{
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    "# Modelos e Estratégias de Trading\n",
    "## Ajustando um modelo VAR ao Dolar Futuro\n",
    "\n",
    "Uirá Caiado. 05 de Setembro, 2016"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Resumo**\n",
    "\n",
    "*Uma das principais necessidades quando falamos trading é realizar algum tipo de previsão sobre o estado futuro do instrumento operado para que possamos posicionar nossas ofertas. Como um dos objetivos da análise de séries temporais multivariadas é a realização de forecasts, nesta atividade vou implementar um modelo desta classe chamado Vetor Auto Regressivo (VAR). Vou ajustar o modelo às informações de book do DOL.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Introdução\n",
    "\n",
    "Quando operamos, frequentemente preciasamos tomar decisões como manter uma posição ou não, comprar, vender, não fazer nada. Se possuírmos uma série temporal de observações relacionadas à variável de interesse (o instrumento ou spread operado, por exemplo) e se estes dados possuírem informação sobre a dinâmica dela, Lutkepohl afirma que é razoável utilizarmos para a previsão alguma função dos dados já coletados, de maneira que:\n",
    "\n",
    "$$\\hat{y}_{K,\\, T+1} = f \\left( y_{1, T}, y_{2, T}, y_{1, T-1}, \\dots \\right)$$\n",
    "\n",
    "Onde $y_{k, t}$ é uma variável aleatória, onde $t$ denota o índice dela no tempo e $k$, o índice da própria variável. A equação de *forecast* acima implica que pode haver interdependência entre as varíaveis utilizadas. Estas multiplas variáveis podem ser os retornos de diferentes ativos, variáveis macro-econômica e etc.\n",
    "\n",
    "Dado que a série temporal é um conjunto de variáveis aleatórias, assumimos que essa série é gerada por um processo estocástico com um espaço de probabilidade $\\left ( \\Omega, \\, \\mathscr{F}, \\, P \\right )$ associado, onde $\\Omega$ é o espaço amostral, $\\mathscr{F}$ ou $\\sigma-algebra$ representa todos os subconjuntos possíveis de $\\Omega$ e $P$, a medida de probabilidade. Definimos que uma variel aleatória é uma função que associa elementos de um espaço amostral $\\Omega$ a valores no conjunto de números Reais.\n",
    "\n",
    "Assim, assumindo que os nossos dados são realizações de variáveis aleatórias, que a mesma processo gerador de dados prevalece sobre todo o período $T$ (ainda que não conhecido), que funções lineares (nos parâmetros) são relativamente fáceis de lidar, podemos escrever um processo auto regressivo vetorial de forma que:\n",
    "\n",
    "$$y_t = \\upsilon + A_q y_{t-1} +  \\dots + A_p y_{t-p} + u_t$$\n",
    "\n",
    "onde $y_t := \\left( y_{1t}, \\dots, y_{Kt}\\right)'$ é um vetor de variáveis aleatórias, $\\upsilon := \\left( \\upsilon_{t}, \\dots, \\upsilon_{K}\\right)'$ é um vetor de constantes, $A$ é uma matriz quadrada de parâmetros e $u_t = \\left( u_{1t}, \\dots, u_{Kt}\\right)$ é uma sequência dops erros de previsão, tidos como *iid* com média $0$. Segundo notas de aula, isto é equivalente a dizer que toda a informação útil contida no  $\\sigma-algebra$ foi incorporada ao $y_t$ e não existem erros sistemáticos nos *forecasts*.\n",
    "\n",
    "Neste trabalho vou estimar os parâmetros do modelo acima, que também é chamado de modelo de vetor auto regressivo (VAR). Dado que é um AR, é esperado que os dados utilizados como input sejam estacionários (primeiro e segundo momento invariante) e que o modelo produzido seja estável (todos os autovalores de $A$ possuem módulo menor do que 1).\n",
    "\n",
    "Depois vou utilizá-lo para realizar previsões (aqui também referenciados como *forecast*) e estimar os critérios de seleção: erro de predição (FPE), critério de informação de Akaike (AIC), critério de Hannan-Quinn e critério de Schwarz. Por fim, vou ajustar o modelo à alguns dados atuais de mercado."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Implementando o Modelo\n",
    "\n",
    "Nesta sessão vou detalhar o processo de estimação dos parâmetros, *forecast* e o cálculo dos critérios de seleção.\n",
    "\n",
    "### 2.1. Estimando os Parâmetros\n",
    "\n",
    "Dado que o modelo foi descrito como uma relação linear entre as variáveis, podemos estimar os parâmetros do modelo através da minimização dos erros quadrados (de estimação) utilizando o estimador de mínimos quadrados multivariado. Primeiro, assumindo que a série temporal $y_1, ..., y_T$ de tamanho T e \"largura\" K (o número de varipaveis disponíveis), de forma que:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   0         1         2         3         4\n",
      "2014-01-01  0.004082  0.007782  0.033859  0.023865  0.041760\n",
      "2014-01-02  0.012377  0.019575  0.052446  0.056654 -0.010573\n",
      "2014-01-03 -0.006921 -0.011853 -0.005707 -0.017716 -0.019980\n",
      "2014-01-04  0.000579  0.005753 -0.020576 -0.004274 -0.036814\n",
      "2014-01-05  0.001156  0.011407 -0.003350  0.003459  0.000000\n",
      "\n"
     ]
    },
    {
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rrwQR4aGHHsLDDz+Mo0eP4uTJk/jXv/6FEydO9BqzzYYpU6Zg3bp1OHToEPbv34/bb7/d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\nvj95jrdO/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nUu+1Nma25bCWFeKCAGx6GzLLpuRLjFILlwBiGiuIocEF4jVDBSmPSXg3bn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\nBKENAIBHENoAAHgEoQ0AgEf8AAO5OYOoACUgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3b56148ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_excel('data/VAR3_inputs_e_outputs.xlsx', header=None)\n",
    "l_index = pd.date_range(start= '01/01/2014', end='01/12/2016')\n",
    "df.index = l_index[:df.shape[0]]\n",
    "print df.head()\n",
    "print\n",
    "ax = df.plot(legend=False)\n",
    "ax.set_title('Dados Utilizados Para testes\\n', fontsize=16);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_original = df.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Onde as colunas representam $K$ e as linhas, $T$. Também vamos assumir que os dados utilizandos são estacionários (o que realmente parece, olhando para o gráfico). Definindo:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "Y &:= \\left(  y_1, \\dots, y_T \\right)  \\;\\;\\;\\;\\; &\\left(K \\times T \\right)\\\\\n",
    "B &:= \\left(  \\upsilon,\\, A_1 \\dots, A_p \\right)  \\;\\;\\;\\;\\; &\\left(K \\times (Kp + 1) \\right)\\\\\n",
    "Z_t &:= \\left(  1, y_t, \\dots, y_{t-p+1} \\right)'  \\;\\;\\;\\;\\; &\\left(1 \\times (Kp + 1) \\right)\\\\\n",
    "Z &:= \\left(  Z_0, \\dots, Z_T \\right)  \\;\\;\\;\\;\\; &\\left((Kp + 1) \\times T \\right)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Utilizando notação de mtraiz, reescrevemos o var como sendo da forma $Y = B Z + U$, implicando que os residuos são da forma $U = Y - BZ$. Para determinar o estimador de mínimos quadrados (*Econometric Methods with Application in Business and Economics*, pg. 121), escrevemos a soma do quadrado dos resíduos como:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "S(b) &= \\sum U^2 = U'U = \\left( Y - BZ \\right)' \\left( Y - BZ \\right)\\\\\n",
    "     &= Y'Y - Y'BZ - B'Z'Y + B'Z'ZB\\\\\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Como $Y'ZB = B'Z'Y$, podemos reescrever a equação acima como:\n",
    "\n",
    "$$S(b) = Y'Y - 2B'Z'Y + B'Z'ZB$$\n",
    "\n",
    "Derivando em relação a $B$ e igualando a zero, finalmente chegamos que:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "S(b) &= \\sum U^2 = U'U = \\left( Y - BZ \\right)' \\left( Y - BZ \\right)\\\\\n",
    "     &= Y'Y - Y'BZ - B'Z'Y + B'Z'ZB\\\\\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Foi criada uma biblioteca chamada *var_model* no repositório deste arquivo implementando este modelo. Os valores serão comparados com os valores obtidos com implementação deste modelo da biblioteca [*statsmodel*](http://statsmodels.sourceforge.net/), do Python. Vamos começar expondo os valores de matriz $B$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import var_model.vector_autoregression as var\n",
    "reload(var)\n",
    "self = var.VectorAutoregression(df)\n",
    "self.fit(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A1:\n",
      "           0         1         2         3         4\n",
      "0 -0.043374  0.128951 -0.127479  0.049648 -0.071250\n",
      "1  0.005321  0.178780  0.003759  0.032509 -0.072283\n",
      "2  0.008242  0.115180 -0.050708  0.007212 -0.041946\n",
      "3  0.035804  0.166959  0.048654 -0.117873 -0.049864\n",
      "4 -0.064091 -0.059743 -0.097786  0.268141 -0.054190\n",
      "\n",
      "A2:\n",
      "           0         1         2         3         4\n",
      "0  0.013431  0.001495 -0.242662  0.245055 -0.075217\n",
      "1 -0.244118 -0.004717 -0.345717  0.413840 -0.032270\n",
      "2 -0.047898  0.179970 -0.487353  0.295174  0.055272\n",
      "3 -0.043729  0.159101 -0.365092  0.193884  0.068610\n",
      "4 -0.028104  0.096378 -0.391956  0.162951 -0.030571\n",
      "\n",
      "A3:\n",
      "           0         1         2         3         4\n",
      "0 -0.044115  0.015434  0.056729 -0.180469  0.065909\n",
      "1 -0.075600 -0.076008  0.070572  0.017278  0.042417\n",
      "2 -0.110870  0.027031 -0.034428 -0.013438 -0.022812\n",
      "3 -0.040539  0.032051 -0.016870 -0.037124 -0.001811\n",
      "4 -0.046125 -0.081289  0.247950 -0.131097 -0.025088\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# imprime matrizes A\n",
    "import pandas as pd\n",
    "for idx, A in enumerate(self.na_A):\n",
    "    print \"A{}:\\n {}\".format(idx + 1, pd.DataFrame(A))\n",
    "    print \n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O matriz $\\Sigma_U$ foi estimado direto pela definição $\\tilde{\\Sigma}_U = \\mathbf{E} \\left[ u_t u_t '\\right]$, ou seja, calculei a matriz $U = Y - BZ$ e fiz o dot product dela por ela transposta e dividi por T (por causa do operador Esperança). Depois ajustei o resultado pelo grau de liberdade do modelo, de maneira que $\\hat{\\Sigma}_{U} = \\frac{T}{T - Kp -1} \\tilde{\\Sigma}_{U}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sigma_U:\n",
      "           0         1         2         3         4\n",
      "0  0.000195  0.000068  0.000056  0.000077  0.000064\n",
      "1  0.000068  0.000283  0.000154  0.000166  0.000117\n",
      "2  0.000056  0.000154  0.000309  0.000255  0.000126\n",
      "3  0.000077  0.000166  0.000255  0.000267  0.000130\n",
      "4  0.000064  0.000117  0.000126  0.000130  0.000461\n"
     ]
    }
   ],
   "source": [
    "# imprime matriz Sigma_U\n",
    "import pandas as pd\n",
    "print \"Sigma_U:\\n {}\".format(pd.DataFrame(self.na_Sigma))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora vamos comparar estes valores com os valores obtidos pela implementação do *statsmodel*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.tsa.api import VAR\n",
    "import statsmodels.tsa.vector_ar.util as util\n",
    "model = VAR(df)\n",
    "results = model.fit(3)\n",
    "aux = util.get_var_endog(df.values, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "error in Z: 0.00000000\n",
      "error in A: 0.00000000\n",
      "error in B: 0.00000000\n",
      "error in Sigma_U: 0.00000000\n"
     ]
    }
   ],
   "source": [
    "# calcula erros para implementacao do statsmodel\n",
    "print \"error in Z: {:0.8f}\".format(sum(sum(abs(self.na_Z.T - aux))))\n",
    "print \"error in A: {:0.8f}\".format(sum(sum(sum(abs(self.na_A - results.coefs)))))\n",
    "print \"error in B: {:0.8f}\".format(sum(sum(abs(self.na_betahat - results.params.values))))\n",
    "print \"error in Sigma_U: {:0.8f}\".format(sum(sum(abs(self.na_Sigma - results.sigma_u.values))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Como pode-se ver, até a oitava casa decimal, os valores obtidos foram identicos ao obtidos pela biblioteca benchmark."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2. Forecast\n",
    "\n",
    "Segundo notas de aula, para se afirmar o que ocorrerá no futuro $\\left (  y_1, ..., y_k \\right )$, tendo um processo $VAR(p)$ ajustado a um conjunto de dados $\\Omega_t = \\{ y_s \\mid s \\leq t \\}$ para um horizonte de tempo $h$, precisamos determinar qual o *forecast* ótimo determinando aquele que minimiza uma função custo associada à seus erros (quadráticos médios - MSE na sigla em inglês). O preditor que minimiza estes erros é a esperança condicional (Lutkepohl, p. 33)\n",
    "\n",
    "$$\\mathbf{E}\\left [ y_{t+h} \\right ] := \\mathbf{E}\\left [ y_{t+h} \\mid  \\Omega_t \\right ] = \\mathbf{E}\\left [ y_{t+h} \\mid  \\{ y_s \\mid s \\leq t \\} \\right ]$$\n",
    "\n",
    "Lutkepohl ainda demonstra que a otimização da esperança condicional impica que:\n",
    "\n",
    "$$\n",
    "\\mathbf{E}\\left [ y_{t+1} \\right ] = \\upsilon + A_1 y_t + ... + A_p y_{t-p + 1} \\\\\n",
    "\\mathbf{E}\\left [ y_{t+2} \\right ] = \\upsilon + A_1 \\mathbf{E}\\left [ y_{t+1} \\right ] + A_2 y_t + ... + A_p y_{t-p + 2} \\\\\n",
    "\\vdots\n",
    "$$\n",
    "\n",
    "\n",
    "Aplicando este método e comparando com a implementação benchmark, chegamos que:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "my_forecast, my_max, my_min = self.forecast(df[-3:].values, 1)\n",
    "na_forecast = results.forecast_interval(df[-3:].values, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "error in Forecast: 0.00000000\n",
      "\n",
      "0    0.001801\n",
      "1    0.006724\n",
      "2    0.006905\n",
      "3    0.005442\n",
      "4    0.000813\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# previsão para 1 periodo para cada variavel\n",
    "print \"error in Forecast: {:0.8f}\\n\".format((sum(abs(my_forecast - na_forecast[0][0]))))\n",
    "print pd.Series(my_forecast)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3. Intervalo de Confiança\n",
    "\n",
    "Segundo Lutkepohl (p. 38), o erro de previsão (e consequentemente, o intervalo de confiança) pode ser obtido através da matriz de covariância dos erros (ou, da sigla em inglês, MSE matrix). Porém, quando se deseja realizar *forecasts* para mais de um período, é necessário definir também a matriz de coeficientes de Média Móvel (MA), que para um VAR(2) fica:\n",
    "\n",
    "$$\n",
    "\\phi_1 = A_1 \\\\\n",
    "\\phi_2 = \\phi_1 A_1 + A2 \\\\\n",
    "\\phi_3 = \\phi_2 A_1 + \\phi_1 A2 \\\\\n",
    "\\vdots \\\\\n",
    "\\phi_i = \\phi_{i-1} A_1 + \\phi_{i-2} A_2\n",
    "$$\n",
    "\n",
    "Assim, a matriz MSE de *forecast* são obtidas recursivamente aplicando\n",
    "\n",
    "$$\n",
    "\\Gamma_y(0) = \\Sigma_y = \\sum_{i=0}^{\\infty} \\phi_i \\Sigma_u \\phi_i^{'}\n",
    "$$\n",
    "\n",
    "Sendo que:\n",
    "$$\n",
    "\\Sigma_y (1) = \\Sigma_u \\\\\n",
    "\\Sigma_y (2) = \\Sigma_u + \\phi_{1} \\Sigma_u \\phi_{1}' \\\\\n",
    "\\Sigma_y (3) = \\Sigma_y (2) + \\phi_{2} \\Sigma_u \\phi_{2}' \\\\\n",
    "\\vdots\n",
    "$$\n",
    "\n",
    "O $h$ em $\\Sigma_y (h)$ se refere a quantos passos para frente se aplica a função de forecast. Como o modelo de VAR assume que os erros $u_t \\sim N \\left( 0, \\, \\Sigma_y(h) \\right)$, podemos assumir que o erro de *forecast* também é normalmente distribuído. Com este pressuposto, podemos definir um [intervalo de confiança](https://en.wikipedia.org/wiki/Confidence_interval) na forma: \n",
    "$$\\left[ y_{k, \\, t} (h) - z_{(\\alpha / 2)} \\sigma_k (h), \\, \\, \\, \\, \\, y_{k, \\, t} (h) + z_{(\\alpha / 2)} \\sigma_k (h) \\right]$$\n",
    "\n",
    "Onde $\\sigma(h)$ é a raiz quadrada do ** *k-ésimo* elemento da diagonal** $\\Sigma_y(h)$. Assim, seguindo exemplo do livro, se tivermos:\n",
    "$$\n",
    "\\Sigma_y (1) =\n",
    "\\begin{pmatrix}\n",
    "  \\textbf{2.25} & 0 & 0 \\\\\n",
    "  0 & \\textbf{1.0} & .5 \\\\\n",
    "  0 & .5 & \\textbf{.74}\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "\n",
    "Os intervalos de confiança são dados por:\n",
    "\n",
    "$$\n",
    "y_{1, t} (1) \\pm z_{(\\alpha / 2)} \\sqrt{2.25} \\\\\n",
    "y_{2, t} (1) \\pm z_{(\\alpha / 2)} \\sqrt{1.0} \\\\\n",
    "y_{3, t} (1) \\pm z_{(\\alpha / 2)} \\sqrt{.74}\n",
    "$$\n",
    "\n",
    "Assim, vamos calcular os intervalos de confiança para 3 perídos para frente e comparar com a implementação do *benchmark*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import var_model.vector_autoregression as var\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "reload(var)\n",
    "self = var.VectorAutoregression(df)\n",
    "self.fit(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "my_forecast, my_max, my_min = self.forecast(df[-5:].values, 3)\n",
    "na_forecast, na_min, na_max = results.forecast_interval(df[-3:].values, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Erro no limite inferior: 0.0030550\n",
      "Erro no Forecast: 0.0000000\n",
      "Erro no limite superior: 0.0030550\n",
      "\n",
      "\n",
      "\n",
      "                   0         1         2         3         4\n",
      "Minimo                                                      \n",
      "meu modelo -0.030019 -0.035569 -0.037285 -0.034497 -0.046392\n",
      "statsmodel -0.030496 -0.036200 -0.037916 -0.035087 -0.047116\n",
      "\n",
      "                   0         1         2         3         4\n",
      "Maximo                                                      \n",
      "meu modelo  0.026364  0.033363  0.034616  0.032315  0.040077\n",
      "statsmodel  0.026841  0.033994  0.035248  0.032906  0.040801\n"
     ]
    }
   ],
   "source": [
    "print \"Erro no limite inferior: {:0.7f}\".format(sum(abs(na_min[-1] - my_min)))\n",
    "print \"Erro no Forecast: {:0.7f}\".format(sum(abs(na_forecast[-1] - my_forecast)))\n",
    "print \"Erro no limite superior: {:0.7f}\".format(sum(abs(na_max[-1] - my_max)))\n",
    "print '\\n\\n'\n",
    "df_plot = pd.DataFrame([my_min, na_min[-1]], index=['meu modelo', 'statsmodel'])\n",
    "df_plot.index.name = 'Minimo'\n",
    "print str(df_plot)\n",
    "print ''\n",
    "\n",
    "df_plot = pd.DataFrame([my_max, na_max[-1]], index=['meu modelo', 'statsmodel'])\n",
    "df_plot.index.name = 'Maximo'\n",
    "print df_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Apesar do *forecast* ter ficado igual à implementação do *statsmodel*, os intervalos encontrados foram um pouco diferentes. Porém o erro em relação a implementação do *benchmark* foram simétricos, o que sugere que utilizaram um método de estimação diferente do implementado aqui."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4. Selecionando a Ordem do VAR\n",
    "\n",
    "Como visto, além dos dados anteriores, o modelo VAR tem mais uma variável: A ordem do processo auto regressivo. Segundo notas de aula, devemos escolher esta ordem de maneira que as projeções tenham a melhor precisão (ou o menor erro quadrático médio). Lutkepohl argumenta que não há uma única maneira de se fazer isso. Uma opção, por exemplo, é utilizar o critério de erro de predição final (FPE), definido como:\n",
    "\n",
    "$$FPE(m) = \\left[ \\frac{T + Km + 1}{T - Km -1} \\right]^{K} \\left |  \\Sigma_u(m) \\right | $$\n",
    "\n",
    "Onde $\\left |  . \\right |$ é o determinante e $m$ a ordem testada (p. 147, Lutkepohl). Outro critério é O Critério de informação de Akaike (AIC), definido como:\n",
    "\n",
    "$$AIC(m) = \\ln \\left |  \\Sigma_u(m) \\right | + \\frac{2mK^2}{T}$$\n",
    "\n",
    "Uma terceira opção é o Critério de Hannan-Quinn, que possui propriedades amostrais interessantes (consistência, neste caso). Ele é da forma:\n",
    "\n",
    "$$HQ(m) = \\ln \\left |  \\Sigma_u(m) \\right | + \\frac{2\\ln \\ln T}{T}mK^2$$\n",
    "\n",
    "A última opção implementada será outro com a mesma propriedade assintótica do critério anterior. O critério de Schwarz (SC ou BIC), é da forma:\n",
    "\n",
    "$$SC(m) = BIC(m) = \\ln \\left |  \\Sigma_u(m) \\right | + \\frac{\\ln T}{T}mK^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import var_model.vector_autoregression as var; reload(var)\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "self = var.VectorAutoregression(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ordem com menor valor para cada Critério:\n",
      "  Critério FPE:  \t\tOrd. 1\n",
      "  Critério AIC:  \t\tOrd. 1\n",
      "  Critério HQ:  \t\tOrd. 1\n",
      "  Critério SC(BIC):  \t\tOrd. 1\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "           AIC  FPE       HQ  SC(BIC)\n",
      "Ordem                                \n",
      "1     -42.6786  0.0 -42.5111 -42.2648\n",
      "2     -42.5899  0.0 -42.2538 -41.7596\n",
      "3     -42.2861  0.0 -41.7801 -41.0361\n",
      "4     -42.0422  0.0 -41.3651 -40.3697\n",
      "5     -41.7619  0.0 -40.9124 -39.6638\n",
      "6     -41.5320  0.0 -40.5089 -39.0053\n",
      "7     -41.2570  0.0 -40.0589 -38.2986\n",
      "8     -40.9928  0.0 -39.6185 -37.5996\n",
      "9     -40.7496  0.0 -39.1978 -36.9184\n",
      "10    -40.4579  0.0 -38.7272 -36.1855\n"
     ]
    }
   ],
   "source": [
    "self.select_order(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 3. Aplicando o modelo VAR\n",
    "\n",
    "Nesta seção vamos tentar aplicar o modelo à dado de alta frequência de Dolar Futuro. Os dados serão agrupados em intervalores de 10 segundos e, ao invés de ajustar o modelo aos retornos, o modelo será aplicado à primeira diferença das variáveis selecionadas.\n",
    "\n",
    "### 3.1. Order Flow Imbalance\n",
    "\n",
    "Cont at all argumenta que os eventos do book - ordens a mercado, ordens limite e cancelamentos - impactam na dinâmica do preço do ativo e que este impacto pode ser modelado através de uma única variável: o *order flow imbalance* (OFI), que representa o *net* de quantidade que entrou e saiu das filas do bid e do ask. Assim, para cada evento $e_n$ no Book de ofertas:\n",
    "\n",
    "$$e_n = \\mathbb{1}_{P_{n}^{B} \\geq P_{n-1}^{B}} q^{B}_{n} - \\mathbb{1}_{P_{n}^{B} \\leq P_{n-1}^{B}}  q^{B}_{n-1} - \\mathbb{1}_{P_{n}^{A} \\leq P_{n-1}^{A}} q^{A}_{n} + \\mathbb{1}_{P_{n}^{A} \\geq P_{n-1}^{A}}  q^{A}_{n-1}$$\n",
    "\n",
    "Onde $q^{B}_{n}$, $q^{A}_{n}$ se refere a quantidade no melhor preço no Bid e no Ask, respectivamente no período atual $n$. O subscrito $n-1$ se refere ao estado anterior. $\\mathbb{1}$ é uma função [Indicadora](https://en.wikipedia.org/wiki/Indicator_function). Como os eventos que afetam o book acontecem em tempos $\\tau_n$ aleatórios, definimos $N(t) = \\max \\{ n \\mid \\tau_n \\leq t \\}$ o número de eventos que ocorreram entre $\\left [ 0, \\, t\\right ]$. A variável OFI é definida sobre o intervalo $\\left [ t_{k-1}, \\, t_k\\right ]$ e é a soma de cada $e_n$ que ocorreu neste período, de maneira que:\n",
    "\n",
    "$$OFI_k = \\sum^{N(t_k)}_{n=N(t_{k-1})+1} e_n$$\n",
    "\n",
    "Eles alegam que esta variável consegue explicar utilizando uma relação linear simples a mudança no mid-price em curtos espaços de tempo. A intuição, segundo eles, é que \"precisa de volume para movimentar o preço\". A mudança no mid-price, no estudo deles, é definido em ticks. Assim:\n",
    "\n",
    "$$\\Delta P_k = \\frac{\\left( P_k - P_{k-1}\\right)}{\\delta}$$\n",
    "\n",
    "Onde $\\delta$ é o tamanho do tick do instrumento analisado."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2. Computando o OFI do DOL\n",
    "\n",
    "Vamos começar computando o OFI para dois dias de [dados de Nível I](http://www.investopedia.com/terms/l/level1.asp) do book do contrato DOLV16. Primeiro, vamos checar o tamnho do arquivo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import var_model.vector_autoregression as var; reload(var)\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20160913_dol.txt:\t756,137 rows\t24.60 MB\n",
      "CPU times: user 2.14 s, sys: 0 ns, total: 2.14 s\n",
      "Wall time: 2.14 s\n"
     ]
    }
   ],
   "source": [
    "import zipfile\n",
    "s_fname = \"data/20160913_dol.zip\"\n",
    "archive = zipfile.ZipFile(s_fname, 'r')\n",
    "def foo():\n",
    "    f_total = 0.\n",
    "    f_tot_rows = 0.\n",
    "    for i, x in enumerate(archive.infolist()):\n",
    "        f_total += x.file_size/ 1024.**2\n",
    "        for num_rows, row in enumerate(archive.open(x)):\n",
    "            f_tot_rows += 1\n",
    "        print \"{}:\\t{:,.0f} rows\\t{:0.2f} MB\".format(x.filename, num_rows + 1, x.file_size/ 1024.**2)\n",
    "\n",
    "%time foo()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora, vamos calcula linha por linha o valor do $e_n$ e acumulá-lo por 10 segundos. Cada vez que passar deste tempo, vou imprimir o dado acumulado em um novo arquivo e zerar os valores. Também vou parear estes dados com a mudança no mid-price do ativo, já noromalizado pelo tick-size (de meio ponto). Também vou guardar o log retorno nestes 10 segundos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def measure_e_n(row, last_best):\n",
    "    '''\n",
    "    Measure the e_n of the current event\n",
    "    :param row: dictionary. current row from the file\n",
    "    :param last_best: tuple. best price and best quantity\n",
    "    '''\n",
    "    e_n = 0\n",
    "    if row['Type'] == 'BID':\n",
    "        e_n += (row['Price'] >= last_best[0]) * row['Size']\n",
    "        e_n -= (row['Price'] <= last_best[0]) * last_best[1]\n",
    "    elif row['Type'] == 'ASK':\n",
    "        e_n -= (row['Price'] <= last_best[0]) * row['Size']\n",
    "        e_n += (row['Price'] >= last_best[0]) * last_best[1]\n",
    "    return e_n\n",
    "\n",
    "def convert_float_to_time(f_time):\n",
    "    '''\n",
    "    Converst number of seconds in string time format\n",
    "    '''\n",
    "    i_hour = int(f_time / 3600)\n",
    "    i_minute = int((f_time - i_hour * 3600) / 60)\n",
    "    i_seconds = int((f_time - i_hour * 3600 - i_minute *60 ))\n",
    "    return '{:02d}:{:02d}:{:02d}'.format(i_hour, i_minute, i_seconds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 591,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tempo para processar: 19.56 s\n"
     ]
    }
   ],
   "source": [
    "import zipfile\n",
    "import csv\n",
    "import time\n",
    "f_start = time.time()\n",
    "s_fname = \"data/20160913_dol.zip\"\n",
    "fw_out = open('data/ofi_dol.txt', 'w')\n",
    "fw_out.write('TIME\\tOFI\\tDELTA_MID\\tLOG_RET\\n')\n",
    "archive = zipfile.ZipFile(s_fname, 'r')\n",
    "f_total = 0.\n",
    "f_tot_rows = 0.\n",
    "d_best_price = {'BID': (0., 0.), 'ASK': (0., 0.)}\n",
    "f_min_time = 10.  # em segundos\n",
    "for i, x in enumerate(archive.infolist()):\n",
    "    # le cada arquivo dentro do arquivo zip (neste caso, ha apenas 1 arquivo)\n",
    "    f_ofi = 0.\n",
    "    f_mid = None\n",
    "    f_next_time = 9 * 3600 + f_min_time\n",
    "    for idx_row, row in enumerate(csv.DictReader(archive.open(x), delimiter='\\t')):\n",
    "        if idx_row == 0:\n",
    "            f_first_price = row['Price']\n",
    "        # nao preciso lidar com os trades, pois jah esta refletido no bid e ask\n",
    "        if row['Type'] in ['BID', 'ASK']:\n",
    "            # converte string para float\n",
    "            row['Price'] = float(row['Price'].replace(',', '.')) \n",
    "            row['Size'] = float(row['Size'])\n",
    "            f_current_time = sum([float(x)*60**(2.-i_aux)  for i_aux, x in enumerate(row['Date'][-8:].split(\":\"))])\n",
    "            if f_current_time > f_next_time:\n",
    "                # imprime resultado\n",
    "                s_time = convert_float_to_time(f_next_time)\n",
    "                f_change = 0\n",
    "                f_logrtn = 0.\n",
    "                if f_mid:\n",
    "                    f_curent_mid = (d_best_price['ASK'][0] + d_best_price['BID'][0])/2.\n",
    "                    f_change = int((f_curent_mid - f_mid)/0.5)\n",
    "                    f_logrtn = np.log((f_curent_mid/f_mid))\n",
    "                f_mid = (d_best_price['ASK'][0] + d_best_price['BID'][0])/2.\n",
    "                s_out = '{}\\t{}\\t{}\\t{}\\n'.format(s_time, f_ofi, f_change, f_logrtn)              \n",
    "                fw_out.write(s_out)\n",
    "                # zera valor\n",
    "                f_ofi = 0\n",
    "                 # imprime de 10 em 10 s\n",
    "                f_next_time  = (int(f_current_time/f_min_time) + 1)*f_min_time\n",
    "            elif abs(f_current_time - f_next_time) > 3600:\n",
    "                # new day\n",
    "                f_next_time = 9 * 3600\n",
    "                f_mid = None\n",
    "                f_ofi = 0\n",
    "            # compara com valor anterior\n",
    "            last_best = d_best_price[row['Type']]\n",
    "            f_e_n = measure_e_n(row, last_best)\n",
    "            # atualiza last best\n",
    "            d_best_price[row['Type']] = (row['Price'], row['Size'])\n",
    "            row['Date'] = row['Date'][-8:]\n",
    "            f_ofi += f_e_n\n",
    "            \n",
    "            \n",
    "             \n",
    "    \n",
    "print 'Tempo para processar: {:0.2f} s'.format(time.time() - f_start)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos dar uma olhada em como ficaram os dados"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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IiIjsx+ZV2goLC9He3g61Wo3jx4/jySefBND7ST4/Px8LFy7sE9gGgwG+vr5QKBQwGAzm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114a71bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_csv('data/ofi_dol.txt', sep='\\t')\n",
    "df.drop('TIME', axis=1, inplace=True)\n",
    "df.dropna(inplace=True)\n",
    "ax = df[['OFI', 'DELTA_MID']].hist(bins=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parece que temos alguns outliers. Vamos excluir os pontos mais extremos. Para classificar estes pontos, vou calcular o valor entre os percentis 1 e 90 e checar quais pontos ficam fora de 1.5 vezes este intervalo além dos percentis citados."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Número de ponto de dados considerado outlier para a variável\n",
      "\n",
      "OFI               \t2                 \n",
      "DELTA_MID         \t6                 \n",
      "LOG_RET           \t4                 \n",
      "-------------------------\n",
      "TOTAL: Outliers: 12 | Outliers Únicos: 7\n",
      "\n",
      "\n",
      "Pontos considerados outliers:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>OFI</th>\n",
       "      <th>DELTA_MID</th>\n",
       "      <th>LOG_RET</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3176</th>\n",
       "      <td>265.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0.005345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>835.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.001204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>655.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.001428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4782</th>\n",
       "      <td>1395.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.001122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6036</th>\n",
       "      <td>1025.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0.001875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1881</th>\n",
       "      <td>-2380.0</td>\n",
       "      <td>-14.0</td>\n",
       "      <td>-0.002128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3132</th>\n",
       "      <td>675.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.001302</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         OFI  DELTA_MID   LOG_RET\n",
       "3176   265.0       35.0  0.005345\n",
       "10     835.0        8.0  0.001204\n",
       "11     655.0        9.0  0.001428\n",
       "4782  1395.0        7.0  0.001122\n",
       "6036  1025.0       12.0  0.001875\n",
       "1881 -2380.0      -14.0 -0.002128\n",
       "3132   675.0        8.0  0.001302"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "# Para cada colouna, acha valores extremos maximos e minimos\n",
    "d_unique_idx = dict()\n",
    "d_iqr = {}\n",
    "print u\"Número de ponto de dados considerado outlier para a variável\\n\"\n",
    "for feature in df.keys():\n",
    "    \n",
    "    # Calculate Q1 (25th percentile of the data) for the given feature\n",
    "    Q1 = np.percentile(df[feature], 1)\n",
    "    \n",
    "    # Calculate Q3 (75th percentile of the data) for the given feature\n",
    "    Q3 = np.percentile(df[feature], 90)\n",
    "    \n",
    "    # calcula intervalo interquartil e calcula o tamanho para ser outlier\n",
    "    d_iqr[feature] = (Q3-Q1)\n",
    "    step = 1.5*(Q3-Q1)\n",
    "    \n",
    "    # Mostra outliers\n",
    "    df_out_lier = df[~((df[feature] >= Q1 - step) & (df[feature] <= Q3 + step))]\n",
    "    i_nfeatures = df_out_lier.shape[0]\n",
    "    print \"{:18s}\\t{:18s}\".format(feature, str(i_nfeatures))\n",
    "    for x in df_out_lier.index:\n",
    "        if x not in d_unique_idx.keys():\n",
    "            d_unique_idx[x] = 1\n",
    "        else:\n",
    "            d_unique_idx[x] += 1\n",
    "\n",
    "print \"-------------------------\"\n",
    "print u\"TOTAL: Outliers: {} | Outliers Únicos: {}\".format(sum(d_unique_idx.values()),\n",
    "                                                          len(d_unique_idx.keys()))\n",
    "# filtra dados considerados outliers\n",
    "print u\"\\n\\nPontos considerados outliers:\"\n",
    "df.ix[d_unique_idx.keys(), :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora, vamos plotar o scatter plot dos dados sem os pontos acima"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df2 = df.loc[[x for x in df.index if x not in d_unique_idx.keys()]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2G7qm43M4aezuSjSuKUocHvZ3d+A1nOg2G3abjYPxbhZYZmKWY1nELQvDZsOw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1178e9f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.lmplot(x=\"OFI\", y=\"DELTA_MID\", data=df2, markers=[\"x\"], palette=\"Set2\", size=4, aspect=1.5)\n",
    "ax.ax.set_title(u'Relação entre o $\\Delta Mid$ e o $OFI$\\n', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como era esperado, há uma relação linear clara entre o volume que entrou ou saiu do book e a mudança de prço do ativo, quando considerado um intervalo curto de tempo. Na próxima seção, vou usar esta variável para tentar melhorar o resultado do modelo VAR para fazer *forecast* do retorno do DOLV16."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3. Ajustando um modelo VAR aos dados calculados"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primeiro, é necessário checar se as variáveis são estacionárias. Porém, faremos isso apenas visualmente aqui. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7/bXdeafvy8o8CAA+K8/BDYPmuW/HRAb27t0LkUiEEydOoLCwEKtXr8Y///lP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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1044f7ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "df_plot = df2.unstack().reset_index()\n",
    "df_plot.drop('level_1', axis=1, inplace=True)\n",
    "df_plot.columns = ['Variable', 'Value']\n",
    "g = sns.FacetGrid(df_plot, col=\"Variable\", sharey=False,  size=4, aspect=1.2)\n",
    "g = g.map(plt.plot, \"Value\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "A média parece ser constante, já o desvio padrão não deve ser. Note também que todas as variáveis tem escala diferente. Agora, vamos ver qual a melhor ordem de VAR se ajusta a estes dados (desconsiderando o log retorno)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df3 = df2.copy()\n",
    "# df3/=pd.Series(d_iqr)\n",
    "# df3['OFI'] /= d_iqr['OFI']  # normaliza valores de OFI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ordem com menor valor para cada Critério:\n",
      "  Critério FPE:  \t\tOrd. 16\n",
      "  Critério AIC:  \t\tOrd. 16\n",
      "  Critério HQ:  \t\tOrd. 6\n",
      "  Critério SC(BIC):  \t\tOrd. 1\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "          AIC     FPE      HQ  SC(BIC)\n",
      "Ordem                                 \n",
      "1      9.2636  1.6930  9.2651   9.2680\n",
      "2      9.2636  1.6927  9.2666   9.2723\n",
      "3      9.2573  1.6818  9.2618   9.2703\n",
      "4      9.2544  1.6766  9.2604   9.2717\n",
      "5      9.2504  1.6697  9.2579   9.2720\n",
      "6      9.2487  1.6666  9.2577   9.2747\n",
      "7      9.2489  1.6667  9.2594   9.2792\n",
      "8      9.2494  1.6672  9.2614   9.2840\n",
      "9      9.2497  1.6675  9.2633   9.2887\n",
      "10     9.2501  1.6679  9.2651   9.2934\n",
      "11     9.2498  1.6671  9.2663   9.2975\n",
      "12     9.2499  1.6669  9.2679   9.3018\n",
      "13     9.2487  1.6647  9.2682   9.3050\n",
      "14     9.2502  1.6669  9.2712   9.3108\n",
      "15     9.2482  1.6634  9.2708   9.3132\n",
      "16     9.2459  1.6593  9.2700   9.3153\n",
      "17     9.2479  1.6623  9.2734   9.3216\n",
      "18     9.2482  1.6625  9.2752   9.3262\n"
     ]
    }
   ],
   "source": [
    "import var_model.vector_autoregression as var; reload(var)\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "self = var.VectorAutoregression(pd.DataFrame(df3[['OFI', 'DELTA_MID']]))\n",
    "self.select_order(18)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Os critérios indicaram ordens diferentes. Vamos ver como ficam as projeções com um modelo de ordem 16, inicialmente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "reload(var)\n",
    "\n",
    "def measure_on_data(i_var_order, l_col):\n",
    "    var_6 = var.VectorAutoregression(df3[l_col])\n",
    "    var_6.fit(i_var_order)\n",
    "    l_rtn = []\n",
    "#     f_val = float(f_first_price.replace(',', '.'))\n",
    "    f_val = 0\n",
    "    df4 = df3[l_col].reset_index(drop=True)\n",
    "    l_label = df4.columns\n",
    "    for i_idx in xrange(i_var_order, df4.shape[0]):\n",
    "        na_y = df4.ix[(i_idx-i_var_order):i_idx-1, :].values\n",
    "        na_rtn, na_max, na_min= var_6.forecast(na_y, 1)\n",
    "        na_yr = df4.ix[i_idx, :]\n",
    "\n",
    "        d_aux = {'ID': i_idx}\n",
    "        for x in xrange(len(l_label)):\n",
    "            d_aux[l_label[x] + '_OBSV'] = na_yr[x]\n",
    "            d_aux[l_label[x] + '_FORC'] = na_rtn[x]\n",
    "            d_aux[l_label[x] + '_MAX'] = na_max[x]\n",
    "            d_aux[l_label[x] + '_MIN'] = na_min[x]\n",
    "\n",
    "        l_rtn.append(d_aux)\n",
    "\n",
    "    df_test = pd.DataFrame(l_rtn)\n",
    "    df_test.index = df_test['ID']\n",
    "    df_test.drop('ID', axis=1, inplace=True)\n",
    "    \n",
    "    return df_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mtnZLRRnu90/AWjcp4cXQZI9V2rmcvxs6lb1wsnN8U6OKMsQOL8wzy4Y8hUoB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\nEARBEAXI/wdKYPJDd+ccSQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117b091d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_test = measure_on_data(16, l_col=['OFI'])\n",
    "ax = df_test.plot(alpha=0.7)\n",
    "ax.set_title(u'Comparação entre Valor real do $OFI$ e projetado\\n', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Note que o valor projetado ($OFI\\_FORC$) ficou distante do observado. Assim, ao invés de olharmos para o valor projetado, vamos nos concentrar no sinal dos valores e checar se a projeção apontou para o mesmo lado do realizado. Abaixo vou plotar o percentual de vezes que o modelo acertou o lado de mercado, ajustando várias um VAR de diferentes ordens há combinaçòes de variáveis diferentes. O objetivo é sempre prever a primeira variável de cada linha, de acordo com a legenda."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 658,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DPA3GtPhz2zTw9+/fj+zsbADAwIEDUVtbC7PZjPDwcAAAEYGIAtYLNo0xxhhr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\nS+99+oMHD9Y6TlNhUgk/X+r3QghhVtRqNS+//HKV9/k7d+7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3b56048450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = None\n",
    "for l_col in [['LOG_RET'], ['OFI'], ['DELTA_MID'], ['LOG_RET', 'OFI'], ['DELTA_MID', 'OFI']]:\n",
    "    d_rtn = {}\n",
    "    l_orders_to_test = [1, 6, 16, 30, 90]  # 10 seg, 40 seg, 2 min e 40 seg, 5 min, 15 min\n",
    "    for i_ord in l_orders_to_test:\n",
    "        df_test = measure_on_data(i_ord, l_col=l_col)\n",
    "        d_rtn[i_ord] = ((df_test[l_col[0] + '_FORC'] / df_test[l_col[0] + '_OBSV'])>=0).sum() * 1. / df_test.shape[0]\n",
    "\n",
    "    if not ax:\n",
    "        ax = pd.Series(d_rtn).plot(ax=ax, label = str(l_col)[1:-1])\n",
    "    else:\n",
    "        pd.Series(d_rtn).plot(label = str(l_col)[1:-1])\n",
    "ax.set_title(u'Observação e Forecast\\ncom Mesmo Sinal', fontsize=16)\n",
    "ax.legend(loc='lower right')\n",
    "ax.set_xlabel('Ordem do Modelo')\n",
    "ax.set_ylabel('Percentual');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Quando um modelo VAR foi ajustado apenas à uma variável, o que melhor se saiu em ordens baixas foi o ajustado para prever o OFI, acertando o da próxima observação desta variável em pouco mais de 50% das vezes. Porém, quando aumentamos a ordem do modelo, os modelos ajustados ao log retorno e ao delta-mid  superarm o modelo ajustado apenas ao OFI. Já quando usamos mais de uma variável, os modelos utilizando o OFI e o mid-price ou o OFI e o log-retorno apresentaram desempenho semelhante em modelos de ordem até 50, chegando perto de acertarem a direção do mercado em quase 55% das vezes. Porém, em ordens mais altas, o modelo que utilizou o OFI e o delta-mid foi o que melhor se saiu, superando 55% de acerto."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## 4. Conclusão\n",
    "\n",
    "Os testes com modelo VAR utilizando as variáveis propostas para dados de alta frequência indicaram ele é pouco adequado se for necessários fazer *forecasts* precisos. Porém, ao considerarmos a direção do sinal dado pelo modelo, os resultados sugerem que este pode ser uma ferramenta útil no contexto de *trading*.\n",
    "\n",
    "\n",
    "## 5. Últimas Considerações\n",
    "\n",
    "Seria interessante realizar um back-test com os modelos criados e tentar agregar mais variáveis para tentar melhorar o percentual de acerto deles.\n",
    "\n",
    "## Referências\n",
    "\n",
    "1. H. Lütkepohl.  *New Introduction to Multiple Time Series Analysis*. Springer-Verlag, 2005. [*link*](http://www.springer.com/br/book/9783540401728)\n",
    "2. Heij, C. and de Boer, P. and Franses, P.H. and Kloek, T. and van Dijk, H.K. and Rotterdam.  *Econometric Methods with Applications in Business and Economics*. OUP Oxford, 2004. [*link*](https://books.google.com.br/books?id=hp4vQZZHfbUC)\n",
    "3. Cont, R. and Kukanov, A. and Stoikov.  *The Price Impact of Order Book Events*. Journal Of Financial Econometrics, 2014. [*link*](http://ssrn.com/abstract=1712822)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Style notebook and change matplotlib defaults*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "\n",
       "\n",
       "\n",
       "<style>\n",
       "    table {\n",
       "        overflow:hidden;\n",
       "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        font-size: 12px;\n",
       "        margin: 10px;\n",
       "        width: 480px;\n",
       "        text-align: left;\n",
       "        border-collapse: collapse;\n",
       "        border: 1px solid #d3d3d3;\n",
       "        -moz-border-radius:5px; FF1+;\n",
       "        -webkit-border-radius:5px; Saf3-4;\n",
       "        border-radius:5px;\n",
       "        -moz-box-shadow: 0 0 4px rgba(0, 0, 0, 0.01);\n",
       "    }\n",
       "    th\n",
       "    {\n",
       "        padding: 12px 17px 12px 17px;\n",
       "        font-weight: normal;\n",
       "        font-size: 14px;\n",
       "        border-bottom: 1px dashed #69c;\n",
       "    }\n",
       "\n",
       "    td\n",
       "    {\n",
       "        padding: 7px 17px 7px 17px;\n",
       "\n",
       "    }\n",
       "\n",
       "    tbody tr:hover th\n",
       "    {\n",
       "\n",
       "        background:  #E9E9E9;\n",
       "    }\n",
       "\n",
       "    tbody tr:hover td\n",
       "    {\n",
       "\n",
       "        background:  #E9E9E9;\n",
       "    }\n",
       "\n",
       "</style>\n",
       "\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#loading style sheet\n",
    "from IPython.core.display import HTML\n",
    "HTML(open('ipython_style.css').read())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#changing matplotlib defaults\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "sns.set_palette(\"deep\", desat=.6)\n",
    "sns.set_context(rc={\"figure.figsize\": (8, 4)})\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_palette(sns.color_palette(\"Set2\", 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}