分析股票价格共振网络

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目录

准备一批股票数据

先调用一些包

    import datetime
    import numpy as np
    import pylab as pl
    from matplotlib import finance
    from matplotlib.collections import LineCollection
    from sklearn import cluster, covariance, manifold

接着确定时间段和股票名称,使用sklearn自带的finance.quotes_historical_yahoo命令来下载数据。以下命令中带井号的是测试时发现下载有问题的。

    # ======Retrieve the data from Internet=========
    # Choose a time period reasonnably calm (not too long ago so that we get
    # high-tech firms, and before the 2008 crash)
    d1 = datetime.datetime(2003, 01, 01)
    d2 = datetime.datetime(2008, 01, 01)
 
    # kraft symbol has now changed from KFT to MDLZ in yahoo
    symbol_dict = {
        'TOT': 'Total',
        'XOM': 'Exxon',
        'CVX': 'Chevron',
        'COP': 'ConocoPhillips',
    #    'VLO': 'Valero Energy',
        'MSFT': 'Microsoft',
        'IBM': 'IBM',
    #    'TWX': 'Time Warner',
    #    'CMCSA': 'Comcast',
        'CVC': 'Cablevision',
        'YHOO': 'Yahoo',
    #    'DELL': 'Dell',
        'HPQ': 'HP',
        'AMZN': 'Amazon',
        'TM': 'Toyota',
        'CAJ': 'Canon',
        'MTU': 'Mitsubishi',
        'SNE': 'Sony',
        'F': 'Ford',
        'HMC': 'Honda',
        'NAV': 'Navistar',
        'NOC': 'Northrop Grumman',
        'BA': 'Boeing',
    #    'KO': 'Coca Cola',
        'MMM': '3M',
        'MCD': 'Mc Donalds',
        'PEP': 'Pepsi',
        'MDLZ': 'Kraft Foods',
    #    'K': 'Kellogg',
        'UN': 'Unilever',
        'MAR': 'Marriott',
        'PG': 'Procter Gamble',
        'CL': 'Colgate-Palmolive',
    #    'NWS': 'News Corp',
        'GE': 'General Electrics',
        'WFC': 'Wells Fargo',
        'JPM': 'JPMorgan Chase',
        'AIG': 'AIG',
        'AXP': 'American express',
        'BAC': 'Bank of America',
        'GS': 'Goldman Sachs',
        'AAPL': 'Apple',
        'SAP': 'SAP',
        'CSCO': 'Cisco',
        'TXN': 'Texas instruments',
        'XRX': 'Xerox',
        'LMT': 'Lookheed Martin',
        'WMT': 'Wal-Mart',
        'WAG': 'Walgreen',
        'HD': 'Home Depot',
        'GSK': 'GlaxoSmithKline',
        'PFE': 'Pfizer',
        'SNY': 'Sanofi-Aventis',
        'NVS': 'Novartis',
        'KMB': 'Kimberly-Clark',
        'R': 'Ryder',
        'GD': 'General Dynamics',
        'RTN': 'Raytheon',
        'CVS': 'CVS',
        'CAT': 'Caterpillar',
    #    'DD': 'DuPont de Nemours'
    }
    symbols, names = np.array(symbol_dict.items()).T
    quotes = [finance.quotes_historical_yahoo(symbol, d1, d2, asobject=True)
              for symbol in symbols]
    open = np.array([q.open for q in quotes]).astype(np.float)
    close = np.array([q.close for q in quotes]).astype(np.float)
    variation = close - open

构建网络

现在,我们要根据股票价格变动之间的相关性来得到一个相关性矩阵,并且通过确定阈值来将这个矩阵变成一个邻接矩阵,以得到一个网络。

    # Learn a graphical structure from the correlations
    edge_model = covariance.GraphLassoCV()
    # standardize the time series: using correlations rather than covariance
    # is more efficient for structure recovery
    X = variation.copy().T
    X /= X.std(axis=0)
    edge_model.fit(X)

识别社区

我们使用Affinity Propagation的方法在这个网络上划分社区。使用AP的好处是它聚类时不用预先给出cluster的个数。

    _, labels = cluster.affinity_propagation(edge_model.covariance_)
    n_labels = labels.max()
    for i in range(n_labels + 1):
        print('Cluster %i: %s' % ((i + 1), ', '.join(names[labels == i])))

绘制网络

绘制网络包括一系列步骤:


首先要给节点选定合适的位置。我们的思路是使用manifold.LocallyLinearEmbedding的方法将股票的协方差数据(1258维)降到二维,分别作为xy坐标绘制股票。

    _, labels = cluster.affinity_propagation(edge_model.covariance_)
    n_labels = labels.max()
    for i in range(n_labels + 1):
        print('Cluster %i: %s' % ((i + 1), ', '.join(names[labels == i])))

然后根据我们生产的节点坐标,绘制网络。在这个过程中,还要让同一个社区的节点颜色保持一致,并且要求节点的标签不与节点重合。

    # Find a low-dimension embedding for visualization: find the best position of
    # the nodes (the stocks) on a 2D plane
 
    # We use a dense eigen_solver to achieve reproducibility (arpack is
    # initiated with random vectors that we don't control). In addition, we
    # use a large number of neighbors to capture the large-scale structure.
    node_position_model = manifold.LocallyLinearEmbedding(
        n_components=2, eigen_solver='dense', n_neighbors=6)
    embedding = node_position_model.fit_transform(X.T).T
 
    # Visualization
    pl.figure(1, facecolor='w', figsize=(10, 8))
    pl.clf()
    ax = pl.axes([0., 0., 1., 1.])
    pl.axis('off')
 
    # Display a graph of the partial correlations
    partial_correlations = edge_model.precision_.copy()
    d = 1 / np.sqrt(np.diag(partial_correlations))
    partial_correlations *= d
    partial_correlations *= d[:, np.newaxis]
    non_zero = (np.abs(np.triu(partial_correlations, k=1)) > 0.02)
 
    # Plot the nodes using the coordinates of our embedding
    pl.scatter(embedding[0], embedding[1], s=100 * d ** 2, c=labels,
               cmap=pl.cm.spectral)
 
    # Plot the edges
    start_idx, end_idx = np.where(non_zero)
    #a sequence of (*line0*, *line1*, *line2*), where::
    #            linen = (x0, y0), (x1, y1), ... (xm, ym)
    segments = [[embedding[:, start], embedding[:, stop]]
                for start, stop in zip(start_idx, end_idx)]
    values = np.abs(partial_correlations[non_zero])
    lc = LineCollection(segments,
                        zorder=0, cmap=pl.cm.hot_r,
                        norm=pl.Normalize(0, .7 * values.max()))
    lc.set_array(values)
    lc.set_linewidths(15 * values)
    ax.add_collection(lc)
 
    # Add a label to each node. The challenge here is that we want to
    # position the labels to avoid overlap with other labels
    for index, (name, label, (x, y)) in enumerate(
            zip(names, labels, embedding.T)):
        dx = x - embedding[0]
        dx[index] = 1
        dy = y - embedding[1]
        dy[index] = 1
        this_dx = dx[np.argmin(np.abs(dy))]
        this_dy = dy[np.argmin(np.abs(dx))]
        if this_dx > 0:
            horizontalalignment = 'left'
            x = x + .002
        else:
            horizontalalignment = 'right'
            x = x - .002
        if this_dy > 0:
            verticalalignment = 'bottom'
            y = y + .002
        else:
            verticalalignment = 'top'
            y = y - .002
        pl.text(x, y, name, size=10,
                horizontalalignment=horizontalalignment,
                verticalalignment=verticalalignment,
                bbox=dict(facecolor='w',
                          edgecolor=pl.cm.spectral(label / float(n_labels)),
                          alpha=.6))
 
    pl.xlim(embedding[0].min() - .15 * embedding[0].ptp(),
            embedding[0].max() + .10 * embedding[0].ptp(),)
    pl.ylim(embedding[1].min() - .03 * embedding[1].ptp(),
            embedding[1].max() + .03 * embedding[1].ptp())
 
    #pl.show()

最后得到的图如下所示

Stockmarket correlation network 1.png

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