspect of the private sectors in terms of the fiscal policy, the private sectors cause problem in the monetary policy set by the ECB (Footnote 4.). The private sectors are willing to raise their profit and the wage for their executives, and detest the high interest rate. These characteristics of the private sectors perpetuate the inflation which discourages an economic growth of both countries and private sectors themselves in the long term. Generally speaking, the private sectors are uncooperative to the European economic stabilisation. Although the stabilised European economy which the ECB expects to establish benefits to the private sectors in the long term, these private sectors are less interested in it than the ECB.
This aspect infers a danger for European economy which is now also fund by the private sectors. This could be the reason why Mr. Trichet is modest about the private sector contribution to rescuing the Eurozone national economies .

6. Conclusion
In conclusion, there is no optimistic prospect on this current Eurozone economic situation. In order to solve these structural instabilities, the Eurozone may need a fundamental radical revolutionary act on altering both economic and political entire structure. But, they cannot stop the European economic integration because the almost all Eurozone economies are highly correlated with each other as proven by the econometric analysis. It seriously needs an IMF of Europe, which the ECB is trying to act like. The ECB should have a much stronger authority to instruct the fiscal policy of national governments in the Eurozone as same as the IMF does to the national governments in the globe. In addition, if the priority is saving the European economy, the heavy reliance on the private sectors contribution is very risky. Hence, the ECB policy based on Trichetian Monetarism, which is tough against the irrational egos of both the national government fiscal policy and the private sectors’ short-termism, seems to be only the reliable tool, and the economic agents had better listen to it.


-------------------------------------------------------------------------------
Footnotes:

1. When a variable is positively skewed, it needs to be logged or transformed into the root (E.g. square root and cube root) in order to offer a reliable, unbiased, and consistent statistical analysis.

2.


---------------------
My Additional Comment added on 4th of August 2011:

Well, as I mentioned in my essay, it depends on the hamonisation of the business cycles in these candidate nations (I referred to the price inflation rate as an indicator of the business cycle). When the business cycle is harmonised (Synchronised), the monetary union becomes necessary or inevitable, such as the Greek and the other Eurozone countries' case. Otherwise, such as Irish case, it should not join the monetary union or it has to have a great intervention to artificially harmonise the cycles.

Some African nations might be benefited because they trade each other often, and their economy is not self-sustainable i.e. needs to be corroborated each other. But, they indeed need to have a common fiscal policy to modernise and tighten the fiscal policy of all these nations.

South American nations should not have the monetary union yet. These individual South American countries are too big by means of the land mass relative to their population density (I.e. The cost of the inter-country trade inside South America is higher than the benefit from it). Furthermore, these countries do not trade each other often compared to the other blocks of countries in this world such as Europe, North America, Africa, and Asia (According to the statistics shown in Economics of Monetary Union (Paul De Grauwe)).

The trade frequency of among Asian nations is the highest of all the international trade made in this world. So, as Lee Kuan Yew, the first Singaporean prime minister, said forming Asian trade community could benefit Asian nations. However, other than economic factors, the political factors exist as the obstacles which disrupt forming this trade community.

Only the person concerning the EMU whom I can truely respect and trust is Mr. Trichet and his ECB. I claim that not only the EMU national fiscal policies but also all the private enterprises in the Eurozone economy should be instructed by the ECB based on Trichetian Monetarism...!

Friday, August 05, 2022

Recession in 2024

 

The major recession is coming in 2024 for certain by means of both the international financial analysis and the astrological analysis (from the later half of 2024)! In terms of the international finance, the short-term United State (US) bond interest rate is higher than the long-term counterpart now. This infers to forecast the economic outlook of a few years ahead is worse than the one at the recent time period. In terms of the astrological analysis, the square aspect of Jupiter and Neptune has almost always triggered the world gross domestic product (GDP) decline. This is econometrically experimented in my own research.

The current interest rate hike of the US and the Western European central banks is recently notable due to the ongoing price inflation pressure. However, the long-term (3 to 5 years) rate still stays low, and this implies the low growth of both the GDP representing the combination of both the price inflation and the production output level in a few years ahead. This phenomenon has almost always taken place approximately 2 years before the world-wide recession strikes owing to the financial statistics. Therefore, it is most likely to have the recession in 2024.

The modern Western astrology denotes the aspects of Jupiter and Neptune combined representing the financial flow. Jupiter represents expansion and wealth whilst Neptune represents ambiguity and flash-flood. Therefore, the combination of what each of these two plants represents indeed explains the financial market. The soft aspects such as the triangle 120 degree and the sextile 60 degree tend to induce the reasonable financial wealth growth whereas the hard aspects such as the opposition 180 degree and the square 90 degree tend to induce hard challenges for the financial wealth creation.

When the world GBP (US$ base) is regressed on three explanatory variables based on trigonometric functions, their correlation shows that astrological representation actually holds as it explains! The first explanatory variable is based on the equation of the cube root of 1 minus two times the modulus of 0.5 subtracted by the modulus of the cosine. This variable is maximised at the 60 and 120 degrees whilst it is minimised at 0, 90, and 180 degrees. The second explanatory variable is the modulus of the sine which is maximised at the 90 degree square aspect. The third explanatory variable is simply the cosine which is maximised at the 0 degree conjunction whereas it is minimised at the 180 degree opposition. 

All these three coefficients' confidence levels are above 90 percent. The third variable's correlation was mild whereas the conjunction aspect is positively correlated while the opposition aspect is negatively correlated. The first variable's correlation is slightly below 95 percent which is still convincing. It seems to be difficult to use the 95 percent confidential interval to determine the confidence level by using such a relatively rough fluctuant indicator like the world GDP level.  Then, using the 90 percent confidence level is worth off to be used for the alternative measure. 

The most intensive and interesting result is the second explanatory variable's correlation which is above 95 percent with its negative correlation with the dependent variable, the world GDP! By means of the statistical inference, this can conclude that this is certain to happen in the future when this correlation takes place. Thus, this is certain that the world GDP declines when Jupiter and Neptune from the square aspect which is going to take place in 2024.

Saturday, April 09, 2022

The correlation betweeen currency value based on JPY vs the great circle distance from Kiev, Ukraine

 

 
I have been surprised at how much depreciated Japanese Yen (JPY) against the other currencies has been already.  However, I have realised that the appreciation of each currency by means of JPY is different.  I have guessed that the appreciation rate is lower as the region using this currency is closer to Ukraine where the conflict with Russia is ongoing.  Therefore, I have regressed these FX rate based on JPY with the natural log of their great circle distance from Kiev minus 6.6, and the coefficient is as predicted as shown this graph.

Data from Mizuho Bank: https://uranaisearchastrology.files.wordpress.com/2022/04/2021-2204_fx_mizuho_dist.xlsx

Sunday, November 28, 2021

Econometrics meets Astrology: Regressing the world GDP on the aspects of Jupiter and Neptune

In the European astrology, the aspects of Jupiter and Neptune denote the economic/financial prosperity.  Since I started the European astrology, I have become keen to test if the astrological chart can actually be interpreted by econometrical analysis because these aspects are based on the numerical values of these aspects' angles.  

The combination of Jupiter (expansion and growth) and Neptune (ambiguity and liquidity) represents the financial fortune of individuals, companies, and each different time transit.  It is believed that it is a bubble aspect when these two planets form the soft aspects such as the conjunction 0 degree (while it simultaneously induces the hard), the triangle 120 degree, and the sextile 60 degree. On the other hand, it is a broke/crisis aspect when these two planets form the hard aspects such as the opposition 180 degree and the square 90 degree (and also the conjunction simultaneously).  

Then, the following 3 explanatory variables generated by the trigonometric function are created: 

1. The most complex indicator showing a higher value when the aspect angle is close to the soft aspect while a lower value when the aspect angle is close to the hard aspect.  

This could not catch up the positive effect of the zero degree. But, instead of making the valuable excessively complex, the 3rd explanatory variable represents the positive effect of the zero degree angle (Conjunction). 

2. Just a modulus of the sine of the radians representing the effect of the square 90 degree aspect.  The negative effect of another hard aspect angle 180 degree angle (Opposition) is shown by the following 3rd explanatory variable.

3.  The most simple cosine of the radians indicating the highest value at the zero degree angle (Conjunction) and the lowest value at the 180 degree angle (Opposition).

Therefore, the equation for the ordinary least squares (OLS) becomes as the displayed one. 

The coefficient of B1 is expected to be positive, B2 is negative, and B3 is mildly positive.

The result is amazing!  The coefficients of these explanatory variables have turned up to be what expected to be! 

These significances cannot expected to be so strong and the model in general looks rough because this statistical analysis based on a rough and extraordinarily big picture such as a transit aspect of the world GDP in a single chart. 

In order to expect to create a stronger model with stronger significance levels, it requires more precise pictures of the target objects such as the more complex aspects, each individual regional aspects', etc.  

Nevertheless, this can be said to be a big achievement for an econometrician and an astrologist because this analysis actually indicates such a rough estimator as the astrological aspect is able to estimate the world economic outlook to the certain extend! 


Data references:

* You may download the excel file basing this analysis by clicking here.*

Thursday, April 08, 2021

Strange Daily JPY Negative Correlation with TOPIX


It is said that Japanese Yen (JPY) moves awkwardly in the market because JPY tends to be appreciated while Japanese economy indicates the sign of downturn at least in the short run. This trend is often perpetuated even in the middle run. This surprises majority investors observing JPY trends.

In the long run, this awkward trend of JPY is usually corrected to follow the major indices of Japanese economy, such as major Japanese corporate stocks, with their positive correlation as same as the other major currencies of OECD countries such as US dollar (USD). Nevertheless, the market almost always demonstrates the notable negative correlation between JPY and a major Japanese stock index such as Tokyo Stock Price Index (TOPIX) while the observers and the participants monitoring it.

Majority of these individuals monitor JPY with the USD, the most traded pair of JPY, so USD/JPY (USD value based on JPY) is frequently used for the main reference to scale the change in JPY value. The following regression analysis based on the Ordinary Least Squares (OLS) for the time series analysis assesses this phenomenon by regressing the log difference of daily USD/JPY on the log difference of daily TOPIX in the time series.

*** Please note that the positve correlation of USD/JPY means the negative correlation of JPY/USD, and vice versa ! ***

 




The sign is positive , and its t-value is 13.3 which is way higher than the Dickey-Fuller critical value t = 2.89.

Then, in order to determine whether this time series correlation is valid or just a coincidence with no statistical validity, the residuals (the error terms) of the aforementioned OLS are tested by the autocorrelation analysis as follows. The first difference of the residuals are regressed on the lagged residuals. The test is to detect whether or the error term is corrected itsself, so the eroor correction model is recognised.




The sign is negative, and its t-value is -26.43 so the absolute value is way higher than the Dickey-Fuller critical value 2.89, and then the error correlation model holds.

The equation of this estimates of the autocorrelation is expanded as follows.



Then it can be expressed as shown in the graph below:



This pattern of JPY mechanism is caused by the obsolete transaction system of the entire banking and monetary function. The obsoleteness is characterised by both the inefficient physical mechanical equipment of the currency transaction of money and assets among banks and investors and the rigid traditional bureaucracy of government, central bank, and private banks in Japan.

Whenever, the market participants switch their holding assets with the others, the system requires them to convert their assets to the national currency JPY before purchasing the alternative asset. Furthermore, due to the slow transaction in this inefficiency, there is a significant lag of exchanging different assets. Therefore, it consequently induces them to hold JPY cash in their transaction process.

In addition, majority Japanese citizens have a strong faith in holding cash and the middle to high income Japanese citizens have a remarkably high propensity of saving (This is why the majority share of the government bonds is owned by these middle to high income earners. They have a strong tendency to hold cash all the more when the value of stock, bonds, and other equities started being depreciated. This accelerates the appreciation of JPY during the downturn on the top of the obsolete system inefficiency.

By contrast, during the upward market, the short run JPY depreciation may seem to be depreciated when TOPIX rises. Instead of TOPIX affecting JPY, this case scenario is that the depreciation of JPY causes to stimulate TOPIX because of the two reasons. Japanese economy is a heavily export driving economy so JPY depreciation increases the export demand and the revenue of the exporters trading by means of foreign currencies. Another reason is simply because of the transactional motive of the traders attempting to mitigate the fincial loss of their revenue from the depreciated JPY by replacing JPY with the other foreign currencies or any available, safe, and stable assets.