Is there a better way to map time-series data to reflect the (presumably) non-linear perception and memory of market events?

Log transformation of the price axis seems a reasonable approximation for reaction to price. But what about transformation of timescale as well? How long do significant market events influence current judgement, how are they weighted, and at what rate does this influence fade in comparison with recent events?

Let's assume that traders are not influenced by events more than 1600 trading days ago. SP500 daily return 1960-present was log transformed:

lnRET = ln (today's close / yesterday's close)

These traders care more about recent events than past events. Partly because memory is not conserved, and partly because many processes in the biological world are more logarithmic than linear (eg visual and auditory dynamic range). "Countback days" are simply the count of days from the present to the past, from 1 to 1600. Weighting consisted of scaling each day's lnRET by it's respective ln(countback day)

Current "return perception" of SP500 is the sum of 1600 prior lnRET values, each weighted by ln(countback day):

Current return perception = sum (1-1600) {lnRET/lncountback day}

This process was repeated back in time, starting from March 2013 to Jan 1960 (attached)

current transformed perceived return = sum (lnprice/lncountback days)

The chart of current return perception shows an all-time peak in year 2000. There were large amplitude variations in the 1970's-1980's, then in the early 90's return perception took off. In terms of 1600 day perception, the 2001 bear market never fully recovered, and the 2008-09 decline appears similar to the bear market ca early 1970's.


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