Difference between revisions of "File:2014rubleDollar2param.png"

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(Importing image file)
 
 
Line 1: Line 1:
  +
Price of 100 Russian roubles evaluated in the USA cents versus time.
−
Importing image file
  
  +
  +
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==
  +
<poem><nomathjax><nowiki>
  +
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  +
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  +
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  +
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  +
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  +
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  +
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  +
-13 250.70
  +
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  +
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  +
-10 250.70
  +
-9 245.59
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-8 245.59
  +
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-5 243.90
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-4 240.73
  +
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  +
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  +
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  +
0 238.18
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1 235.07
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2 233.92
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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
  +
</nowiki></nomathjax></poem>
  +
==Mathematica generator of lines==
  +
<poem><nomathjax><nowiki>
  +
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}}]
  +
  +
</nowiki></nomathjax></poem>
  +
  +
==Latex generator of labels==
  +
<poem><nomathjax><nowiki>
  +
\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}
  +
</nowiki></nomathjax></poem>
  +
  +
[[Category:Rouble]]
  +
[[Category:Ruble]]
  +
[[Category:Dollar]]
  +
[[Category:Inflation]]
  +
[[Category:Linear approximation]]
  +
[[Category:Mathematica]]
  +
[[Category:Latex]]

Latest revision as of 08:26, 1 December 2018

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


-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}

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