Economic Forecasting White Paper

Transcription

1 Economic Forecasting White Paper Introduction The final CECL Accounting Standards Update released by the Financial Accounting Standards Board (FASB) in June of 2016 introduces the requirement that calculation of loss provisions should consider past events, current conditions, and reasonable and supportable forecasts. 1 This information should include both internal (institution or loan-level) and external (environmental/economic) factors. The purpose of this document is to explain Visible Equity s models for producing economic forecasts. The Methods There are two general approaches that Visible Equity offers for forecasting economic variables: statistical and modified industry-produced (MIP). While both methods are appropriate for several economic factors, this paper focuses on applying them to unemployment and house price indices (HPIs) as these are the factors Visible Equity has found to be most relevant to loan portfolio risk. Statistical Time series forecasting is a widely researched area of statistics and economics. Given a time series (or sequence of values over time), there are many techniques for projecting the series into the future. Visible Equity employs a technique called Differenced Gaussian Process Regression (DGPR), which uses long-term trends and autocorrelation patterns to estimate projections. The resulting forecasts maintain recent trends in the short term, but will smoothly revert to long-term trends in the long term. As an example, consider the HPI for Colorado Springs illustrated in Figure 1. The HPI (provided by the Federal Housing Financial Agency, or FHFA) represents house price trends in Colorado Springs since the 1970s. As evidenced in the graph, house prices have increased at a fairly steady rate over the last years, with a slight hiccup during the recent recession. This longterm rate is one piece of information that will be leveraged in the forecast. Another element of the time series used by DGPR is the level of correlation between subsequent points in time. Generally, house prices have a high level of autocorrelation, which is manifest by the relative absence of changes in direction. 1 FASB ASU

2 Let s focus first on the long-term trend or slope. In a mathematical sense, the slope is the rate of change in the HPI over time. Notice in Figure 1 that the slope (or steepness) itself changes over time, and sometimes even changes directions. In fact, at any point in the time series, we can approximate the local (not long-term) slope (this is the discrete equivalent of a calculus derivative). We do so by calculating the difference between subsequent points in time. Hence, the Differenced piece of the Differenced Gaussian Process Regression. If we do this for every pair of subsequent points, we end up with a new time series (see the black line in Figure 2). The differenced series now represents the local trend at each point in time, such that the average of the differenced series is equal to the long-term trend. When interpreting Figure 2, keep in mind that anything above 0 on the y-axis indicates a house price increase, while anything below 0 indicates a decrease. Figure 1: FHFA house price index time series for Colorado Springs, CO This is where the GPR (Gaussian Process Regression) piece of DGPR comes in. GPR is a type of regression that relies on correlations in time or space to model nonlinearity. In this case, we are modelling the behavior of the differenced HPI time series to capture things like smoothness and the tendency to change direction. The blue line in Figure 2 illustrates the results of GPR. The line is a mathematical approximation of the differenced time series. The portion of the line that we care most about is after the end of the observed time series, as it is an estimation of future trends. One reason DGPR is preferable to ARIMA (another forecasting method) is that GPR will smoothly revert to the overall average beyond the point of observed data. Importantly, the manner in which it reverts is dictated by the behavior of the historical trend (e.g. smoothness, changes in direction, etc.). The stickier the historical series, the stickier will be the forecast. 2

3 We mentioned previously that the future portion of the blue line is our estimate of future trends. Let s explore this idea further. Notice that the blue line is increasing from 2011 to the current date. This indicates that not only have house prices been on the increase (indicated by the line being above 0), but the degree of increase has increased. So, the decrease beginning at the current date does not indicate a decrease in house prices, but rather a decrease in the rate at which prices are increasing. In the long term, the increase settles in around 1.22 index points per quarter. Applying these rates of change to the tail of Figure 1 yields the HPI forecasts in Figure 3. Figure 2: Differenced FHFA house price index time series for Colorado Springs, CO 3

4 Figure 3: HPI Forecasts for Colorado Springs, CO Modified Industry-Produced Some forecasts are publicly available from both private and government entities. While these can be helpful, they are often at a national rather than local level. Statistics such as unemployment can vary widely across the United States, making national forecasts less helpful in the CECL setting. The Modified Industry Produced (MIP) forecasting method uses historical data to approximate relationships between national and local metrics, then produces local forecasts by applying those relationships to national forecasts. For instance, Figure 4 displays historical unemployment at a national and MSA level (Flagstaff, AZ) as a scatterplot. Notice the clear positive correlation. While the relationship isn t perfect, knowledge of national unemployment is certainly helpful in estimating Flagstaff s unemployment. Linear regression is used to model the relationship between the two metrics (orange line in Figure 4), yielding a mathematical equation that approximates Flagstaff unemployment given national unemployment. U flagstaff = β 0 + β 1 U national Figure 5 presents historical unemployment along with the forecasts produced with this method. The national forecasts (blue dotted line) provided by the Federal Reserve Bank of St. Louis (FRED) are used in the regression equation to produce forecasts for Flagstaff (black dotted line). Because FRED only produces 3 calendar years of unemployment forecasts, we revert to the historical average for the MSA after that point. Rather than reverting immediately to the average, we use a straight line to gradually approach it over a year. 4

5 Figure 4: National vs Flagstaff, AZ unemployment Figure 5: Unemployment forecasts for Flagstaff, AZ 5

6 Conclusion To assist in complying with requirements to consider economic forecasting in loss allowance calculations, Visible Equity has developed two forecasting methods: Differenced Gaussian Process Regression and Modified Industry-Produced. Both techniques generate local (MSA or state) forecasts of economic conditions. Beyond the point of forecasts being reasonable and supportable, Visible Equity s techniques revert to historical averages. 6