3 research outputs found
An algebraic approach to the estimation of the order of FIR filters from complete and partial magnitude and phase specifications
Published versio
Poisson relationships with applications to digital signal processing
Imperial Users onl
Forecasting Financial Time Series using Linear Predictive Filters
Forecasting financial time series is regarded as one of the most challenging applications
of time series prediction due to their dynamic nature. However, it is the fundamental
element of most investment activities thus attracting the attention of practitioners and
researchers for many decades.
The purpose of this research is to investigate and develop novel methods for the prediction
of financial time series considering their dynamic nature. The predictive performance
of asset prices time series themselves is exploited by applying digital signal
processing methods to their historical observations. The novelty of the research lies in
the design of predictive filters by maximising their spectrum flatness of forecast errors.
The filters are then applied to forecast linear combinations of daily open, high, low
and close prices of financial time series.
Given the assumption that there are no structural breaks or switching regimes in a
time series, the sufficient and necessary conditions that a time series can be predicted
with zero errors by linear filters are examined. It is concluded that a band-limited
time series can be predicted with zero errors by a predictive filter that has a constant
magnitude response and constant group delay over the bandwidth of the time series.
Because real world time series are not band-limited thus cannot be forecasted without
errors, statistical tests of spectrum flatness which evaluate the departure of the spectral
density from a constant value are introduced as measures of the predictability of
time series. Properties of a time series are then investigated in the frequency domain using its spectrum flatness. A predictive filter is designed by maximising the error
spectrum flatness that is equivalent to maximise the “whiteness” of forecast errors in
the frequency domain.
The focus is then placed on forecasting real world financial time series. By applying
spectrum flatness tests, it is found that the property of the spectrum of a linear
combination of daily open, high, low and close prices, which is called target prices, is
different from that of a random walk process as there are much more low frequency
components than high frequency ones in its spectrum. Therefore, an objective function
is proposed to derive the target price time series from the historical observations of
daily open, high, low and close prices. A predictive filter is then applied to obtain
the one-step ahead forecast of the target prices, while profitable trading strategies
are designed based on the forecast of target prices series. As a result, more than
70% success ratio could be achieved in terms of one-step ahead out-of-sample forecast
of direction changes of the target price time series by taking the S&P500 index for
example