**T**he U.S. is on the brink of witnessing some of the largest economic losses in net wealth since the Great Depression. The US Wealth To Income index (reported in Credit Suisse Global Wealth Report 2014) has exceed its mean 3rd quartile for only the forth time in history (see below). While the significance of this most recent event can not be overstated, one can determine the actual economic impact likely to be seen with a bit of time series and probabilistic modeling.

**I**n order to quantify the impact on US wealth, we need to forecast the future US Wealth to Income index, along with the expect Median Income for the same period of time. Let’s start by looking at a few of the more interesting characteristics of Wealth to Income index. A stationarity analysis (Augmented Dickey Fuller test) of the index data indicates that we can not reject the null hypothesis that is non-stationary (Dickey-Fuller = -2.3486, Lag order = 0, p-value = 0.4319), which means we can use Autoregressive Integrated Moving Average (ARIMA) time series modeling to forecast future events.

ARIMA are the most general class of models for forecasting a time series which can be made to be “stationary” by differencing (if necessary), perhaps in conjunction with nonlinear transformations such as logging or deflating (if necessary). An ARIMA model is classified as an “ARIMA(p,d,q)” model, where:

- p is the number of autoregressive terms,
- d is the number of nonseasonal differences, and
- q is the number of lagged forecast errors in the prediction equation.

**T**hrough experimental evaluation, the most appropriate ARIMA model is ARIMA (1,1,2), which is forecasted for 10 years and added to the original data series in order to produce the graph below. Here we see the fitted mean, forecasted mean, upper and lower 95% confidence interval, as well as the historical Wealth to Income data.

**A**t first glance, one expects an equal likelihood of realizing either the forecasted upper or lower values. However, history can provide event-oriented insights that will allow a more probabilistic approach to determining the most likely forecast. Given a certain threshold value of the Wealth to Income index, we can count that number of years it takes for the index to return to pre-threshold level, once exceed. For example, if we set a Wealth to Income index threshold of 5.5, the mean number years spent above this threshold is 4.6 yrs, with a standard deviation (sd) of 2.198 and standard error (se) of 0.98. In addition, the upper and lower 95% confidence levels are 6.52 and 2.68 yrs, respectively. Here is a complete table of years spent above aWealth to Income threshold value:

**W**ith this new threshold data, one can see that the Wealth to Income index stays above the 6.0 level for only 1.08 to 4.42 yrs. Given that this phase is 2 yrs into the cycle, it is more likely that the Wealth to Income index will see a decline in the next 2 years. Thus, we can reject the upper bounds of the forecast model and accept the lower bounds (forecasted lower 95%) for modeling purposes.

**A** similar analysis, to the one above, was used to forecast the median US Income (see below). In this case, the ARIMA(2,1,0) model was experimentally found to best represent this time series. The median US income is projected to have low to moderate growth over the next ten years and does not have significant volatility, as seen in the Wealth to Income index. Given some of the downward economic and regulatory pressures, the lower bounds (forecasted lower 95%) of forecast will be used in the analysis.

**T**he last step in the analysis to compute the cumulative percentage change (cumPercentWealthDiff) in wealth as a function of a forecasted Wealth to Income index and US Median Income. The table below show the results of multiplying the respective values and differencing them over the periods in question.

**T**he analysis shows a median wealth loss of 18% to 27% over the next 2 to 5 years, respectively. This means that for a family who has a median net wealth of $182K (Federal Reserve, 2013), they are likely to see it fall to $150K by 2016 and $133K by 2019. In comparison to 2007-2010 recession, the Federal Reserve said the median net worth of families plunged by 39 percent in just three years, from $126,400 in 2007 to $77,300 in 2010. This analysis appears to be consistent with the reality seen over the last few years.

**T**he cause and effect relationship of this correlative model remains unclear. So, while some can probably find faults with this analysis (e.g., assume the Wealth to Income index continues to increase – like during the depression), the final story seem likely to remain the same – an dramatic loss in wealth for the United States over the next few years. The only real question that now remains is identifying and implementing the best investment strategy to undertake given that we are on this brink. I hear there are great specials going on at MattressesAreUs.com.

Categories: Case Study, Data Science

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