Autoregressive Moving Average (ARMA): Sunspots dataΒΆ
In [1]:
from __future__ import print_function
import numpy as np
from scipy import stats
import pandas as pd
import matplotlib.pyplot as plt
import statsmodels.api as sm
In [2]:
from statsmodels.graphics.api import qqplot
Sunpots Data¶
In [3]:
print(sm.datasets.sunspots.NOTE)
:: Number of Observations - 309 (Annual 1700 - 2008) Number of Variables - 1 Variable name definitions:: SUNACTIVITY - Number of sunspots for each year The data file contains a 'YEAR' variable that is not returned by load.
In [4]:
dta = sm.datasets.sunspots.load_pandas().data
In [5]:
dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008'))
del dta["YEAR"]
In [6]:
dta.plot(figsize=(12,8));
Error in callback <function post_execute at 0x7fb786441500> (for post_execute):
--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) /usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc in post_execute() 145 def post_execute(): 146 if matplotlib.is_interactive(): --> 147 draw_all() 148 149 # IPython >= 2 /usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc in draw_all(cls, force) 148 for f_mgr in cls.get_all_fig_managers(): 149 if force or f_mgr.canvas.figure.stale: --> 150 f_mgr.canvas.draw_idle() 151 152 atexit.register(Gcf.destroy_all) /usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc in draw_idle(self, *args, **kwargs) 2024 if not self._is_idle_drawing: 2025 with self._idle_draw_cntx(): -> 2026 self.draw(*args, **kwargs) 2027 2028 def draw_cursor(self, event): /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in draw(self) 472 473 try: --> 474 self.figure.draw(self.renderer) 475 finally: 476 RendererAgg.lock.release() /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/figure.pyc in draw(self, renderer) 1157 dsu.sort(key=itemgetter(0)) 1158 for zorder, a, func, args in dsu: -> 1159 func(*args) 1160 1161 renderer.close_group('figure') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc in draw(self, renderer, inframe) 2322 2323 for zorder, a in dsu: -> 2324 a.draw(renderer) 2325 2326 renderer.close_group('axes') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in draw(self, renderer, *args, **kwargs) 1106 ticks_to_draw = self._update_ticks(renderer) 1107 ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw, -> 1108 renderer) 1109 1110 for tick in ticks_to_draw: /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in _get_tick_bboxes(self, ticks, renderer) 1056 for tick in ticks: 1057 if tick.label1On and tick.label1.get_visible(): -> 1058 extent = tick.label1.get_window_extent(renderer) 1059 ticklabelBoxes.append(extent) 1060 if tick.label2On and tick.label2.get_visible(): /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in get_window_extent(self, renderer, dpi) 959 raise RuntimeError('Cannot get window extent w/o renderer') 960 --> 961 bbox, info, descent = self._get_layout(self._renderer) 962 x, y = self.get_unitless_position() 963 x, y = self.get_transform().transform_point((x, y)) /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in _get_layout(self, renderer) 350 tmp, lp_h, lp_bl = renderer.get_text_width_height_descent('lp', 351 self._fontproperties, --> 352 ismath=False) 353 offsety = (lp_h - lp_bl) * self._linespacing 354 /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in get_text_width_height_descent(self, s, prop, ismath) 227 fontsize = prop.get_size_in_points() 228 w, h, d = texmanager.get_text_width_height_descent(s, fontsize, --> 229 renderer=self) 230 return w, h, d 231 /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in get_text_width_height_descent(self, tex, fontsize, renderer) 673 else: 674 # use dviread. It sometimes returns a wrong descent. --> 675 dvifile = self.make_dvi(tex, fontsize) 676 dvi = dviread.Dvi(dvifile, 72 * dpi_fraction) 677 try: /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in make_dvi(self, tex, fontsize) 420 'string:\n%s\nHere is the full report generated by ' 421 'LaTeX: \n\n' % repr(tex.encode('unicode_escape')) + --> 422 report)) 423 else: 424 mpl.verbose.report(report, 'debug') RuntimeError: LaTeX was not able to process the following string: 'lp' Here is the full report generated by LaTeX:
<matplotlib.figure.Figure at 0x7fb773c5af50>
In [7]:
fig = plt.figure(figsize=(12,8))
ax1 = fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40, ax=ax1)
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(dta, lags=40, ax=ax2)
Error in callback <function post_execute at 0x7fb786441500> (for post_execute):
--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) /usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc in post_execute() 145 def post_execute(): 146 if matplotlib.is_interactive(): --> 147 draw_all() 148 149 # IPython >= 2 /usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc in draw_all(cls, force) 148 for f_mgr in cls.get_all_fig_managers(): 149 if force or f_mgr.canvas.figure.stale: --> 150 f_mgr.canvas.draw_idle() 151 152 atexit.register(Gcf.destroy_all) /usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc in draw_idle(self, *args, **kwargs) 2024 if not self._is_idle_drawing: 2025 with self._idle_draw_cntx(): -> 2026 self.draw(*args, **kwargs) 2027 2028 def draw_cursor(self, event): /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in draw(self) 472 473 try: --> 474 self.figure.draw(self.renderer) 475 finally: 476 RendererAgg.lock.release() /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/figure.pyc in draw(self, renderer) 1157 dsu.sort(key=itemgetter(0)) 1158 for zorder, a, func, args in dsu: -> 1159 func(*args) 1160 1161 renderer.close_group('figure') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc in draw(self, renderer, inframe) 2322 2323 for zorder, a in dsu: -> 2324 a.draw(renderer) 2325 2326 renderer.close_group('axes') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in draw(self, renderer, *args, **kwargs) 1106 ticks_to_draw = self._update_ticks(renderer) 1107 ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw, -> 1108 renderer) 1109 1110 for tick in ticks_to_draw: /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in _get_tick_bboxes(self, ticks, renderer) 1056 for tick in ticks: 1057 if tick.label1On and tick.label1.get_visible(): -> 1058 extent = tick.label1.get_window_extent(renderer) 1059 ticklabelBoxes.append(extent) 1060 if tick.label2On and tick.label2.get_visible(): /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in get_window_extent(self, renderer, dpi) 959 raise RuntimeError('Cannot get window extent w/o renderer') 960 --> 961 bbox, info, descent = self._get_layout(self._renderer) 962 x, y = self.get_unitless_position() 963 x, y = self.get_transform().transform_point((x, y)) /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in _get_layout(self, renderer) 350 tmp, lp_h, lp_bl = renderer.get_text_width_height_descent('lp', 351 self._fontproperties, --> 352 ismath=False) 353 offsety = (lp_h - lp_bl) * self._linespacing 354 /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in get_text_width_height_descent(self, s, prop, ismath) 227 fontsize = prop.get_size_in_points() 228 w, h, d = texmanager.get_text_width_height_descent(s, fontsize, --> 229 renderer=self) 230 return w, h, d 231 /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in get_text_width_height_descent(self, tex, fontsize, renderer) 673 else: 674 # use dviread. It sometimes returns a wrong descent. --> 675 dvifile = self.make_dvi(tex, fontsize) 676 dvi = dviread.Dvi(dvifile, 72 * dpi_fraction) 677 try: /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in make_dvi(self, tex, fontsize) 420 'string:\n%s\nHere is the full report generated by ' 421 'LaTeX: \n\n' % repr(tex.encode('unicode_escape')) + --> 422 report)) 423 else: 424 mpl.verbose.report(report, 'debug') RuntimeError: LaTeX was not able to process the following string: 'lp' Here is the full report generated by LaTeX:
<matplotlib.figure.Figure at 0x7fb773c6a810>
In [8]:
arma_mod20 = sm.tsa.ARMA(dta, (2,0)).fit()
print(arma_mod20.params)
const 49.659366 ar.L1.SUNACTIVITY 1.390656 ar.L2.SUNACTIVITY -0.688571 dtype: float64
In [9]:
arma_mod30 = sm.tsa.ARMA(dta, (3,0)).fit()
In [10]:
print(arma_mod20.aic, arma_mod20.bic, arma_mod20.hqic)
2622.63633806 2637.56970317 2628.60672591
In [11]:
print(arma_mod30.params)
const 49.749796 ar.L1.SUNACTIVITY 1.300810 ar.L2.SUNACTIVITY -0.508093 ar.L3.SUNACTIVITY -0.129650 dtype: float64
In [12]:
print(arma_mod30.aic, arma_mod30.bic, arma_mod30.hqic)
2619.4036287 2638.07033508 2626.86661351
- Does our model obey the theory?
In [13]:
sm.stats.durbin_watson(arma_mod30.resid.values)
Out[13]:
1.9564806905406757
In [14]:
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
ax = arma_mod30.resid.plot(ax=ax);
Error in callback <function post_execute at 0x7fb786441500> (for post_execute):
--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) /usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc in post_execute() 145 def post_execute(): 146 if matplotlib.is_interactive(): --> 147 draw_all() 148 149 # IPython >= 2 /usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc in draw_all(cls, force) 148 for f_mgr in cls.get_all_fig_managers(): 149 if force or f_mgr.canvas.figure.stale: --> 150 f_mgr.canvas.draw_idle() 151 152 atexit.register(Gcf.destroy_all) /usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc in draw_idle(self, *args, **kwargs) 2024 if not self._is_idle_drawing: 2025 with self._idle_draw_cntx(): -> 2026 self.draw(*args, **kwargs) 2027 2028 def draw_cursor(self, event): /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in draw(self) 472 473 try: --> 474 self.figure.draw(self.renderer) 475 finally: 476 RendererAgg.lock.release() /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/figure.pyc in draw(self, renderer) 1157 dsu.sort(key=itemgetter(0)) 1158 for zorder, a, func, args in dsu: -> 1159 func(*args) 1160 1161 renderer.close_group('figure') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc in draw(self, renderer, inframe) 2322 2323 for zorder, a in dsu: -> 2324 a.draw(renderer) 2325 2326 renderer.close_group('axes') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in draw(self, renderer, *args, **kwargs) 1106 ticks_to_draw = self._update_ticks(renderer) 1107 ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw, -> 1108 renderer) 1109 1110 for tick in ticks_to_draw: /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in _get_tick_bboxes(self, ticks, renderer) 1056 for tick in ticks: 1057 if tick.label1On and tick.label1.get_visible(): -> 1058 extent = tick.label1.get_window_extent(renderer) 1059 ticklabelBoxes.append(extent) 1060 if tick.label2On and tick.label2.get_visible(): /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in get_window_extent(self, renderer, dpi) 959 raise RuntimeError('Cannot get window extent w/o renderer') 960 --> 961 bbox, info, descent = self._get_layout(self._renderer) 962 x, y = self.get_unitless_position() 963 x, y = self.get_transform().transform_point((x, y)) /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in _get_layout(self, renderer) 350 tmp, lp_h, lp_bl = renderer.get_text_width_height_descent('lp', 351 self._fontproperties, --> 352 ismath=False) 353 offsety = (lp_h - lp_bl) * self._linespacing 354 /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in get_text_width_height_descent(self, s, prop, ismath) 227 fontsize = prop.get_size_in_points() 228 w, h, d = texmanager.get_text_width_height_descent(s, fontsize, --> 229 renderer=self) 230 return w, h, d 231 /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in get_text_width_height_descent(self, tex, fontsize, renderer) 673 else: 674 # use dviread. It sometimes returns a wrong descent. --> 675 dvifile = self.make_dvi(tex, fontsize) 676 dvi = dviread.Dvi(dvifile, 72 * dpi_fraction) 677 try: /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in make_dvi(self, tex, fontsize) 420 'string:\n%s\nHere is the full report generated by ' 421 'LaTeX: \n\n' % repr(tex.encode('unicode_escape')) + --> 422 report)) 423 else: 424 mpl.verbose.report(report, 'debug') RuntimeError: LaTeX was not able to process the following string: 'lp' Here is the full report generated by LaTeX:
<matplotlib.figure.Figure at 0x7fb77827ba10>
In [15]:
resid = arma_mod30.resid
In [16]:
stats.normaltest(resid)
Out[16]:
NormaltestResult(statistic=49.845037117754686, pvalue=1.5006786874160669e-11)
In [17]:
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
fig = qqplot(resid, line='q', ax=ax, fit=True)
Error in callback <function post_execute at 0x7fb786441500> (for post_execute):
--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) /usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc in post_execute() 145 def post_execute(): 146 if matplotlib.is_interactive(): --> 147 draw_all() 148 149 # IPython >= 2 /usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc in draw_all(cls, force) 148 for f_mgr in cls.get_all_fig_managers(): 149 if force or f_mgr.canvas.figure.stale: --> 150 f_mgr.canvas.draw_idle() 151 152 atexit.register(Gcf.destroy_all) /usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc in draw_idle(self, *args, **kwargs) 2024 if not self._is_idle_drawing: 2025 with self._idle_draw_cntx(): -> 2026 self.draw(*args, **kwargs) 2027 2028 def draw_cursor(self, event): /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in draw(self) 472 473 try: --> 474 self.figure.draw(self.renderer) 475 finally: 476 RendererAgg.lock.release() /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/figure.pyc in draw(self, renderer) 1157 dsu.sort(key=itemgetter(0)) 1158 for zorder, a, func, args in dsu: -> 1159 func(*args) 1160 1161 renderer.close_group('figure') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc in draw(self, renderer, inframe) 2322 2323 for zorder, a in dsu: -> 2324 a.draw(renderer) 2325 2326 renderer.close_group('axes') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in draw(self, renderer, *args, **kwargs) 1106 ticks_to_draw = self._update_ticks(renderer) 1107 ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw, -> 1108 renderer) 1109 1110 for tick in ticks_to_draw: /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in _get_tick_bboxes(self, ticks, renderer) 1056 for tick in ticks: 1057 if tick.label1On and tick.label1.get_visible(): -> 1058 extent = tick.label1.get_window_extent(renderer) 1059 ticklabelBoxes.append(extent) 1060 if tick.label2On and tick.label2.get_visible(): /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in get_window_extent(self, renderer, dpi) 959 raise RuntimeError('Cannot get window extent w/o renderer') 960 --> 961 bbox, info, descent = self._get_layout(self._renderer) 962 x, y = self.get_unitless_position() 963 x, y = self.get_transform().transform_point((x, y)) /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in _get_layout(self, renderer) 350 tmp, lp_h, lp_bl = renderer.get_text_width_height_descent('lp', 351 self._fontproperties, --> 352 ismath=False) 353 offsety = (lp_h - lp_bl) * self._linespacing 354 /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in get_text_width_height_descent(self, s, prop, ismath) 227 fontsize = prop.get_size_in_points() 228 w, h, d = texmanager.get_text_width_height_descent(s, fontsize, --> 229 renderer=self) 230 return w, h, d 231 /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in get_text_width_height_descent(self, tex, fontsize, renderer) 673 else: 674 # use dviread. It sometimes returns a wrong descent. --> 675 dvifile = self.make_dvi(tex, fontsize) 676 dvi = dviread.Dvi(dvifile, 72 * dpi_fraction) 677 try: /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in make_dvi(self, tex, fontsize) 420 'string:\n%s\nHere is the full report generated by ' 421 'LaTeX: \n\n' % repr(tex.encode('unicode_escape')) + --> 422 report)) 423 else: 424 mpl.verbose.report(report, 'debug') RuntimeError: LaTeX was not able to process the following string: 'lp' Here is the full report generated by LaTeX:
<matplotlib.figure.Figure at 0x7fb773ad7c50>
In [18]:
fig = plt.figure(figsize=(12,8))
ax1 = fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(resid.values.squeeze(), lags=40, ax=ax1)
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(resid, lags=40, ax=ax2)
Error in callback <function post_execute at 0x7fb786441500> (for post_execute):
--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) /usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc in post_execute() 145 def post_execute(): 146 if matplotlib.is_interactive(): --> 147 draw_all() 148 149 # IPython >= 2 /usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc in draw_all(cls, force) 148 for f_mgr in cls.get_all_fig_managers(): 149 if force or f_mgr.canvas.figure.stale: --> 150 f_mgr.canvas.draw_idle() 151 152 atexit.register(Gcf.destroy_all) /usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc in draw_idle(self, *args, **kwargs) 2024 if not self._is_idle_drawing: 2025 with self._idle_draw_cntx(): -> 2026 self.draw(*args, **kwargs) 2027 2028 def draw_cursor(self, event): /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in draw(self) 472 473 try: --> 474 self.figure.draw(self.renderer) 475 finally: 476 RendererAgg.lock.release() /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/figure.pyc in draw(self, renderer) 1157 dsu.sort(key=itemgetter(0)) 1158 for zorder, a, func, args in dsu: -> 1159 func(*args) 1160 1161 renderer.close_group('figure') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc in draw(self, renderer, inframe) 2322 2323 for zorder, a in dsu: -> 2324 a.draw(renderer) 2325 2326 renderer.close_group('axes') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in draw(self, renderer, *args, **kwargs) 1106 ticks_to_draw = self._update_ticks(renderer) 1107 ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw, -> 1108 renderer) 1109 1110 for tick in ticks_to_draw: /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in _get_tick_bboxes(self, ticks, renderer) 1056 for tick in ticks: 1057 if tick.label1On and tick.label1.get_visible(): -> 1058 extent = tick.label1.get_window_extent(renderer) 1059 ticklabelBoxes.append(extent) 1060 if tick.label2On and tick.label2.get_visible(): /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in get_window_extent(self, renderer, dpi) 959 raise RuntimeError('Cannot get window extent w/o renderer') 960 --> 961 bbox, info, descent = self._get_layout(self._renderer) 962 x, y = self.get_unitless_position() 963 x, y = self.get_transform().transform_point((x, y)) /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in _get_layout(self, renderer) 350 tmp, lp_h, lp_bl = renderer.get_text_width_height_descent('lp', 351 self._fontproperties, --> 352 ismath=False) 353 offsety = (lp_h - lp_bl) * self._linespacing 354 /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in get_text_width_height_descent(self, s, prop, ismath) 227 fontsize = prop.get_size_in_points() 228 w, h, d = texmanager.get_text_width_height_descent(s, fontsize, --> 229 renderer=self) 230 return w, h, d 231 /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in get_text_width_height_descent(self, tex, fontsize, renderer) 673 else: 674 # use dviread. It sometimes returns a wrong descent. --> 675 dvifile = self.make_dvi(tex, fontsize) 676 dvi = dviread.Dvi(dvifile, 72 * dpi_fraction) 677 try: /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in make_dvi(self, tex, fontsize) 420 'string:\n%s\nHere is the full report generated by ' 421 'LaTeX: \n\n' % repr(tex.encode('unicode_escape')) + --> 422 report)) 423 else: 424 mpl.verbose.report(report, 'debug') RuntimeError: LaTeX was not able to process the following string: 'lp' Here is the full report generated by LaTeX:
<matplotlib.figure.Figure at 0x7fb773993f90>
In [19]:
r,q,p = sm.tsa.acf(resid.values.squeeze(), qstat=True)
data = np.c_[range(1,41), r[1:], q, p]
table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"])
print(table.set_index('lag'))
AC Q Prob(>Q) lag 1 0.009179 0.026287 8.712008e-01 2 0.041793 0.573048 7.508690e-01 3 -0.001334 0.573607 9.024469e-01 4 0.136089 6.408955 1.706181e-01 5 0.092469 9.111881 1.046840e-01 6 0.091949 11.793308 6.674192e-02 7 0.068748 13.297273 6.518822e-02 8 -0.015020 13.369300 9.975911e-02 9 0.187592 24.641988 3.393810e-03 10 0.213718 39.322079 2.229398e-05 11 0.201082 52.361229 2.344860e-07 12 0.117182 56.804288 8.573905e-08 13 -0.014055 56.868423 1.893827e-07 14 0.015398 56.945664 3.997499e-07 15 -0.024967 57.149416 7.741175e-07 16 0.080916 59.296873 6.871888e-07 17 0.041138 59.853844 1.110899e-06 18 -0.052021 60.747533 1.548371e-06 19 0.062496 62.041796 1.831572e-06 20 -0.010301 62.077084 3.381114e-06 21 0.074453 63.926758 3.193467e-06 22 0.124955 69.154873 8.978021e-07 23 0.093162 72.071136 5.799571e-07 24 -0.082152 74.346787 4.712847e-07 25 0.015695 74.430143 8.288748e-07 26 -0.025037 74.643000 1.367237e-06 27 -0.125861 80.041239 3.722446e-07 28 0.053225 81.010073 4.716129e-07 29 -0.038693 81.523899 6.916415e-07 30 -0.016904 81.622318 1.151625e-06 31 -0.019296 81.751031 1.868708e-06 32 0.104990 85.575151 8.927700e-07 33 0.040086 86.134651 1.247474e-06 34 0.008829 86.161894 2.047769e-06 35 0.014588 86.236531 3.263719e-06 36 -0.119329 91.248977 1.084426e-06 37 -0.036665 91.723945 1.521884e-06 38 -0.046193 92.480592 1.938687e-06 39 -0.017768 92.592961 2.990607e-06 40 -0.006220 92.606784 4.696872e-06
- This indicates a lack of fit.
- In-sample dynamic prediction. How good does our model do?
In [20]:
predict_sunspots = arma_mod30.predict('1990', '2012', dynamic=True)
print(predict_sunspots)
1990-12-31 167.047353 1991-12-31 140.992848 1992-12-31 94.858876 1993-12-31 46.860614 1994-12-31 11.242300 1995-12-31 -4.721532 1996-12-31 -1.167078 1997-12-31 16.185598 1998-12-31 39.021839 1999-12-31 59.449843 2000-12-31 72.170093 2001-12-31 75.376689 2002-12-31 70.436311 2003-12-31 60.731396 2004-12-31 50.201584 2005-12-31 42.075817 2006-12-31 38.114099 2007-12-31 38.454487 2008-12-31 41.963690 2009-12-31 46.869181 2010-12-31 51.423160 2011-12-31 54.399610 2012-12-31 55.321566 Freq: A-DEC, dtype: float64
In [21]:
fig, ax = plt.subplots(figsize=(12, 8))
ax = dta.ix['1950':].plot(ax=ax)
fig = arma_mod30.plot_predict('1990', '2012', dynamic=True, ax=ax, plot_insample=False)
Error in callback <function post_execute at 0x7fb786441500> (for post_execute):
--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) /usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc in post_execute() 145 def post_execute(): 146 if matplotlib.is_interactive(): --> 147 draw_all() 148 149 # IPython >= 2 /usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc in draw_all(cls, force) 148 for f_mgr in cls.get_all_fig_managers(): 149 if force or f_mgr.canvas.figure.stale: --> 150 f_mgr.canvas.draw_idle() 151 152 atexit.register(Gcf.destroy_all) /usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc in draw_idle(self, *args, **kwargs) 2024 if not self._is_idle_drawing: 2025 with self._idle_draw_cntx(): -> 2026 self.draw(*args, **kwargs) 2027 2028 def draw_cursor(self, event): /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in draw(self) 472 473 try: --> 474 self.figure.draw(self.renderer) 475 finally: 476 RendererAgg.lock.release() /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/figure.pyc in draw(self, renderer) 1157 dsu.sort(key=itemgetter(0)) 1158 for zorder, a, func, args in dsu: -> 1159 func(*args) 1160 1161 renderer.close_group('figure') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc in draw(self, renderer, inframe) 2322 2323 for zorder, a in dsu: -> 2324 a.draw(renderer) 2325 2326 renderer.close_group('axes') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in draw(self, renderer, *args, **kwargs) 1106 ticks_to_draw = self._update_ticks(renderer) 1107 ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw, -> 1108 renderer) 1109 1110 for tick in ticks_to_draw: /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in _get_tick_bboxes(self, ticks, renderer) 1056 for tick in ticks: 1057 if tick.label1On and tick.label1.get_visible(): -> 1058 extent = tick.label1.get_window_extent(renderer) 1059 ticklabelBoxes.append(extent) 1060 if tick.label2On and tick.label2.get_visible(): /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in get_window_extent(self, renderer, dpi) 959 raise RuntimeError('Cannot get window extent w/o renderer') 960 --> 961 bbox, info, descent = self._get_layout(self._renderer) 962 x, y = self.get_unitless_position() 963 x, y = self.get_transform().transform_point((x, y)) /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in _get_layout(self, renderer) 350 tmp, lp_h, lp_bl = renderer.get_text_width_height_descent('lp', 351 self._fontproperties, --> 352 ismath=False) 353 offsety = (lp_h - lp_bl) * self._linespacing 354 /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in get_text_width_height_descent(self, s, prop, ismath) 227 fontsize = prop.get_size_in_points() 228 w, h, d = texmanager.get_text_width_height_descent(s, fontsize, --> 229 renderer=self) 230 return w, h, d 231 /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in get_text_width_height_descent(self, tex, fontsize, renderer) 673 else: 674 # use dviread. It sometimes returns a wrong descent. --> 675 dvifile = self.make_dvi(tex, fontsize) 676 dvi = dviread.Dvi(dvifile, 72 * dpi_fraction) 677 try: /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in make_dvi(self, tex, fontsize) 420 'string:\n%s\nHere is the full report generated by ' 421 'LaTeX: \n\n' % repr(tex.encode('unicode_escape')) + --> 422 report)) 423 else: 424 mpl.verbose.report(report, 'debug') RuntimeError: LaTeX was not able to process the following string: 'lp' Here is the full report generated by LaTeX:
<matplotlib.figure.Figure at 0x7fb7737c7c10>
In [22]:
def mean_forecast_err(y, yhat):
return y.sub(yhat).mean()
In [23]:
mean_forecast_err(dta.SUNACTIVITY, predict_sunspots)
Out[23]:
5.6371143703450644
Exercise: Can you obtain a better fit for the Sunspots model? (Hint: sm.tsa.AR has a method select_order)¶
Simulated ARMA(4,1): Model Identification is Difficult¶
In [24]:
from statsmodels.tsa.arima_process import arma_generate_sample, ArmaProcess
In [25]:
np.random.seed(1234)
# include zero-th lag
arparams = np.array([1, .75, -.65, -.55, .9])
maparams = np.array([1, .65])
Let's make sure this model is estimable.
In [26]:
arma_t = ArmaProcess(arparams, maparams)
In [27]:
arma_t.isinvertible()
--------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-251-d3a1a0e5898b> in <module>() ----> 1 arma_t.isinvertible() TypeError: 'bool' object is not callable
In [28]:
arma_t.isstationary()
--------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-252-55a9b2cc43b1> in <module>() ----> 1 arma_t.isstationary() TypeError: 'bool' object is not callable
- What does this mean?
In [29]:
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
ax.plot(arma_t.generate_sample(size=50));
--------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-253-d059f8971c1a> in <module>() 1 fig = plt.figure(figsize=(12,8)) 2 ax = fig.add_subplot(111) ----> 3 ax.plot(arma_t.generate_sample(size=50)); TypeError: generate_sample() got an unexpected keyword argument 'size'
Error in callback <function post_execute at 0x7fb786441500> (for post_execute):
--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) /usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc in post_execute() 145 def post_execute(): 146 if matplotlib.is_interactive(): --> 147 draw_all() 148 149 # IPython >= 2 /usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc in draw_all(cls, force) 148 for f_mgr in cls.get_all_fig_managers(): 149 if force or f_mgr.canvas.figure.stale: --> 150 f_mgr.canvas.draw_idle() 151 152 atexit.register(Gcf.destroy_all) /usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc in draw_idle(self, *args, **kwargs) 2024 if not self._is_idle_drawing: 2025 with self._idle_draw_cntx(): -> 2026 self.draw(*args, **kwargs) 2027 2028 def draw_cursor(self, event): /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in draw(self) 472 473 try: --> 474 self.figure.draw(self.renderer) 475 finally: 476 RendererAgg.lock.release() /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/figure.pyc in draw(self, renderer) 1157 dsu.sort(key=itemgetter(0)) 1158 for zorder, a, func, args in dsu: -> 1159 func(*args) 1160 1161 renderer.close_group('figure') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc in draw(self, renderer, inframe) 2322 2323 for zorder, a in dsu: -> 2324 a.draw(renderer) 2325 2326 renderer.close_group('axes') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in draw(self, renderer, *args, **kwargs) 1106 ticks_to_draw = self._update_ticks(renderer) 1107 ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw, -> 1108 renderer) 1109 1110 for tick in ticks_to_draw: /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in _get_tick_bboxes(self, ticks, renderer) 1056 for tick in ticks: 1057 if tick.label1On and tick.label1.get_visible(): -> 1058 extent = tick.label1.get_window_extent(renderer) 1059 ticklabelBoxes.append(extent) 1060 if tick.label2On and tick.label2.get_visible(): /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in get_window_extent(self, renderer, dpi) 959 raise RuntimeError('Cannot get window extent w/o renderer') 960 --> 961 bbox, info, descent = self._get_layout(self._renderer) 962 x, y = self.get_unitless_position() 963 x, y = self.get_transform().transform_point((x, y)) /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in _get_layout(self, renderer) 350 tmp, lp_h, lp_bl = renderer.get_text_width_height_descent('lp', 351 self._fontproperties, --> 352 ismath=False) 353 offsety = (lp_h - lp_bl) * self._linespacing 354 /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in get_text_width_height_descent(self, s, prop, ismath) 227 fontsize = prop.get_size_in_points() 228 w, h, d = texmanager.get_text_width_height_descent(s, fontsize, --> 229 renderer=self) 230 return w, h, d 231 /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in get_text_width_height_descent(self, tex, fontsize, renderer) 673 else: 674 # use dviread. It sometimes returns a wrong descent. --> 675 dvifile = self.make_dvi(tex, fontsize) 676 dvi = dviread.Dvi(dvifile, 72 * dpi_fraction) 677 try: /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in make_dvi(self, tex, fontsize) 420 'string:\n%s\nHere is the full report generated by ' 421 'LaTeX: \n\n' % repr(tex.encode('unicode_escape')) + --> 422 report)) 423 else: 424 mpl.verbose.report(report, 'debug') RuntimeError: LaTeX was not able to process the following string: 'lp' Here is the full report generated by LaTeX:
<matplotlib.figure.Figure at 0x7fb77397d3d0>
In [30]:
arparams = np.array([1, .35, -.15, .55, .1])
maparams = np.array([1, .65])
arma_t = ArmaProcess(arparams, maparams)
arma_t.isstationary()
--------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-254-317f1b2ac56b> in <module>() 2 maparams = np.array([1, .65]) 3 arma_t = ArmaProcess(arparams, maparams) ----> 4 arma_t.isstationary() TypeError: 'bool' object is not callable
In [31]:
arma_rvs = arma_t.generate_sample(size=500, burnin=250, scale=2.5)
--------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-255-e0a3cc13cb6e> in <module>() ----> 1 arma_rvs = arma_t.generate_sample(size=500, burnin=250, scale=2.5) TypeError: generate_sample() got an unexpected keyword argument 'size'
In [32]:
fig = plt.figure(figsize=(12,8))
ax1 = fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(arma_rvs, lags=40, ax=ax1)
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(arma_rvs, lags=40, ax=ax2)
--------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-256-8e761b44cfae> in <module>() 1 fig = plt.figure(figsize=(12,8)) 2 ax1 = fig.add_subplot(211) ----> 3 fig = sm.graphics.tsa.plot_acf(arma_rvs, lags=40, ax=ax1) 4 ax2 = fig.add_subplot(212) 5 fig = sm.graphics.tsa.plot_pacf(arma_rvs, lags=40, ax=ax2) NameError: name 'arma_rvs' is not defined
Error in callback <function post_execute at 0x7fb786441500> (for post_execute):
--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) /usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc in post_execute() 145 def post_execute(): 146 if matplotlib.is_interactive(): --> 147 draw_all() 148 149 # IPython >= 2 /usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc in draw_all(cls, force) 148 for f_mgr in cls.get_all_fig_managers(): 149 if force or f_mgr.canvas.figure.stale: --> 150 f_mgr.canvas.draw_idle() 151 152 atexit.register(Gcf.destroy_all) /usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc in draw_idle(self, *args, **kwargs) 2024 if not self._is_idle_drawing: 2025 with self._idle_draw_cntx(): -> 2026 self.draw(*args, **kwargs) 2027 2028 def draw_cursor(self, event): /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in draw(self) 472 473 try: --> 474 self.figure.draw(self.renderer) 475 finally: 476 RendererAgg.lock.release() /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/figure.pyc in draw(self, renderer) 1157 dsu.sort(key=itemgetter(0)) 1158 for zorder, a, func, args in dsu: -> 1159 func(*args) 1160 1161 renderer.close_group('figure') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc in draw(self, renderer, inframe) 2322 2323 for zorder, a in dsu: -> 2324 a.draw(renderer) 2325 2326 renderer.close_group('axes') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in draw(self, renderer, *args, **kwargs) 1106 ticks_to_draw = self._update_ticks(renderer) 1107 ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw, -> 1108 renderer) 1109 1110 for tick in ticks_to_draw: /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in _get_tick_bboxes(self, ticks, renderer) 1056 for tick in ticks: 1057 if tick.label1On and tick.label1.get_visible(): -> 1058 extent = tick.label1.get_window_extent(renderer) 1059 ticklabelBoxes.append(extent) 1060 if tick.label2On and tick.label2.get_visible(): /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in get_window_extent(self, renderer, dpi) 959 raise RuntimeError('Cannot get window extent w/o renderer') 960 --> 961 bbox, info, descent = self._get_layout(self._renderer) 962 x, y = self.get_unitless_position() 963 x, y = self.get_transform().transform_point((x, y)) /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in _get_layout(self, renderer) 350 tmp, lp_h, lp_bl = renderer.get_text_width_height_descent('lp', 351 self._fontproperties, --> 352 ismath=False) 353 offsety = (lp_h - lp_bl) * self._linespacing 354 /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in get_text_width_height_descent(self, s, prop, ismath) 227 fontsize = prop.get_size_in_points() 228 w, h, d = texmanager.get_text_width_height_descent(s, fontsize, --> 229 renderer=self) 230 return w, h, d 231 /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in get_text_width_height_descent(self, tex, fontsize, renderer) 673 else: 674 # use dviread. It sometimes returns a wrong descent. --> 675 dvifile = self.make_dvi(tex, fontsize) 676 dvi = dviread.Dvi(dvifile, 72 * dpi_fraction) 677 try: /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in make_dvi(self, tex, fontsize) 420 'string:\n%s\nHere is the full report generated by ' 421 'LaTeX: \n\n' % repr(tex.encode('unicode_escape')) + --> 422 report)) 423 else: 424 mpl.verbose.report(report, 'debug') RuntimeError: LaTeX was not able to process the following string: 'lp' Here is the full report generated by LaTeX:
<matplotlib.figure.Figure at 0x7fb773a572d0>
- For mixed ARMA processes the Autocorrelation function is a mixture of exponentials and damped sine waves after (q-p) lags.
- The partial autocorrelation function is a mixture of exponentials and dampened sine waves after (p-q) lags.
In [33]:
arma11 = sm.tsa.ARMA(arma_rvs, (1,1)).fit()
resid = arma11.resid
r,q,p = sm.tsa.acf(resid, qstat=True)
data = np.c_[range(1,41), r[1:], q, p]
table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"])
print(table.set_index('lag'))
--------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-257-03653831c71c> in <module>() ----> 1 arma11 = sm.tsa.ARMA(arma_rvs, (1,1)).fit() 2 resid = arma11.resid 3 r,q,p = sm.tsa.acf(resid, qstat=True) 4 data = np.c_[range(1,41), r[1:], q, p] 5 table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"]) NameError: name 'arma_rvs' is not defined
In [34]:
arma41 = sm.tsa.ARMA(arma_rvs, (4,1)).fit()
resid = arma41.resid
r,q,p = sm.tsa.acf(resid, qstat=True)
data = np.c_[range(1,41), r[1:], q, p]
table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"])
print(table.set_index('lag'))
--------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-258-30d9c2f35894> in <module>() ----> 1 arma41 = sm.tsa.ARMA(arma_rvs, (4,1)).fit() 2 resid = arma41.resid 3 r,q,p = sm.tsa.acf(resid, qstat=True) 4 data = np.c_[range(1,41), r[1:], q, p] 5 table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"]) NameError: name 'arma_rvs' is not defined
Exercise: How good of in-sample prediction can you do for another series, say, CPI¶
In [35]:
macrodta = sm.datasets.macrodata.load_pandas().data
macrodta.index = pd.Index(sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3'))
cpi = macrodta["cpi"]
Hint:¶
In [36]:
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
ax = cpi.plot(ax=ax);
ax.legend();
Error in callback <function post_execute at 0x7fb786441500> (for post_execute):
--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) /usr/lib/python2.7/dist-packages/matplotlib/pyplot.pyc in post_execute() 145 def post_execute(): 146 if matplotlib.is_interactive(): --> 147 draw_all() 148 149 # IPython >= 2 /usr/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc in draw_all(cls, force) 148 for f_mgr in cls.get_all_fig_managers(): 149 if force or f_mgr.canvas.figure.stale: --> 150 f_mgr.canvas.draw_idle() 151 152 atexit.register(Gcf.destroy_all) /usr/lib/python2.7/dist-packages/matplotlib/backend_bases.pyc in draw_idle(self, *args, **kwargs) 2024 if not self._is_idle_drawing: 2025 with self._idle_draw_cntx(): -> 2026 self.draw(*args, **kwargs) 2027 2028 def draw_cursor(self, event): /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in draw(self) 472 473 try: --> 474 self.figure.draw(self.renderer) 475 finally: 476 RendererAgg.lock.release() /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/figure.pyc in draw(self, renderer) 1157 dsu.sort(key=itemgetter(0)) 1158 for zorder, a, func, args in dsu: -> 1159 func(*args) 1160 1161 renderer.close_group('figure') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc in draw(self, renderer, inframe) 2322 2323 for zorder, a in dsu: -> 2324 a.draw(renderer) 2325 2326 renderer.close_group('axes') /usr/lib/python2.7/dist-packages/matplotlib/artist.pyc in draw_wrapper(artist, renderer, *args, **kwargs) 59 def draw_wrapper(artist, renderer, *args, **kwargs): 60 before(artist, renderer) ---> 61 draw(artist, renderer, *args, **kwargs) 62 after(artist, renderer) 63 /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in draw(self, renderer, *args, **kwargs) 1106 ticks_to_draw = self._update_ticks(renderer) 1107 ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw, -> 1108 renderer) 1109 1110 for tick in ticks_to_draw: /usr/lib/python2.7/dist-packages/matplotlib/axis.pyc in _get_tick_bboxes(self, ticks, renderer) 1056 for tick in ticks: 1057 if tick.label1On and tick.label1.get_visible(): -> 1058 extent = tick.label1.get_window_extent(renderer) 1059 ticklabelBoxes.append(extent) 1060 if tick.label2On and tick.label2.get_visible(): /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in get_window_extent(self, renderer, dpi) 959 raise RuntimeError('Cannot get window extent w/o renderer') 960 --> 961 bbox, info, descent = self._get_layout(self._renderer) 962 x, y = self.get_unitless_position() 963 x, y = self.get_transform().transform_point((x, y)) /usr/lib/python2.7/dist-packages/matplotlib/text.pyc in _get_layout(self, renderer) 350 tmp, lp_h, lp_bl = renderer.get_text_width_height_descent('lp', 351 self._fontproperties, --> 352 ismath=False) 353 offsety = (lp_h - lp_bl) * self._linespacing 354 /usr/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.pyc in get_text_width_height_descent(self, s, prop, ismath) 227 fontsize = prop.get_size_in_points() 228 w, h, d = texmanager.get_text_width_height_descent(s, fontsize, --> 229 renderer=self) 230 return w, h, d 231 /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in get_text_width_height_descent(self, tex, fontsize, renderer) 673 else: 674 # use dviread. It sometimes returns a wrong descent. --> 675 dvifile = self.make_dvi(tex, fontsize) 676 dvi = dviread.Dvi(dvifile, 72 * dpi_fraction) 677 try: /usr/lib/python2.7/dist-packages/matplotlib/texmanager.pyc in make_dvi(self, tex, fontsize) 420 'string:\n%s\nHere is the full report generated by ' 421 'LaTeX: \n\n' % repr(tex.encode('unicode_escape')) + --> 422 report)) 423 else: 424 mpl.verbose.report(report, 'debug') RuntimeError: LaTeX was not able to process the following string: 'lp' Here is the full report generated by LaTeX:
<matplotlib.figure.Figure at 0x7fb773b01990>
P-value of the unit-root test, resoundly rejects the null of no unit-root.
In [37]:
print(sm.tsa.adfuller(cpi)[1])
0.990432818834