Long term Dow Jones Industrial Average Support and Resistance Levels using ARIMA, Monte Carlo Simulation and Gaussian Mixture Model

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Data as of 14 August 2025

If you believe that the US economy still has potential (which I do not) and if you also believe that MAGA Man's antics will not destroy it (which I do not) then you may want to sit on the Dow Jones Index (through an ETF) for a long time. If the $37 Trillion debt, the rout in the Bond Market, de-dollarization, and Stagflation does not deter you, see above for the Support (cut loss if price breaks from above) and Resistance price levels (take profit  if price crosses from below) for the DJI. 

How the S/R levels were determined
It's rather technical but I shall try to explain in simple language.  We first smoothed and fitted the raw 270 data points time series of the DJI Close price with ARIMA (1,1,1,) We then ran the fitted ARIMA data through 5000 trials of Monte Carlo Simulation to see how it behaved. The post-Simulation data was then put though a Gaussian Mixture Model (GMM) with K=3 components. The highest density interval (HDI) at 60% probability at the primary (1st) peak (shaded area) was determined . And the results are the Support and Resistance prices produced. The width of the S/R band is intentionally wide so this is not a model for trading, but for long-term investment.

What the model has done  
  • ARIMA by accounting for auto-correlation, by differencing, and smoothing has increased the Stationarity of the series and made the series more predictable.
  • 5000 trials of Monte Carlo Simulation looks at the range of possibilities that the price may go to. The highest price that came out of the simulation was DJI=69,000 and the lowest was DJI=36,000. DJI as of 15 Aug was 44964. So High-15AugPrice=24054. 15AugPrice-Low= 8946. So you can see that there is bias towards the high i.e. an optimistic probability. 
  • GMM took the post-simulation data and generated 3 components (K-3) to fit it. Just like in PCA (Principal Components Analysis) we took the first (Primary) component and looked for the Highest Density Interval at the 60% level of the Probability Density Function. 
  • Why 60% 60% HDI focuses on the densest mass in the GMM primary peak and yields a band wide  enough to hold on for econonomic fundamentals to take shape as the impact of MAGA Man's antics gradually crystalize. And you believe that the US always bounces back from crises. [while I believe the West is in decline and this is the Asian century led by demographic and economic giants China and India]. Wider HDIs (75–90%) are safer in coverage but often too wide to act on; tighter HDIs (40–50%) can be fast but may whipsaw.

 




 

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