File:2014rubleDollar2param.png
Original file (1,527 × 1,004 pixels, file size: 232 KB, MIME type: image/png)
Price of 100 Russian roubles evaluated in the USA cents versus time.
TIme$x$ is measured in days since the beginning of the project, 2014.10.27.
Pink dots represent the experimental data by https://www.mataf.net/en/currency/converter-USD-RUB
10 red lines represent the linear approximations,
$fx)=L(x)=a+b x$
Parameters $a$ and $b$ are evaluated, minimising the mean square deviation
$\displaystyle Q(m)=\sqrt{ \sum_{n=1}^m (F_n-f(X_n))^2 }$
for $M-10\le m \le M$; in such a way, for function $f=L$, 10 curves are plotted, and these curve form the red strip.
The same is plotted also $f=J$ and for $f=K$, where
$K(x)=a \exp(-b x)$
$J(x)=a / (1+b x)$
References
The image is used as Fig.1 in the article
http://mizugadro.mydns.jp/PAPERS/2015ruble.pdf D.Kouznetsov. Currency band and the approximations: Fitting of rouble with 3-parametric functions. 2015, under consideration.
Input file
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Mathematica generator of lines
g0 = Import["~/Q/RUBLE/BUL/TRY01/ddat.txt", "Table"];
T0[i_] := Extract[Extract[g0, i], 1];
G0[i_] := Extract[Extract[g0, i], 2]; M0 = Length[g0]
lp = ListPlot[g0, PlotRange -> All, PlotStyle -> {RGBColor[1, 0, 1], PointSize[.04]}]
For[i = M0 - 52, i < M0, i++; Print[i];
g = Table[{T0[j], G0[j]}, {j, 1, i}]; M = Length[g];
T[i_] := Extract[Extract[g, i], 1];
G[i_] := Extract[Extract[g, i], 2];
F[x_] = a + b x ; sub = FindFit[g, F[x], {a, b}, x];
Print[{f[x_] = ReplaceAll[F[x], sub], ReplaceAll[a, sub],
ReplaceAll[100 + b, sub],
Sum[Abs[f[T[i]] - G[i]], {i, 1, M}]/M,
Sqrt[Sum[(f[T[i]] - G[i])^2, {i, 1, M}]/M],
plo21[i] =
Plot[f[x], {x, -261, 261}, PlotStyle -> {RGBColor[1, 0, 0]},
PlotRange -> All]; Show[lp, plo21[i]]}]
]
For[i = M0 - 11, i < M0, i++; Print[i];
g = Table[{T0[j], G0[j]}, {j, 1, i}]; M = Length[g];
T[i_] := Extract[Extract[g, i], 1];
G[i_] := Extract[Extract[g, i], 2];
F[x_] = Exp[a + b x] ; sub = FindFit[g, F[x], {a, b}, x];
Print[{f[x_] = ReplaceAll[F[x], sub], ReplaceAll[a, sub],
ReplaceAll[100 + b, sub],
Sum[Abs[f[T[i]] - G[i]], {i, 1, M}]/M,
Sqrt[Sum[(f[T[i]] - G[i])^2, {i, 1, M}]/M],
plo22[i] =
Plot[f[x], {x, -261, 261}, PlotStyle -> {RGBColor[0, 1, 0]},
PlotRange -> All]; Show[lp, plo22[i]]}]
]
For[i = M0 - 11, i < M0, i++; Print[i];
g = Table[{T0[j], G0[j]}, {j, 1, i}]; M = Length[g];
T[i_] := Extract[Extract[g, i], 1];
G[i_] := Extract[Extract[g, i], 2];
F[x_] = 300 a/(100 + .001 b x) ; sub = FindFit[g, F[x], {a, b}, x];
Print[{f[x_] = ReplaceAll[F[x], sub], ReplaceAll[a, sub],
ReplaceAll[100 + b, sub],
Sum[Abs[f[T[i]] - G[i]], {i, 1, M}]/M,
Sqrt[Sum[(f[T[i]] - G[i])^2, {i, 1, M}]/M],
plo23[i] =
Plot[f[x], {x, -261, 261}, PlotStyle -> {RGBColor[0, 0, 1]},
PlotRange -> All]; Show[lp, plo23[i]]}]
]
p23 = Show[lp, Table[plo21[n], {n, M0 - 10, M0}],
Table[plo22[n], {n, M0 - 10, M0}],
Table[plo23[n], {n, M0 - 10, M0}],
PlotRange -> {{-251, 251}, {0, 310}}, AspectRatio -> Automatic,
GridLines -> {{-250, -200, -150, -100, -50, 50, 100, 150, 200,
250}, {50, 100, 150, 200, 250, 300}}]
Latex generator of labels
\documentclass[12pt]{article}
\usepackage{geometry}
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\topmargin -66pt
\oddsidemargin -70pt
\usepackage{hyperref}
\usepackage{graphicx}
\usepackage{rotating}
\newcommand \sx {\scalebox}
\newcommand \be {\begin{eqnarray}}
\newcommand \ee {\end{eqnarray}}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
%\renewcommand{\baselinestretch}{1}
%\setcounter{page}{1}
%\setlength{\textheight}{21.6cm}
%\setlength{\textwidth}{14cm}
%\setlength{\oddsidemargin}{1cm}
%\setlength{\evensidemargin}{1cm}
%\pagestyle{myheadings}
\thispagestyle{empty}
\parindent 0pt
\begin{document}
%\begin{figure}
%\begin{center}
\begin{picture}(400,200)
\put(0,0){\includegraphics{p23}}
\put(6,19){\sx{1.}{\rot{90}{\bf 2014.02.19}\ero}}
\put(42,19){\sx{1.}{\rot{90}{\bf 2014.04.10}\ero}}
\put(77,19){\sx{1.}{\rot{90}{\bf 2014.05.30}\ero}}
\put(114,19){\sx{1.}{\rot{90}{\bf 2014.07.19}\ero}} %
\put(151,19){\sx{1.}{\rot{90}{\bf 2014.09.07}\ero}} %
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\put(220,19){\sx{1.}{\rot{90}{\bf 2014.12.16}\ero}} %
\put(256,19){\sx{1.}{\rot{90}{\bf 2015.02.23}\ero}}
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\put(168,238){\sx{1.1}{$y$}}
%\put(324,163){\sx{1.1}{\rot{-4}$f_{23}(x)$\ero}}
%\put(324,150){\sx{1.1}{\rot{-6}$f_{22}(x)$\ero}}
\put(329,161){\sx{1.1}{\rot{-4}$J(x)$\ero}}
\put(328,142){\sx{1.1}{\rot{-11}$K(x)$\ero}}
\put(328,120){\sx{1.1}{\rot{-16}$L(x)$\ero}}
\put(190,105){\sx{1.2}{experimental}}
\put(204,92){\sx{1.2}{data}}
\put(355,2){\sx{1.1}{$x$}}
\end{picture}
\end{document}
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Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 06:09, 1 December 2018 | 1,527 × 1,004 (232 KB) | Maintenance script (talk | contribs) | Importing image file |
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