Ticket #3356: sage-3356-part9.patch

File sage-3356-part9.patch, 13.9 KB (added by was, 14 years ago)

this patch gets doctest coverage to 100%

  • sage/finance/markov_multifractal.py 

    # HG changeset patch
# User William Stein <wstein@gmail.com>
# Date 1214893576 25200
# Node ID 62116b6e86e394cf5610481d41def0bc0e03a857
# Parent  c7f6d59ded4158b6d2d3bad091a3f74237500185
trac #3356 -- get doctest coverage up to 100% and fix some minor issues with hurst exponent.

diff -r c7f6d59ded41 -r 62116b6e86e3 sage/finance/markov_multifractal.py
    a b class MarkovSwitchingMultifractal: 
    174174            n -- a positive integer
    175175
    176176        EXAMPLES:
     177            sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1.0,0.95,3)
     178            sage: msm.simulation(5)
     179            [0.0059, -0.0097, -0.0101, -0.0110, -0.0067]
     180            sage: msm.simulation(3)
     181            [0.0055, -0.0084, 0.0141]
    177182        """
    178183        return self.simulations(n, 1)[0]
    179184

  • sage/finance/markov_multifractal_cython.pyx 

    diff -r c7f6d59ded41 -r 62116b6e86e3 sage/finance/markov_multifractal_cython.pyx
    a b def simulations(Py_ssize_t n, Py_ssize_t 
    1414def simulations(Py_ssize_t n, Py_ssize_t k,
    1515               double m0, double sigma,
    1616               int kbar, gamma):
     17    """
     18    Return k simulations of length n using the Markov switching
     19    multifractal model.
     20
     21    INPUT:
     22        n, k -- positive integers
     23        m0, sigma -- floats
     24        kbar -- integer
     25        gamma -- list of floats
     26
     27    OUTPUT:
     28        list of lists
     29
     30    EXAMPLES:
     31        sage: set_random_seed(0)
     32        sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1.0,0.95,3)
     33        sage: sage.finance.markov_multifractal_cython.simulations(5,2,1.278,0.262,8,msm.gamma())
     34        [[0.0014, -0.0023, -0.0028, -0.0030, -0.0019], [0.0020, -0.0020, 0.0034, -0.0010, -0.0004]]
     35    """
    1736    cdef double m1 = 2 - m0
    1837    cdef Py_ssize_t i, j, a, c
    1938    cdef TimeSeries t, eps

  • sage/finance/stock.py 

    diff -r c7f6d59ded41 -r 62116b6e86e3 sage/finance/stock.py
    a b class Stock: 
    164164        def get_data(exchange=''):
    165165            """
    166166            This function is used internally.
     167
     168            EXAMPLES:
     169            This indirectly tests the use of get_data.
     170                sage: finance.Stock('aapl').historical()[:2]    # optional -- requires internet
     171                [
     172                  2-Jan-90 8.81 9.38 8.75 9.31    6542800,
     173                  3-Jan-90 9.50 9.50 9.38 9.38    7428400
     174                ]
    167175            """
    168176            url = 'http://finance.google.com/finance/historical?q=%s%s&output=csv&startdate=%s'%(
    169177                 exchange, symbol.upper(),startdate)

  • sage/finance/time_series.pyx 

    diff -r c7f6d59ded41 -r 62116b6e86e3 sage/finance/time_series.pyx
    a b cdef class TimeSeries: 
    502502        return v
    503503
    504504    def linear_filter(self, M):
     505        """
     506        Return a linear filter using the first M autocovariance values
     507        of self.  This is useful in forcasting by taking a weighted
     508        average of previous values of a time series.
     509
     510        WARNING: The input sequence is assumed to be stationary, which
     511        means that the autocovariance $\langle y_j y_k \rangle$ depends
     512        only on the difference $|j-k|$.
     513
     514        INPUT:
     515            M -- integer
     516
     517        OUTPUT:
     518            TimeSeries -- the weights in the linear filter.
     519
     520        EXAMPLES:
     521            sage: set_random_seed(0)
     522            sage: v = finance.TimeSeries(10^4).randomize('normal').sums()
     523            sage: F = v.linear_filter(100)
     524            sage: v
     525            [0.6767, 0.2756, 0.6332, 0.0469, -0.8897 ... 87.6759, 87.6825, 87.4120, 87.6639, 86.3194]
     526            sage: v.linear_forecast(F)
     527            86.017728504280015
     528            sage: F
     529            [1.0148, -0.0029, -0.0105, 0.0067, -0.0232 ... -0.0106, -0.0068, 0.0085, -0.0131, 0.0092]
     530        """
    505531        acvs = [self.autocovariance(i) for i in range(M+1)]
    506532        return linear_filter(acvs)
    507533
    508534    def linear_forecast(self, filter):
     535        """
     536        Given a linear filter as output by the linear_filter command,
     537        compute the forecast for the next term in the series.
     538
     539        INPUT:
     540            filter -- a time series output by the linear filter command.
     541
     542        EXAMPLES:
     543            sage: set_random_seed(0)
     544            sage: v = finance.TimeSeries(100).randomize('normal').sums()
     545            sage: F = v[:-1].linear_filter(5); F
     546            [1.0019, -0.0524, -0.0643, 0.1323, -0.0539]
     547            sage: v.linear_forecast(F)
     548            11.782029861181114
     549            sage: v
     550            [0.6767, 0.2756, 0.6332, 0.0469, -0.8897 ... 9.2447, 9.6709, 10.4037, 10.4836, 12.1960]
     551        """
    509552        cdef TimeSeries filt
    510553        if isinstance(filter, TimeSeries):
    511554            filt = filter
    … … cdef class TimeSeries: 
    828871        return v
    829872
    830873    def show(self, *args, **kwds):
     874        """
     875        Calls plot and passes all arguments onto the plot function.  This is thus
     876        just an alias for plot.
     877
     878        EXAMPLES:
     879        Draw a plot of a time series:
     880            sage: finance.TimeSeries([1..10]).show()
     881        """
    831882        return self.plot(*args, **kwds)
    832883
    833884    def plot(self, Py_ssize_t plot_points=1000, points=False, **kwds):
    … … cdef class TimeSeries: 
    924975            t._values[i] = s/k
    925976        return t
    926977
    927     def exponential_moving_average(self, double alpha, double t0 = 0):
     978    def exponential_moving_average(self, double alpha):
    928979        """
    929         Return the exponential moving average time series over the
    930         last .  Assumes the input time series was constant
    931         with its starting value for negative time.  The t-th step of
    932         the output is the sum of the previous k-1 steps of self and
    933         the kth step divided by k.
     980        Return the exponential moving average time series.  Assumes
     981        the input time series was constant with its starting value for
     982        negative time.  The t-th step of the output is the sum of the
     983        previous k-1 steps of self and the kth step divided by k.
     984
     985        The 0th term is formally undefined, so we define it to be 0,
     986        and we define the first term to be self[0].
    934987
    935988        INPUT:
    936             alpha -- float; a smoothing factor with 0 <= alpha <= 1.
     989            alpha -- float; a smoothing factor with 0 <= alpha <= 1
    937990
    938991        OUTPUT:
    939992            a time series with the same number of steps as self.
    … … cdef class TimeSeries: 
    941994        EXAMPLES:
    942995            sage: v = finance.TimeSeries([1,1,1,2,3]); v
    943996            [1.0000, 1.0000, 1.0000, 2.0000, 3.0000]
    944             sage: v.exponential_moving_average(0,0)
     997            sage: v.exponential_moving_average(0)
    945998            [0.0000, 1.0000, 1.0000, 1.0000, 1.0000]
    946             sage: v.exponential_moving_average(1,0)
     999            sage: v.exponential_moving_average(1)
    9471000            [0.0000, 1.0000, 1.0000, 1.0000, 2.0000]
    948             sage: v.exponential_moving_average(0.5,0)
     1001            sage: v.exponential_moving_average(0.5)
    9491002            [0.0000, 1.0000, 1.0000, 1.0000, 1.5000]
     1003
     1004        Some more examples:
     1005            sage: v = finance.TimeSeries([1,2,3,4,5])
     1006            sage: v.exponential_moving_average(1)
     1007            [0.0000, 1.0000, 2.0000, 3.0000, 4.0000]
     1008            sage: v.exponential_moving_average(0)
     1009            [0.0000, 1.0000, 1.0000, 1.0000, 1.0000]
    9501010        """
    9511011        if alpha < 0 or alpha > 1:
    9521012            raise ValueError, "alpha must be between 0 and 1"
    … … cdef class TimeSeries: 
    9541014        cdef TimeSeries t = new_time_series(self._length)
    9551015        if self._length == 0:
    9561016            return t
    957         t._values[0] = t0
     1017        t._values[0] = 0
    9581018        if self._length == 1:
    9591019            return t
    9601020        t._values[1] = self._values[0]
    … … cdef class TimeSeries: 
    11041164            double
    11051165
    11061166        EXAMPLES:
    1107            
     1167            sage: v = finance.TimeSeries([1,2,3])
     1168            sage: v.central_moment(2)
     1169            0.66666666666666663
     1170
     1171        Note that the central moment is different than the moment
     1172        here, since the mean is not $0$:
     1173            sage: v.moment(2)     # doesn't subtract off mean
     1174            4.666666666666667
     1175
     1176        We compute the central moment directly:
     1177            sage: mu = v.mean(); mu
     1178            2.0
     1179            sage: ((1-mu)^2 + (2-mu)^2 + (3-mu)^2) / 3
     1180            0.66666666666666663
    11081181        """
    11091182        if k == 1:
    11101183            return float(0)
    … … cdef class TimeSeries: 
    13081381        return sqrt(self.variance(bias=bias))
    13091382
    13101383    def range_statistic(self):
    1311         sums = self.sums()
    1312         return (sums.max() - sums.min())/self.standard_deviation()
     1384        """
     1385        Return the range statistic of self, which is the difference
     1386        between the maximum and minimum values of this time series,
     1387        divided by the standard deviation of the series of differences.
     1388
     1389        OUTPUT:
     1390            float
     1391
     1392        EXAMPLES:
     1393        Notice that if we make a Brownian motion random walk, there
     1394        is no difference if we change the standard deviation.
     1395            sage: set_random_seed(0); finance.TimeSeries(10^6).randomize('normal').sums().range_statistic()
     1396            1873.9206979719115
     1397            sage: set_random_seed(0); finance.TimeSeries(10^6).randomize('normal',0,100).sums().range_statistic()
     1398            1873.920697971955
     1399        """
     1400        return (self.max() - self.min())/self.diffs().standard_deviation()
    13131401
    13141402    def hurst_exponent(self):
     1403        """
     1404        Returns a very simple naive estimate of the Hurst exponent of
     1405        this time series.  There are many possible ways to estimate
     1406        this number, and this is perhaps the most naive.  The estimate
     1407        we take here is the log of the range statistic divided by the
     1408        length of this time series.
     1409
     1410        We define the Hurst exponent of a constant time series to be 1.
     1411
     1412        NOTE: This is only a very rough estimator.  There are supposed
     1413        to be better ones that use wavelets.
     1414       
     1415        EXAMPLES:
     1416        The Hurst exponent of Brownian motion is 1/2.  We approximate
     1417        it with some specific samples:
     1418            sage: set_random_seed(0)
     1419            sage: bm = finance.TimeSeries(10^5).randomize('normal').sums(); bm
     1420            [0.6767, 0.2756, 0.6332, 0.0469, -0.8897 ... 152.2437, 151.5327, 152.7629, 152.9169, 152.9084]
     1421            sage: bm.hurst_exponent()
     1422            0.5174890556918027
     1423
     1424        We compute the Hurst exponent of a simulated fractional Brownian
     1425        motion with Hurst parameter 0.7.  This function estimates the
     1426        Hurst exponent as 0.6678...
     1427            sage: set_random_seed(0)
     1428            sage: fbm = finance.fractional_brownian_motion_simulation(0.7,0.1,10^5,1)[0].sums()
     1429            sage: fbm.hurst_exponent()
     1430            0.66787027921443409
     1431
     1432        Another example with small Hurst exponent (notice how bad the prediction is...):
     1433            sage: fbm = finance.fractional_brownian_motion_simulation(0.2,0.1,10^5,1)[0].sums()
     1434            sage: fbm.hurst_exponent()
     1435            0.30450273560706259
     1436
     1437        The above example illustrate that this is not a very good
     1438        estimate of the Hurst exponent.
     1439        """
    13151440        cdef double r = self.range_statistic()
    13161441        if r == 0:
    1317             return 0
     1442            return float(1)
    13181443        return log(r)/log(self._length)
    13191444
    13201445    def min(self, bint index=False):
    … … cdef class TimeSeries: 
    13831508        else:
    13841509            return s
    13851510
    1386     def clip(self, min=None, max=None):
     1511    def clip_remove(self, min=None, max=None):
    13871512        """
    1388         Return new time series obtained from self by removing all values
    1389         <= a certain maximum value, >= a certain minimum, or both.
     1513        Return new time series obtained from self by removing all
     1514        values that are less than or equal to a certain miminum value
     1515        or greater than or equal to a certain maximum.
    13901516
    13911517        INPUT:
    13921518            min -- None or double
    13931519            max -- None or double
    13941520
    13951521        OUTPUT:
    1396             time seriessx
     1522            time series
     1523
     1524        EXAMPLES:
     1525            sage: v = finance.TimeSeries([1..10])
     1526            sage: v.clip_remove(3,7)
     1527            [3.0000, 4.0000, 5.0000, 6.0000, 7.0000]
     1528            sage: v.clip_remove(3)
     1529            [3.0000, 4.0000, 5.0000, 6.0000, 7.0000, 8.0000, 9.0000, 10.0000]
     1530            sage: v.clip_remove(max=7)
     1531            [1.0000, 2.0000, 3.0000, 4.0000, 5.0000, 6.0000, 7.0000]
    13971532        """
    13981533        cdef Py_ssize_t i, j
    13991534        cdef TimeSeries t
    … … cdef class TimeSeries: 
    16411776        We take the above values, and compute the proportion that lie within
    16421777        1, 2, 3, 5, and 6 standard deviations of the mean (0):
    16431778            sage: s = a.standard_deviation()
    1644             sage: len(a.clip(-s,s))/float(len(a))
     1779            sage: len(a.clip_remove(-s,s))/float(len(a))
    16451780            0.68309399999999998
    1646             sage: len(a.clip(-2*s,2*s))/float(len(a))
     1781            sage: len(a.clip_remove(-2*s,2*s))/float(len(a))
    16471782            0.95455900000000005
    1648             sage: len(a.clip(-3*s,3*s))/float(len(a))
     1783            sage: len(a.clip_remove(-3*s,3*s))/float(len(a))
    16491784            0.997228
    1650             sage: len(a.clip(-5*s,5*s))/float(len(a))
     1785            sage: len(a.clip_remove(-5*s,5*s))/float(len(a))
    16511786            0.99999800000000005
    16521787
    16531788        There were no "six sigma events":
    1654             sage: len(a.clip(-6*s,6*s))/float(len(a))
     1789            sage: len(a.clip_remove(-6*s,6*s))/float(len(a))
    16551790            1.0
    16561791        """
    16571792        if distribution == 'uniform':
    … … def unpickle_time_series_v1(v, Py_ssize_ 
    19842119
    19852120def linear_filter(acvs):
    19862121    """
    1987     Create a linear filter with given autococvariance sequence.
     2122    Create a linear filter with given autocovariance sequence.
    19882123   
    19892124    EXAMPLES:
    19902125