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def roll(df, d):
    # stack df.values d-times shifted once at each stack
    roll_array = np.dstack([df.values[i:i + d, :] for i in range(len(df.index) - d + 1)]).T
    # roll_array is now a 3-D array and can be read into
    # a pandas panel object
    panel = pd.Panel(roll_array,
                     items=df.index[d - 1:],
                     major_axis=df.columns,
                     minor_axis=pd.Index(range(d), name='roll'))
    # convert to dataframe and pivot + groupby
    # is now ready for any action normally performed
    # on a groupby object
    return panel.to_frame().unstack().T.groupby(level=0)


def beta(df, d):
    df=df.dropna(thresh=int(d / 2), axis=1)
    df=df.fillna(0)
    # first column is the market
    X = df.values[:, [0]]
    # prepend a column of ones for the intercept
    X = np.concatenate([np.ones_like(X), X], axis=1)
    # matrix algebra
    b = np.linalg.pinv(X.T.dot(X)).dot(X.T).dot(df.values[:, 1:])
    return pd.Series(b[1], df.columns[1:], name='Beta')


def idioVol(df, d):
    df=df.dropna(thresh=int(d / 2), axis=1)
    df=df.fillna(0)
    # first column is the market
    X = df.values[:, [0]]
    # prepend a column of ones for the intercept
    X = np.concatenate([np.ones_like(X), X], axis=1)
    # matrix algebra
    b = np.linalg.pinv(X.T.dot(X)).dot(X.T).dot(df.values[:, 1:]) #beta
    resid=df.values[:,1:]-X.dot(b)# real value - fitted value
    resid_std=np.std(resid,axis=0)
    return resid_std