2014.12.26rubleDollar



2014.12.26rubleDollar is set of approximations of value of hundred of Russian roubles, measured in the USA cents, for the end of year 2014.

The The green thick curve represents the experimental data \(y=g(x)=\mathrm{Measured}(x)\) by https://www.mataf.net/en/currency/converter-USD-RUB ; coordinate \(x\) has sense of time, measured in days since the date of beginning of the project, 2014,10,27.

For each datum stored for specified year,month,day, the time \(x\) is evaluated as

\(x = \rm daju24(year,month, day)- daju24(2014,10, 27)\)

with function daju24 defined below in C++: int daju24(int Y,int M, int D){ int a, y, m; a = (14-M)/12; y = Y + 4800 - a; m = M + 12*a - 3; return D + (153*m+2)/5 + 365*y + y/4 - y/100 + y/400 - 32045 - 2400000; }

These data are stored as array \(\{x_n,g_n\}, \{n,1,M\} ~ ~\), where \(M=209 ~\) is total number of experimental data. Approximating functions are specified below:

\( \begin{array}{c|l|r|r} \rm Label &~ ~ ~ ~ ~ f(x) & D ~ ~ & Q ~ ~\\ \hline \rm Linear &227.323 - 0.583872 x &\! 10.52733 &\! 13.15973\\ %{227.32289289657714` -  0.5838719175561293` x, 10.52725166548383`, 13.15967254961913`} \rm Qu\! & 233.214 - 0.908933 x - 0.00361841 x^2 & 3.94609& 5.84960\\ %3.946087936982961`, 5.849600340588587 \rm Ellipse &~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1.19332 \sqrt{(99.8879 - x) (388.557 + x)} & 3.72305 & 5.74477\\ \rm Ed & -96.8595 +   1.46555 \sqrt{(127.305 - x) (401.761 + x)} & 3.74359 & 5.71801\\ \rm Cu & 234.636 - 0.905604 x - 0.00456087 x^2 - 6.98113\!\times\!10^{-6}~ x^3 & 3.77297 &  5.72430\\ \rm Bell & 291.207 / \cosh(0.715005 + 0.00630878 x)& 4.91540& 6.96990\\ \rm Gauss & 290.656 \exp\Big(-0.0000168642 (116.58 + x)^2\Big) & 4.45347&6.43202\\ \rm Dex &\!\! 100/\Big(0.337261 \exp(0.000020293 x) +   0.0881639 \exp(0.0189706 x)\Big) \!& 3.79927& 5.72350\\ \hline \end{array} \)

The last two columns of the table above characterise the precision of each approximation:

\(\displaystyle D= \frac{1}{M} \sum_{n=1}^{M} |f(x_n)-g_n|\)

\(\displaystyle Q= \sqrt{\frac{1}{M} \sum_{n=1}^{M} (f(x_n)-g_n)^2}\)

Comment
Any scientific concept has limit range of applicability. The approximations and forecasts of the pride of a vault are not exception. The later data show, during two months since the preparation and loading of the approximations, roughly, until 2015.02.04, the "pessimistic" extrapolations still show good agreement with experimental data.. Then, for few years, the price of ruble stabilises between one and two USA cents.

Keywords
Approximations of ruble, Corruption Inflation, Rusisa,

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