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In finance, a stock index, or stock market index, is an index that measures the performance of a stock market, or of a subset of a stock market. It helps investors compare current stock price levels with past prices to calculate market performance. Two of the primary criteria of an index are that it is investable and transparent: The methods of its construction are specified. Investors may be able to invest in a stock market index by buying an index fund, which is structured as either a mutual fund or an exchange-traded fund, and "track" an index. The difference between an index fund's performance and the index, if any, is called tracking error. Stock market indices may be classified and segmented by the set of underlying stocks included in the index, sometimes referred to as the "coverage". The underlying stocks are typically grouped together based on their underlying economics or underlying investor demand that the index is seeking to represent or track. For example, a 'world' or 'global' stock market index—such as the MSCI World or the S&P Global 100—includes stocks from all over the world, and satisfies investor demand for an index for broad global stocks. Regional indices that make up the MSCI World index, such as the MSCI Emerging Markets index, include stocks from countries with a similar level of economic development, which satisfies the investor demand for an index for emerging market stocks that may share similar economic fundamentals. The coverage of a stock market index is separate from the weighting method. For example, the S&P 500 market-cap weighted index covers the 500 largest stocks from the S&P Total Market Index, but an equally weighted S&P 500 index is also available with the same coverage. Global coverage These indices attempt to represent the performance of the global stock market. For example, the FTSE Global Equity Index Series includes over 16,000 companies. Regional coverage These indices represent the performance of the stock market of a single geographical region.
[2]Paolo Prandoni, [3]LCAV, EPFL
In this notebook we will look at the practical issues associated to
plotting the DFT and in particular the DFT of real-world signals. We
will examine how to map the DFT coefficients to real-world frequencies
and we will investigate the frequency resolution of the DFT and the
effects of zero padding.
In [1]:
def rotation_matrix(d):
"""
Calculates a rotation matrix given a vector d. The direction of d
corresponds to the rotation axis. The length of d corresponds to
the sin of the angle of rotation.
Variant of: http://mail.scipy.org/pipermail/numpy-discuss