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2010issue C1252-62

Treat a market as a transfer device before completing a price path

A market-instrument-function construction treats price history as an input signal that a hidden device converts into a future-path output. After the function is recovered, it is applied to historical prices to draw a chart continuation. An editorial check is to reconstruct the same path with a Kalman filter and with Linear regression before relying on a completion that can stretch several years.

  • A market-instrument-function construction treats price history as an input signal that a hidden device converts into a future-path output.
  • The same setup is posed as three inverse problems: recover the instrument function, recover the output from a known function, or recover the input from a known function.
  • Once an instrument function is obtained for a security, it is applied to historical prices to draw a continuation of the price path.
  • Editorial: compare a Kalman filter reconstruction and a Linear regression reconstruction of the same path before treating a multi-year chart completion as settled.
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Current trackKalman filter5 readingsLinear regression7 readings

A market as a transfer device

A market-instrument-function construction treats price history as an input signal that a hidden device converts into a future-path output. The device-plus-signals setup is written as a first-kind Fredholm integral relating input, instrument function, and output.

Three inverse problems

The construction is posed as three inverse problems. One recovers the instrument function. Another recovers the output from a known function. The third recovers the input from a known function.

From a recovered function to a path continuation

Once an instrument function is obtained for a security, it is applied to historical prices to draw a continuation of the price path. The authors state that a recovered instrument function was used to complete the last trading day on charts for a large set of listed securities. The stated prediction horizon for filling missing end-of-chart data varies from three to nine years depending on the security.

SPY actual prices and instrument-function forecast from 31 March 2008

Traders should watch how the reconstructed SPY path tracks the live print into the 2007–08 top, then continues through a crash, a choppy rebound, and a second trough in 2012 before the path turns up. Point values were digitized from the blue (actual) and red (forecast) curves on the source figure, using its printed 70 to 160 price scale and the 31 March 2008 freeze date.
Traders should watch how the reconstructed SPY path tracks the live print into the 2007–08 top, then continues through a crash, a choppy rebound, and a second trough in 2012 before the path turns up. Point values were digitized from the blue (actual) and red (forecast) curves on the source figure, using its printed 70 to 160 price scale and the 31 March 2008 freeze date.SPY · daily · 2003-01-01T00:00:00.000Z to 2013-01-31T00:00:00.000Z

The red path is frozen at the last trading day, 31 March 2008; later prints do not revise it. The authors give the forward window as 1,245 trading days (about five years). Turning points only; the raster does not support tick-level prices.

Assumptions that keep one law in place

The model assumes a limited, stable set of collective patterns so that one mathematical law can describe later price movement. Supporting assumptions include credit, tax, seasonal, reporting, and election cycles; many indicator-based trading programs; natural cycles; and stable participant decision habits.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
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All readings on this track · 5 readings
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  2. 1999Lagged trend filters for neural-network inputs
  3. 2006Linear forecast versus buy-and-hold when price changes cluster
  4. 2010Treat a market as a transfer device before completing a price path
  5. 2018Constructing predictive filters with RSI and walk-forward tests
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