Methods for analysis of financial markets

A method of obtaining predictive information for inhomogeneous financial time series, comprising the steps of:

• electronically receiving financial market transaction data over an electronic network;
• electronically storing in a computer readable medium said received financial market transaction data;
• constructing an inhomogeneous time series z that corresponds to said received financial market transaction data;
• constructing an exponential moving average operator;
• constructing an iterated exponential moving average operator based on said exponential moving average operator;
• constructing a time-translation-invariant, causal operator Ω[z] that is a convolution operator with kernel ω and that is based on said iterated exponential moving average operator;
• constructing a standardized time series {circumflex over (z)};
• electronically calculating values of one or more predictive factors relating to said time series z, wherein said one or more predictive factors are defined in terms of said standardized time series {circumflex over (z)};
• and
• electronically storing in a computer readable medium said calculated values of one or more predictive factors.

A method of obtaining predictive information for inhomogeneous financial time series, comprising the steps of:

• electronically receiving financial market transaction data over an electronic network;
• electronically storing in a computer readable medium said received financial market transaction data;
• constructing an inhomogeneous time series z that corresponds to said received financial market transaction data;
• constructing an exponential moving average operator EMA[τ;
• z];
• constructing an iterated exponential moving average operator based on said exponential moving average operator EMA[τ;
• z];
• constructing a time-translation-invariant, causal operator Ω[z] that is a convolution operator with kernel ω and time range τ, and that is based on said iterated exponential moving average operator;
• constructing a moving average operator MA that depends on said EMA operator;
• constructing a moving standard deviation operator MSD that depends on said MA operator;
• electronically calculating values of one or more predictive factors relating to said time series z, wherein said one or more predictive factors depend on one or more of said operators EMA, MA, and MSD;
• and
• electronically storing in a computer readable medium said calculated values of one or more predictive factors.

A method of obtaining predictive information for inhomogeneous financial time series, comprising the steps of:

• electronically receiving financial market transaction data over an electronic network;
• electronically storing in a computer readable medium said received financial market transaction data;
• constructing an inhomogeneous time series z that corresponds to said received financial market transaction data;
• constructing a complex iterated exponential moving average operator EMA[τ;
• z], with kernel ema;
• constructing a time-translation-invariant, causal operator Ω[z] that is a convolution operator with kernel ω and time range τ, and that is based on said complex iterated exponential moving average operator;
• constructing a windowed Fourier transform WF that depends on said EMA operator;
• electronically calculating values of one or more predictive factors relating to said time series z, wherein said one or more predictive factors depend on said windowed Fourier transform;
• and
• electronically storing in a computer readable medium said calculated values of one or more predictive factors.

A method of obtaining predictive information for inhomogeneous time series, comprising the steps of:

• electronically receiving time series data over an electronic network;
• electronically storing in a computer-readable medium said received time series data;
• constructing an inhomogeneous time series z that represents said time series data;
• constructing an exponential moving average operator;
• constructing an iterated exponential moving average operator based on said exponential moving average operator;
• constructing a time-translation-invariant, causal operator Ω[z] that is a convolution operator with kernel ω and that is based on said iterated exponential moving average operator;
• electronically calculating values of one or more predictive factors relating to said time series z, wherein said one or more predictive factors are defined in terms of said operator Ω[z];
• and
• electronically storing in a computer readable medium said calculated values of one or more predictive factors.