Quantitative Return Forecasting
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Abstract
This page and its main links provide an introduction to
quantitative return forecasting and explain the web service tools that the
Nematrian website makes available to help with this activity. It is based on a
section within Kemp
(2005).
Many different techniques exist for trying to predict or
forecast the future movements of investment markets. These range from purely
judgemental to purely quantitative approaches and from ones that concentrate on
individual securities to ones that are applied to entire markets. Quantitative
return forecasting can in effect be thought of as a special case of time series
analysis.
Traditional time series analysis often assumes that there is
a linear relationship between the different variables of interest and that this
function exhibits time stationarity. The analysis then in effect
typically becomes akin to use of traditional linear regression techniques.
Unfortunately, such models can only describe a relatively
small number of possible market dynamics, in effect just regular cyclicality
and purely exponential growth or decay. Such techniques typically seem to work
rather poorly for direct identification of profitable investment strategies.
Investment markets do show cyclical behaviour, but the frequencies of the
cycles are often far from regular. It is easy to postulate variables that ought
to influence markets, but much more difficult to identify ones that seem to do
so consistently whilst at the same time offering significant predictive power.
Relationships that work well over some time periods often seem to work less
well over others. Perhaps this is not too surprising. If successful forecasting
techniques were easy to find then presumably market prices would have already
reacted, reducing or eliminating their potential to add value in the future.
Better, therefore, are likely to be more sophisticated,
quantitative return forecasting tools including some, like locally linear
regression tools, that do not rely on time stationarity. These tools are
implicitly more akin to how non-quantitative investment managers think and
therefore may be expected to work more effectively in the real world. It is
possible that neural networks could also help, although Nematrian is
somewhat more sceptical about how effective such tools might be in practice for
investment problems (because unless carefully designed they may overfit any
available data).
Contents
1.
Introduction
2. Traditional time series
analysis
3. The spectrum and z-transform
of a time series
4. Generalising linear
regression techniques
5. Chaotic market
behaviour
6. Neural networks
7. Locally linear time
series analysis
References
NAVIGATION LINKS
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