ml-finance-python
python scripts for finance machine learning
git clone https://9o.is/git/ml-finance-python.git
Trend models.ipynb
(294822B)
1 {
2 "cells": [
3 {
4 "cell_type": "markdown",
5 "metadata": {},
6 "source": [
7 "# Trends\n",
8 "By Evgenia \"Jenny\" Nitishinskaya and Delaney Granizo-Mackenzie\n",
9 "\n",
10 "Notebook released under the Creative Commons Attribution 4.0 License.\n",
11 "\n",
12 "---\n",
13 "\n",
14 "Trends estimate tendencies in data over time, such as overall rising or falling amid noise. They use only historical data and not any knowledge about the processes generating them.\n",
15 "\n",
16 "# Linear trend models\n",
17 "\n",
18 "A linear trend model assumes that the variable changes at a constant rate with time, and attempts to find a line of best fit. We want to find coefficients $b_0$, $b_1$ such that the series $y_t$ satisfies\n",
19 "$$ y_t = b_0 + b_1t + \\epsilon_t $$\n",
20 "and so that the sum of the squares of the errors $\\epsilon_t$ is minimized. This can be done using a linear regression. After we have fitted a linear model to our data, we predict the value of the variable to be $y_t = b_0 + b_1 t$ for future time periods $t$. We can also use these parameters to compare the rates of growth or decay of two data series.\n",
21 "\n",
22 "Let's find a linear trend model for the price of XLY, an ETF for consumer goods."
23 ]
24 },
25 {
26 "cell_type": "code",
27 "execution_count": null,
28 "metadata": {
29 "collapsed": true
30 },
31 "outputs": [],
32 "source": [
33 "import numpy as np\n",
34 "import math\n",
35 "from statsmodels import regression\n",
36 "import statsmodels.api as sm\n",
37 "import matplotlib.pyplot as plt"
38 ]
39 },
40 {
41 "cell_type": "code",
42 "execution_count": 227,
43 "metadata": {
44 "collapsed": false,
45 "scrolled": false
46 },
47 "outputs": [
48 {
49 "name": "stderr",
50 "output_type": "stream",
51 "text": [
52 "[2015-06-17 18:33:54.852354] DEBUG: root: Enter SimpleTable.data2rows.\n",
53 "[2015-06-17 18:33:54.853090] DEBUG: root: Exit SimpleTable.data2rows.\n",
54 "[2015-06-17 18:33:54.853612] DEBUG: root: Enter SimpleTable.data2rows.\n",
55 "[2015-06-17 18:33:54.854157] DEBUG: root: Exit SimpleTable.data2rows.\n",
56 "[2015-06-17 18:33:54.855192] DEBUG: root: Enter SimpleTable.data2rows.\n",
57 "[2015-06-17 18:33:54.855716] DEBUG: root: Exit SimpleTable.data2rows.\n",
58 "[2015-06-17 18:33:54.856299] DEBUG: root: Enter SimpleTable.data2rows.\n",
59 "[2015-06-17 18:33:54.856788] DEBUG: root: Exit SimpleTable.data2rows.\n",
60 "[2015-06-17 18:33:54.857276] DEBUG: root: Enter SimpleTable.data2rows.\n",
61 "[2015-06-17 18:33:54.857765] DEBUG: root: Exit SimpleTable.data2rows.\n"
62 ]
63 },
64 {
65 "data": {
66 "text/html": [
67 "<table class=\"simpletable\">\n",
68 "<caption>OLS Regression Results</caption>\n",
69 "<tr>\n",
70 " <th>Dep. Variable:</th> <td>Security(19662 [XLY])</td> <th> R-squared: </th> <td> 0.944</td> \n",
71 "</tr>\n",
72 "<tr>\n",
73 " <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.944</td> \n",
74 "</tr>\n",
75 "<tr>\n",
76 " <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td>2.127e+04</td>\n",
77 "</tr>\n",
78 "<tr>\n",
79 " <th>Date:</th> <td>Wed, 17 Jun 2015</td> <th> Prob (F-statistic):</th> <td> 0.00</td> \n",
80 "</tr>\n",
81 "<tr>\n",
82 " <th>Time:</th> <td>18:33:54</td> <th> Log-Likelihood: </th> <td> -3168.7</td> \n",
83 "</tr>\n",
84 "<tr>\n",
85 " <th>No. Observations:</th> <td> 1258</td> <th> AIC: </th> <td> 6341.</td> \n",
86 "</tr>\n",
87 "<tr>\n",
88 " <th>Df Residuals:</th> <td> 1256</td> <th> BIC: </th> <td> 6352.</td> \n",
89 "</tr>\n",
90 "<tr>\n",
91 " <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
92 "</tr>\n",
93 "<tr>\n",
94 " <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
95 "</tr>\n",
96 "</table>\n",
97 "<table class=\"simpletable\">\n",
98 "<tr>\n",
99 " <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
100 "</tr>\n",
101 "<tr>\n",
102 " <th>const</th> <td> 26.5739</td> <td> 0.169</td> <td> 156.852</td> <td> 0.000</td> <td> 26.242 26.906</td>\n",
103 "</tr>\n",
104 "<tr>\n",
105 " <th>x1</th> <td> 0.0340</td> <td> 0.000</td> <td> 145.846</td> <td> 0.000</td> <td> 0.034 0.034</td>\n",
106 "</tr>\n",
107 "</table>\n",
108 "<table class=\"simpletable\">\n",
109 "<tr>\n",
110 " <th>Omnibus:</th> <td>185.497</td> <th> Durbin-Watson: </th> <td> 0.025</td>\n",
111 "</tr>\n",
112 "<tr>\n",
113 " <th>Prob(Omnibus):</th> <td> 0.000</td> <th> Jarque-Bera (JB): </th> <td> 55.107</td>\n",
114 "</tr>\n",
115 "<tr>\n",
116 " <th>Skew:</th> <td>-0.236</td> <th> Prob(JB): </th> <td>1.08e-12</td>\n",
117 "</tr>\n",
118 "<tr>\n",
119 " <th>Kurtosis:</th> <td> 2.090</td> <th> Cond. No. </th> <td>1.45e+03</td>\n",
120 "</tr>\n",
121 "</table>"
122 ],
123 "text/plain": [
124 "<class 'statsmodels.iolib.summary.Summary'>\n",
125 "\"\"\"\n",
126 " OLS Regression Results \n",
127 "=================================================================================\n",
128 "Dep. Variable: Security(19662 [XLY]) R-squared: 0.944\n",
129 "Model: OLS Adj. R-squared: 0.944\n",
130 "Method: Least Squares F-statistic: 2.127e+04\n",
131 "Date: Wed, 17 Jun 2015 Prob (F-statistic): 0.00\n",
132 "Time: 18:33:54 Log-Likelihood: -3168.7\n",
133 "No. Observations: 1258 AIC: 6341.\n",
134 "Df Residuals: 1256 BIC: 6352.\n",
135 "Df Model: 1 \n",
136 "Covariance Type: nonrobust \n",
137 "==============================================================================\n",
138 " coef std err t P>|t| [95.0% Conf. Int.]\n",
139 "------------------------------------------------------------------------------\n",
140 "const 26.5739 0.169 156.852 0.000 26.242 26.906\n",
141 "x1 0.0340 0.000 145.846 0.000 0.034 0.034\n",
142 "==============================================================================\n",
143 "Omnibus: 185.497 Durbin-Watson: 0.025\n",
144 "Prob(Omnibus): 0.000 Jarque-Bera (JB): 55.107\n",
145 "Skew: -0.236 Prob(JB): 1.08e-12\n",
146 "Kurtosis: 2.090 Cond. No. 1.45e+03\n",
147 "==============================================================================\n",
148 "\n",
149 "Warnings:\n",
150 "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
151 "[2] The condition number is large, 1.45e+03. This might indicate that there are\n",
152 "strong multicollinearity or other numerical problems.\n",
153 "\"\"\""
154 ]
155 },
156 "execution_count": 227,
157 "metadata": {},
158 "output_type": "execute_result"
159 },
160 {
161 "data": {
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/yvS+7hcXdsx1xxMUFECQo565+7/g/J0f0f/5YggyG5txLlvG/rAwps+Yccx1afsKeWHN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\nQmCC\n",
163 "text/plain": [
164 "<matplotlib.figure.Figure at 0x7f5b2b789350>"
165 ]
166 },
167 "metadata": {},
168 "output_type": "display_data"
169 }
170 ],
171 "source": [
172 "start = '2010-01-01'\n",
173 "end = '2015-01-01'\n",
174 "asset = get_pricing('XLY', fields='price', start_date=start, end_date=end)\n",
175 "dates = asset.index\n",
176 "\n",
177 "def linreg(X,Y):\n",
178 " # Running the linear regression\n",
179 " x = sm.add_constant(X)\n",
180 " model = regression.linear_model.OLS(Y, x).fit()\n",
181 " a = model.params[0]\n",
182 " b = model.params[1]\n",
183 "\n",
184 " # Return summary of the regression and plot results\n",
185 " X2 = np.linspace(X.min(), X.max(), 100)\n",
186 " Y_hat = X2 * b + a\n",
187 " plt.plot(X2, Y_hat, 'r', alpha=0.9); # Add the regression line, colored in red\n",
188 " return model.summary()\n",
189 "\n",
190 "_, ax = plt.subplots()\n",
191 "ax.plot(asset)\n",
192 "ticks = ax.get_xticks()\n",
193 "ax.set_xticklabels([dates[i].date() for i in ticks[:-1]]) # Label x-axis with dates\n",
194 "linreg(np.arange(len(asset)), asset)"
195 ]
196 },
197 {
198 "cell_type": "markdown",
199 "metadata": {},
200 "source": [
201 "The summary returned by the regression tells us the slope and intercept of the line, as well as giving us some information about how statistically valid the fit is. Note that the Durbin-Watson statistic is very low here, suggeesting that the errors are correlated. The price of this fund is generally increasing, but because of the variance in the data, the line of best fit changes significantly depending on the sample we take. Because small errors in our model magnify with time, its predictions far into the future may not be as good as the fit statistics would suggest. For instance, we can see what will happen if we find a model for the data through 2012 and use it to predict the data through 2014."
202 ]
203 },
204 {
205 "cell_type": "code",
206 "execution_count": 311,
207 "metadata": {
208 "collapsed": false
209 },
210 "outputs": [
211 {
212 "data": {
213 "image/png": 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2XAzpfUur2/inb+8CIC05lnnTjQpqv9l6Do8nfNPUbGWBgPXbbecAo+rY+YoWwFjD8k/f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214 "text/plain": [
215 "<matplotlib.figure.Figure at 0x7f5b2b332790>"
216 ]
217 },
218 "metadata": {},
219 "output_type": "display_data"
220 }
221 ],
222 "source": [
223 "# Take only some of the data in order to see how predictive the model is\n",
224 "asset_short = get_pricing('XLY', fields='price', start_date=start, end_date='2013-01-01')\n",
225 "\n",
226 "# Running the linear regression\n",
227 "x = sm.add_constant(np.arange(len(asset_short)))\n",
228 "model = regression.linear_model.OLS(asset_short, x).fit()\n",
229 "X2 = np.linspace(0, len(asset), 100)\n",
230 "Y_hat = X2 * model.params[1] + model.params[0]\n",
231 "\n",
232 "# Plot the data for the full time range\n",
233 "_, ax = plt.subplots()\n",
234 "ax.plot(asset)\n",
235 "ticks = ax.get_xticks()\n",
236 "ax.set_xticklabels([dates[i].date() for i in ticks[:-1]]) # Label x-axis with dates\n",
237 "\n",
238 "# Plot the regression line extended to the full time range\n",
239 "ax.plot(X2, Y_hat, 'r', alpha=0.9); "
240 ]
241 },
242 {
243 "cell_type": "markdown",
244 "metadata": {},
245 "source": [
246 "Of course, we can keep updating our model as we go along. Below we use all the previous prices to predict prices 30 days into the future."
247 ]
248 },
249 {
250 "cell_type": "code",
251 "execution_count": 309,
252 "metadata": {
253 "collapsed": false
254 },
255 "outputs": [
256 {
257 "data": {
258 "image/png": 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6a172mV3K3285mQxzOh6vnzQTBIJGm+XB7IHTl/CeKW6Pr9frVIfaLX/z2DnD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5AAAg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\nz75MU6sdt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259 "text/plain": [
260 "<matplotlib.figure.Figure at 0x7f5b2ae35610>"
261 ]
262 },
263 "metadata": {},
264 "output_type": "display_data"
265 }
266 ],
267 "source": [
268 "# Y_hat will be our predictions for the price\n",
269 "Y_hat = [0]*1100\n",
270 "\n",
271 "# Start analysis from day 100 so that we have historical prices to work with\n",
272 "for i in range(100,1200):\n",
273 " temp = asset[:i]\n",
274 " x = sm.add_constant(np.arange(len(temp)))\n",
275 " model = regression.linear_model.OLS(temp, x).fit()\n",
276 " # Plug (i+30) into the linear model to get the predicted price 30 days from now\n",
277 " Y_hat[i-100] = (i+30) * model.params[1] + model.params[0]\n",
278 "\n",
279 "_, ax = plt.subplots()\n",
280 "ax.plot(asset[130:1230]) # Plot the asset starting from the first day we have predictions for\n",
281 "ax.plot(range(len(Y_hat)), Y_hat, 'r', alpha=0.9)\n",
282 "ticks = ax.get_xticks()\n",
283 "ax.set_xticklabels([dates[i].date() for i in ticks[:-1]]) # Label x-axis with dates;"
284 ]
285 },
286 {
287 "cell_type": "markdown",
288 "metadata": {},
289 "source": [
290 "# Log-linear trend models\n",
291 "\n",
292 "A log-linear trend model attempts to fit an exponential curve to a data set:\n",
293 "$$ y_t = e^{b_0 + b_1 t + \\epsilon_t} $$\n",
294 "\n",
295 "To find the coefficients, we can run a linear regression on the equation $ \\ln y_t = b_0 + b_1 t + \\epsilon_t $ with variables $t, \\ln y_t$. (This is the reason for the name of the model — the equation is linear when we take the logarithm of both sides!)\n",
296 "\n",
297 "If $b_1$ is very small, then a log-linear curve is approximately linear. For instance, we can find a log-linear model for our data from the previous example, with fit statistics approximately the same as for the linear model."
298 ]
299 },
300 {
301 "cell_type": "code",
302 "execution_count": 189,
303 "metadata": {
304 "collapsed": false
305 },
306 "outputs": [
307 {
308 "name": "stderr",
309 "output_type": "stream",
310 "text": [
311 "[2015-06-17 18:09:46.847271] DEBUG: root: Enter SimpleTable.data2rows.\n",
312 "[2015-06-17 18:09:46.848002] DEBUG: root: Exit SimpleTable.data2rows.\n",
313 "[2015-06-17 18:09:46.848535] DEBUG: root: Enter SimpleTable.data2rows.\n",
314 "[2015-06-17 18:09:46.849075] DEBUG: root: Exit SimpleTable.data2rows.\n",
315 "[2015-06-17 18:09:46.850109] DEBUG: root: Enter SimpleTable.data2rows.\n",
316 "[2015-06-17 18:09:46.850651] DEBUG: root: Exit SimpleTable.data2rows.\n",
317 "[2015-06-17 18:09:46.851241] DEBUG: root: Enter SimpleTable.data2rows.\n",
318 "[2015-06-17 18:09:46.851741] DEBUG: root: Exit SimpleTable.data2rows.\n",
319 "[2015-06-17 18:09:46.852235] DEBUG: root: Enter SimpleTable.data2rows.\n",
320 "[2015-06-17 18:09:46.852717] DEBUG: root: Exit SimpleTable.data2rows.\n"
321 ]
322 },
323 {
324 "data": {
325 "text/html": [
326 "<table class=\"simpletable\">\n",
327 "<caption>OLS Regression Results</caption>\n",
328 "<tr>\n",
329 " <th>Dep. Variable:</th> <td>Security(19662 [XLY])</td> <th> R-squared: </th> <td> 0.959</td> \n",
330 "</tr>\n",
331 "<tr>\n",
332 " <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.959</td> \n",
333 "</tr>\n",
334 "<tr>\n",
335 " <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td>2.913e+04</td>\n",
336 "</tr>\n",
337 "<tr>\n",
338 " <th>Date:</th> <td>Wed, 17 Jun 2015</td> <th> Prob (F-statistic):</th> <td> 0.00</td> \n",
339 "</tr>\n",
340 "<tr>\n",
341 " <th>Time:</th> <td>18:09:46</td> <th> Log-Likelihood: </th> <td> 1890.5</td> \n",
342 "</tr>\n",
343 "<tr>\n",
344 " <th>No. Observations:</th> <td> 1258</td> <th> AIC: </th> <td> -3777.</td> \n",
345 "</tr>\n",
346 "<tr>\n",
347 " <th>Df Residuals:</th> <td> 1256</td> <th> BIC: </th> <td> -3767.</td> \n",
348 "</tr>\n",
349 "<tr>\n",
350 " <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
351 "</tr>\n",
352 "<tr>\n",
353 " <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
354 "</tr>\n",
355 "</table>\n",
356 "<table class=\"simpletable\">\n",
357 "<tr>\n",
358 " <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
359 "</tr>\n",
360 "<tr>\n",
361 " <th>const</th> <td> 3.3868</td> <td> 0.003</td> <td> 1115.335</td> <td> 0.000</td> <td> 3.381 3.393</td>\n",
362 "</tr>\n",
363 "<tr>\n",
364 " <th>x1</th> <td> 0.0007</td> <td> 4.18e-06</td> <td> 170.663</td> <td> 0.000</td> <td> 0.001 0.001</td>\n",
365 "</tr>\n",
366 "</table>\n",
367 "<table class=\"simpletable\">\n",
368 "<tr>\n",
369 " <th>Omnibus:</th> <td>36.939</td> <th> Durbin-Watson: </th> <td> 0.041</td>\n",
370 "</tr>\n",
371 "<tr>\n",
372 " <th>Prob(Omnibus):</th> <td> 0.000</td> <th> Jarque-Bera (JB): </th> <td> 22.844</td>\n",
373 "</tr>\n",
374 "<tr>\n",
375 " <th>Skew:</th> <td>-0.186</td> <th> Prob(JB): </th> <td>1.10e-05</td>\n",
376 "</tr>\n",
377 "<tr>\n",
378 " <th>Kurtosis:</th> <td> 2.454</td> <th> Cond. No. </th> <td>1.45e+03</td>\n",
379 "</tr>\n",
380 "</table>"
381 ],
382 "text/plain": [
383 "<class 'statsmodels.iolib.summary.Summary'>\n",
384 "\"\"\"\n",
385 " OLS Regression Results \n",
386 "=================================================================================\n",
387 "Dep. Variable: Security(19662 [XLY]) R-squared: 0.959\n",
388 "Model: OLS Adj. R-squared: 0.959\n",
389 "Method: Least Squares F-statistic: 2.913e+04\n",
390 "Date: Wed, 17 Jun 2015 Prob (F-statistic): 0.00\n",
391 "Time: 18:09:46 Log-Likelihood: 1890.5\n",
392 "No. Observations: 1258 AIC: -3777.\n",
393 "Df Residuals: 1256 BIC: -3767.\n",
394 "Df Model: 1 \n",
395 "Covariance Type: nonrobust \n",
396 "==============================================================================\n",
397 " coef std err t P>|t| [95.0% Conf. Int.]\n",
398 "------------------------------------------------------------------------------\n",
399 "const 3.3868 0.003 1115.335 0.000 3.381 3.393\n",
400 "x1 0.0007 4.18e-06 170.663 0.000 0.001 0.001\n",
401 "==============================================================================\n",
402 "Omnibus: 36.939 Durbin-Watson: 0.041\n",
403 "Prob(Omnibus): 0.000 Jarque-Bera (JB): 22.844\n",
404 "Skew: -0.186 Prob(JB): 1.10e-05\n",
405 "Kurtosis: 2.454 Cond. No. 1.45e+03\n",
406 "==============================================================================\n",
407 "\n",
408 "Warnings:\n",
409 "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
410 "[2] The condition number is large, 1.45e+03. This might indicate that there are\n",
411 "strong multicollinearity or other numerical problems.\n",
412 "\"\"\""
413 ]
414 },
415 "execution_count": 189,
416 "metadata": {},
417 "output_type": "execute_result"
418 },
419 {
420 "data": {
421 "image/png": 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mTOyfLWRN3GCevWQuK8+8HEew0YtRXG4nLdMofDB6cEKn27a/Cg4yE2SBGruT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JvJvncH57/L1/fm8+nrqhm/kjpvAw6MiMMrbHNv+y0Vy/Wnfktf09UVnG3AxRHxBuA44KMppZnA\nJcC8iDgEmJ+/huzL93PAp8rU9S3gwoh4HfC6lNKZFbZZqdxisqmm/6eLfb4QWJ2vfyVweYfll5E9\njLQ/6I343QocU+b9ruLSpmycU0pnA0cCbyQ7UH8qpVSxs14A1YxdpZh0VCnGnwN+EBFHAu8Fvllh\nfdveTtWM3xURMZPs7/8te/Dd2QrcEBFH5v92S25yjwDNEfFGsqTqitJ9IOsA9BfVjN/5EXFEXtdI\n4D0Vtlkpfj+MiFl5+/sS8B8V1u/sGNmf4tcbsav0HdtZm+pOueeB4/LYHwNcnFKaXKGOoqhm/Egp\nvQtYx84ZfsvZ235L2XL9sN/Sp3Sa4ETEyoh4LP95PfA0MAk4B7g2L3YtcG5eZmNE3A9sKa0nf8jn\n8IhYkL91Xds63S0XEYsj4nfAji5+p9J9mwu8raT+ZrKzAr/ooo5C2Nfxy+tYEBEryyyqGJcO61eK\n80zg3ojYEREbyaYkr9TRq3nVil2+rFJM2nUR4xVkB3eAUcDyCtXY9nLVil9EbIqIX+U/byPrCE3q\nuL0u4leX/+tqn++JiM35y4eAySXL7gbWd1VHUVS5/a2H9odhDwb+1LFMF8e+dSVFG8utn5ereIzs\nT/Hb17HLy5X9ju2sTXWnXERsK7liNJSs87+x8m9f+6oZv5RSI3Ax8AU6+Q7c235LJ+X6Vb+lr+n2\nPTgppelkmehDwLiIWJUvWgWM61C8Y6Y8iZ3DIyDrIO12kO5Buc5MApYCRMR24OWU0uiU0gDg34FP\n9rC+QthH8etM2bj0YP3fAmemlIamlMYAp1DhYFE0exm77uosxl8G5qSUlgI/ByoNL7PtlVGt+KWU\nRgHvIDt72VFn8WsFzkspPZ5S+nE3zwBfCNzejXKFV434pZTuystviog7yxTp9Ds2pXRRSuk54Gtk\nz5hTN+yj2HVXd9vULuVSSpNTSo8DS4ArI2LNXuxDTalC/C4jO/bsaVLY3X5LpXL9tt/SF3Qrwcmz\n4LnAxzqcTSIiWtnzTtW+Ukc2hvn2iHiebpzNLJICxI+ImEf2pf8bsiEYD9D11bya10di9zXgvyJi\nCtlY4h/0YF3bXhXil1KqB24Avh4Ri3q4Gz8FpkXELGAeO880VtrW+8nGkn+1h9spnGrFLyLOACYA\nQ1JKc3q6HxHxzYiYAXwCqDTEUCX6SuzyfelWmypXLiKW5W33YODj+T2Rhbe38UspHQEcFBG30kvH\nnf7ab+krOp1kANovzc4Fro+IW/K3V6WUxkfEyvzS+gtdVLOcXbPWycCy/MzuI2R/qLcC3y5Trtxw\nmPY/7JTSF4CzgdaIOCovPxV4Pu8UjIyI1Sml44ATUkoXkV3mH5xSWhcRn+3qM6hl+zJ+EfGvXdTR\nMS5r8pv7zmJn/Ert8gUWEV8iG4NOSumHQHSx3zWtSrGrVPdAoIXO217bGeU3A/8CEBEPppQaUkoH\nAB9n19jZ9kpUOX7XABERV+d1dyd+y8lWKj3j+13y8f3l2l5K6VTgs8CJsfvN1H3+REg1Vbv9RcSW\nlNJc4NiU0vXs2bHvxrxs2fiVKBerfhO/fRm7Lo57ZdtUmX5LV22PiFiRUvo1cATwXHf3vRZVKX7H\nAbNTSn8k6+uOTSndDZxK9fstZctB/+u39CVdzaJWR3ZAfCoiripZdBvZzYyX5//f0mHVXbLlvGG+\nklI6FlhAdrPj1RGxg6yxlm5zt3Jl6m6vPyI+R3aDWcd9exA4n3w4R0S8v2Qbc4DZ/aCDtc/j14lK\ncfkn4J/KlN8lznky1ZR3mGcBsyjw/RzVil0lEfEq3W97z5AdFK5N2c2eDRHxIlncSmNn28tVM355\nZ2gE2dAVoGfxa+sU5MXOIZvJbre2l1I6kqzzfEZElLvXoN9cfatW/FJKw4AR+XdoPfB24Bc9Ofal\nlGZERFuH9myycfzd/u6stG9F1Rux62Rfyrapjv2WSuVSSpOANRGxKaXUBLyFyje6F0IV+y3fZufJ\ngGnAzyLirfniavdbypbrb/2WvqautbXySZ2U0vHAvWRfqG0FLyX7Ar6JLGNdRD5dX77OImA42Q15\na4HTIuKZtHMKzKFkw1X+ocI2y5ZLKR1NNl1iE9msGSuizJR/KZuu73qycZuryabLXNShzByyGUvK\n7kNR9FL8rgAuILukvwL4TkT8W3fikq9fNs4ppQayM9YAL5NN1/n4nnwutaDKsSsbkzLbrNT2DiY7\n4IzK9+UfI+KXZda37eWqFT+yG8OXkN1ouzWvp9I0z5Xi9yWyxGY7WVz+LiKeLbP+POAwoC0ZWhwR\n5+bLfg0ksitwq8mmsZ3X08+lVlQxfmuAnwFDyDpgdwGfzofYdNxmpfhdRXaCYRvZFMIXlSQ8petX\nPEb2p/j1UuwqHfcqtqkO65ctl1I6jewekrYhWVdGxHV78rnUiirE7yXg9Ih4pqTO6cBt+VC/ctvc\n235L2XL9rd/S13Sa4EiSJElSLen2LGqSJEmS1NeZ4EiSJEkqDBMcSZIkSYVhgiNJkiSpMExwJEmS\nJBWGCY4kSZKkwjDBkSRJklQY/w+KR8gLgmea7wAAAABJRU5ErkJggg==\n",
422 "text/plain": [
423 "<matplotlib.figure.Figure at 0x7f5b2bc487d0>"
424 ]
425 },
426 "metadata": {},
427 "output_type": "display_data"
428 }
429 ],
430 "source": [
431 "def loglinreg(X,Y):\n",
432 " # Running the linear regression on X, log(Y)\n",
433 " x = sm.add_constant(X)\n",
434 " model = regression.linear_model.OLS(np.log(Y), x).fit()\n",
435 " a = model.params[0]\n",
436 " b = model.params[1]\n",
437 "\n",
438 " # Return summary of the regression and plot results\n",
439 " X2 = np.linspace(X.min(), X.max(), 100)\n",
440 " Y_hat = (math.e)**(X2 * b + a)\n",
441 " plt.plot(X2, Y_hat, 'r', alpha=0.9); # Add the regression curve, colored in red\n",
442 " return model.summary()\n",
443 "\n",
444 "_, ax_log = plt.subplots()\n",
445 "ax_log.plot(asset)\n",
446 "ax_log.set_xticklabels([dates[i].date() for i in ticks[:-1]]) # Label x-axis with dates\n",
447 "loglinreg(np.arange(len(asset)), asset)"
448 ]
449 },
450 {
451 "cell_type": "markdown",
452 "metadata": {},
453 "source": [
454 "In some cases, however, a log-linear model clearly fits the data better."
455 ]
456 },
457 {
458 "cell_type": "code",
459 "execution_count": 193,
460 "metadata": {
461 "collapsed": false
462 },
463 "outputs": [
464 {
465 "name": "stderr",
466 "output_type": "stream",
467 "text": [
468 "[2015-06-17 18:13:08.261281] DEBUG: root: Enter SimpleTable.data2rows.\n",
469 "[2015-06-17 18:13:08.262012] DEBUG: root: Exit SimpleTable.data2rows.\n",
470 "[2015-06-17 18:13:08.262557] DEBUG: root: Enter SimpleTable.data2rows.\n",
471 "[2015-06-17 18:13:08.263098] DEBUG: root: Exit SimpleTable.data2rows.\n",
472 "[2015-06-17 18:13:08.264120] DEBUG: root: Enter SimpleTable.data2rows.\n",
473 "[2015-06-17 18:13:08.264835] DEBUG: root: Exit SimpleTable.data2rows.\n",
474 "[2015-06-17 18:13:08.265443] DEBUG: root: Enter SimpleTable.data2rows.\n",
475 "[2015-06-17 18:13:08.265926] DEBUG: root: Exit SimpleTable.data2rows.\n",
476 "[2015-06-17 18:13:08.266430] DEBUG: root: Enter SimpleTable.data2rows.\n",
477 "[2015-06-17 18:13:08.266916] DEBUG: root: Exit SimpleTable.data2rows.\n"
478 ]
479 },
480 {
481 "data": {
482 "text/html": [
483 "<table class=\"simpletable\">\n",
484 "<caption>OLS Regression Results</caption>\n",
485 "<tr>\n",
486 " <th>Dep. Variable:</th> <td>Security(24 [AAPL])</td> <th> R-squared: </th> <td> 0.935</td> \n",
487 "</tr>\n",
488 "<tr>\n",
489 " <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.935</td> \n",
490 "</tr>\n",
491 "<tr>\n",
492 " <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td>3.783e+04</td>\n",
493 "</tr>\n",
494 "<tr>\n",
495 " <th>Date:</th> <td>Wed, 17 Jun 2015</td> <th> Prob (F-statistic):</th> <td> 0.00</td> \n",
496 "</tr>\n",
497 "<tr>\n",
498 " <th>Time:</th> <td>18:13:08</td> <th> Log-Likelihood: </th> <td> -876.59</td> \n",
499 "</tr>\n",
500 "<tr>\n",
501 " <th>No. Observations:</th> <td> 2624</td> <th> AIC: </th> <td> 1757.</td> \n",
502 "</tr>\n",
503 "<tr>\n",
504 " <th>Df Residuals:</th> <td> 2622</td> <th> BIC: </th> <td> 1769.</td> \n",
505 "</tr>\n",
506 "<tr>\n",
507 " <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
508 "</tr>\n",
509 "<tr>\n",
510 " <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
511 "</tr>\n",
512 "</table>\n",
513 "<table class=\"simpletable\">\n",
514 "<tr>\n",
515 " <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
516 "</tr>\n",
517 "<tr>\n",
518 " <th>const</th> <td> 0.0634</td> <td> 0.013</td> <td> 4.807</td> <td> 0.000</td> <td> 0.038 0.089</td>\n",
519 "</tr>\n",
520 "<tr>\n",
521 " <th>x1</th> <td> 0.0017</td> <td> 8.71e-06</td> <td> 194.500</td> <td> 0.000</td> <td> 0.002 0.002</td>\n",
522 "</tr>\n",
523 "</table>\n",
524 "<table class=\"simpletable\">\n",
525 "<tr>\n",
526 " <th>Omnibus:</th> <td>1022.810</td> <th> Durbin-Watson: </th> <td> 0.005</td>\n",
527 "</tr>\n",
528 "<tr>\n",
529 " <th>Prob(Omnibus):</th> <td> 0.000</td> <th> Jarque-Bera (JB): </th> <td> 145.228</td>\n",
530 "</tr>\n",
531 "<tr>\n",
532 " <th>Skew:</th> <td> 0.179</td> <th> Prob(JB): </th> <td>2.91e-32</td>\n",
533 "</tr>\n",
534 "<tr>\n",
535 " <th>Kurtosis:</th> <td> 1.905</td> <th> Cond. No. </th> <td>3.03e+03</td>\n",
536 "</tr>\n",
537 "</table>"
538 ],
539 "text/plain": [
540 "<class 'statsmodels.iolib.summary.Summary'>\n",
541 "\"\"\"\n",
542 " OLS Regression Results \n",
543 "===============================================================================\n",
544 "Dep. Variable: Security(24 [AAPL]) R-squared: 0.935\n",
545 "Model: OLS Adj. R-squared: 0.935\n",
546 "Method: Least Squares F-statistic: 3.783e+04\n",
547 "Date: Wed, 17 Jun 2015 Prob (F-statistic): 0.00\n",
548 "Time: 18:13:08 Log-Likelihood: -876.59\n",
549 "No. Observations: 2624 AIC: 1757.\n",
550 "Df Residuals: 2622 BIC: 1769.\n",
551 "Df Model: 1 \n",
552 "Covariance Type: nonrobust \n",
553 "==============================================================================\n",
554 " coef std err t P>|t| [95.0% Conf. Int.]\n",
555 "------------------------------------------------------------------------------\n",
556 "const 0.0634 0.013 4.807 0.000 0.038 0.089\n",
557 "x1 0.0017 8.71e-06 194.500 0.000 0.002 0.002\n",
558 "==============================================================================\n",
559 "Omnibus: 1022.810 Durbin-Watson: 0.005\n",
560 "Prob(Omnibus): 0.000 Jarque-Bera (JB): 145.228\n",
561 "Skew: 0.179 Prob(JB): 2.91e-32\n",
562 "Kurtosis: 1.905 Cond. No. 3.03e+03\n",
563 "==============================================================================\n",
564 "\n",
565 "Warnings:\n",
566 "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
567 "[2] The condition number is large, 3.03e+03. This might indicate that there are\n",
568 "strong multicollinearity or other numerical problems.\n",
569 "\"\"\""
570 ]
571 },
572 "execution_count": 193,
573 "metadata": {},
574 "output_type": "execute_result"
575 },
576 {
577 "data": {
578 "image/png": 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zRW6O/06v9nwiJEmSMlFTE1x8MWRlwVVXQWjzR0Fq6pqIJzovALBkZTXPv7mA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\n",
579 "text/plain": [
580 "<matplotlib.figure.Figure at 0x7f5b38655f10>"
581 ]
582 },
583 "metadata": {},
584 "output_type": "display_data"
585 }
586 ],
587 "source": [
588 "start2 = '2002-01-01'\n",
589 "end2 = '2012-06-01'\n",
590 "asset2 = get_pricing('AAPL', fields='price', start_date=start2, end_date=end2)\n",
591 "dates2 = asset2.index\n",
592 "\n",
593 "_, ax2 = plt.subplots()\n",
594 "ax2.plot(asset2)\n",
595 "ticks2 = ax2.get_xticks()\n",
596 "ax2.set_xticklabels([dates2[i].date() for i in ticks2[:-1]]) # Label x-axis with dates\n",
597 "loglinreg(np.arange(len(asset2)), asset2)"
598 ]
599 },
600 {
601 "cell_type": "markdown",
602 "metadata": {},
603 "source": [
604 "# Summary\n",
605 "\n",
606 "From the above we see that trend models can provide a simple representation of a complex data series. However, the errors (deviations from the model) are highly correlated; so, we cannot apply the usual regression statistics to test for correctness, since the regression model assumes serially uncorrelated errors. This also suggests that the correlation can be used to build a finer model."
607 ]
608 }
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