File:2014rubleDollar2param.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

$K(x)=a \exp(-b x)$

$J(x)=a / (1+b x)$

Input file
-249 279.71 -248 281.64 -247 281.64 -246 281.64 -245 281.56 -244 280.07 -243 277.50 -242 277.78 -241 277.42 -240 277.92 -239 277.92 -238 273.87 -237 277.56 -236 277.34 -235 276.41 -234 274.84 -233 274.70 -232 274.70 -231 274.96 -230 274.41 -229 274.21 -228 273.46 -227 273.50 -226 273.10 -225 273.10 -224 276.18 -223 275.95 -222 276.33 -221 275.48 -220 275.90 -219 275.87 -218 275.87 -217 277.05 -216 281.55 -215 281.57 -214 280.78 -213 279.70 -212 279.44 -211 279.44 -210 284.44 -209 285.47 -208 282.07 -207 281.18 -206 283.19 -205 283.17 -204 283.09 -203 281.18 -202 280.30 -201 281.15 -200 281.16 -199 279.74 -198 279.71 -197 279.71 -196 278.24 -195 275.87 -194 277.52 -193 282.08 -192 281.08 -191 280.70 -190 280.89 -189 280.41 -188 280.32 -187 280.15 -186 279.90 -185 277.65 -184 277.51 -183 277.62 -182 278.74 -181 280.71 -180 280.92 -179 280.99 -178 279.16 -177 278.93 -176 278.93 -175 280.37 -174 282.18 -173 278.41 -172 285.43 -171 284.06 -170 283.97 -169 283.97 -168 285.71 -167 286.95 -166 288.73 -165 287.71 -164 287.52 -163 287.67 -162 287.67 -161 289.47 -160 289.79 -159 291.33 -158 291.52 -157 293.12 -156 293.10 -155 293.10 -154 292.65 -153 290.65 -152 289.75 -151 288.28 -150 286.59 -149 286.60 -148 286.60 -147 285.36 -146 285.10 -145 285.95 -144 288.23 -143 290.64 -142 290.62 -141 290.62 -140 291.24 -139 291.63 -138 291.08 -137 291.17 -136 290.78 -135 290.74 -134 290.74 -133 289.00 -132 287.27 -131 290.23 -130 290.55 -129 290.07 -128 290.17 -127 290.17 -126 293.33 -125 295.93 -124 296.41 -123 297.31 -122 296.36 -121 296.34 -120 296.34 -119 296.54 -118 294.24 -117 291.08 -116 291.51 -115 291.50 -114 290.66 -113 290.66 -112 290.80 -111 290.42 -110 292.13 -109 294.83 -108 294.01 -107 293.12 -106 293.12 -105 292.40 -104 291.16 -103 290.70 -102 289.97 -101 283.56 -100 284.43 -99 283.14 -98 283.14 -97 284.33 -96 285.84 -95 286.70 -94 285.03 -93 284.67 -92 284.67 -91 284.78 -90 281.22 -89 279.23 -88 281.23 -87 279.89 -86 279.69 -85 279.69 -84 279.63 -83 279.08 -82 277.01 -81 276.44 -80 275.02 -79 276.63 -78 276.63 -77 276.63 -76 278.19 -75 276.14 -74 277.44 -73 277.55 -72 276.80 -71 276.80 -70 276.90 -69 277.15 -68 276.38 -67 274.97 -66 277.41 -65 276.91 -64 276.91 -63 276.69 -62 276.66 -61 276.51 -60 278.26 -59 272.08 -58 269.77 -57 269.77 -56 269.85 -55 267.89 -54 267.00 -53 271.69 -52 270.57 -51 270.67 -50 270.67 -49 270.45 -48 269.93 -47 269.59 -46 268.02 -45 266.44 -44 264.65 -43 264.65 -42 264.59 -41 261.08 -40 260.85 -39 260.19 -38 259.89 -37 260.18 -36 260.18 -35 260.20 -34 258.19 -33 259.19 -32 261.74 -31 259.78 -30 255.41 -29 255.41 -28 255.47 -27 253.60 -26 251.98 -25 252.71 -24 252.71 -23 252.71 -22 250.12 -21 250.16 -20 250.70 -19 250.70 -18 250.70 -17 250.70 -16 250.70 -15 250.70 -14 250.70 -13 250.70 -12 250.70 -11 250.70 -10 250.70 -9 245.59  -8 245.59  -7 244.29  -6 244.08  -5 243.90  -4 240.73  -3 238.51  -2 238.69  -1 238.69   0 238.18   1 235.07   2 233.92   3 230.48   4 236.57   5 232.41   6 232.41   7 230.63   8 229.33   9 224.56  10 220.42  11 208.61  12 214.13  13 214.54  14 218.75  15 216.71  16 215.48  17 216.06  18 210.84  19 211.21  20 211.68  21 211.00  22 214.45  23 212.92  24 214.27  25 219.87  26 218.47  27 218.47  28 225.32  29 220.79  30 214.30  31 209.51  32 202.55  33 199.15  34 199.15  35 191.10  36 195.33  37 182.72  38 189.91  39 186.14  40 189.83  41 189.83  42 187.19  43 184.48  44 184.11  45 181.95  46 174.51  47 171.89  48 171.89  49 171.08  50 152.41  51 146.39  52 165.41  53 165.88  54 169.84  55 169.84  56 176.53  57 182.76  58 183.13  59 190.59  60 195.90  61 195.89  62 195.89  63 195.89  64 173.54  65 173.57  66 165.16  67 163.92  68 170.27  69 170.27  70 171.73  71 159.74  72 157.38  73 163.57

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} \paperwidth 368pt \paperheight 242pt \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}} % \put(185,19){\sx{1.}{\rot{90}{\bf 2014.10.27}\ero}} % \put(220,19){\sx{1.}{\rot{90}{\bf 2014.12.16}\ero}} % \put(256,19){\sx{1.}{\rot{90}{\bf 2015.02.23}\ero}} \put(292,19){\sx{1.}{\rot{90}{\bf 2015.04.13}\ero}} \put(328,19){\sx{1.}{\rot{90}{\bf 2015.05.15}\ero}} \put(364,19){\sx{1.}{\rot{90}{\bf 2015.07.04}\ero}} \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}