Regression to Trend: Bearish or Bullish?

From dshort.com: Regression to Trend: Two views

The peak in 2000 marked an unprecedented 160% overshooting of the trend, which is double the overshoot in 1929. The index has been above the trend for 17 years. We also see that the major troughs saw declines in excess of 50% below the trend. If the S&P 500 were sitting squarely on the regression, it would be hovering around 820. If the index should decline over the next 12 months to a level comparable to previous major bottoms, it would fall to the vicinity of 400-425.

A critical factor for the reliability of a regression analysis of stock prices over many decades is the accuracy of the inflation adjustment. The Bureau of Labor Statistics (BLS) has been actively tracking inflation since 1919 and has estimated inflation rates back to 1913 using data on food prices. In 1982, however, the BLS began incorporating changes to the Consumer Price Index (CPI), which is used to calculate inflation. These changes have resulted in much lower "official" inflation rates than would have been the case if the method of calculation had remained consistent.

This time adjusted for inflation since 1982 using Williams' Shadow Government Statistics. The change is astonishing. The adjustments to post-1982 data alter the slope of the regression that impacts the variance from the trend across the entire time frame, dramatically so in the last two decades. With this adjustment, the S&P 500 has been below trend since 2002. The current bear market has dropped the monthly average index price 50% below the trend, which puts us in the territory of those secular market troughs. In fact, this regression analysis, the closing low on November 20th came within 2% of the monthly average trough following the Crash of 1929.

"My opinion is that the optimum method for calculating consumer prices is somewhere between the revised BLS method and the historic method preserved by Williams. But for a long-term regression analysis, consistency is essential, which makes me think the chart with the John Williams' Shadow Government Statistics gives a better indication of where the market currently resides."