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The inflation rate may be the most fundamental determinant of the discount rate used to calculate the present value of an investment. Changes in the inflation rate therefore affect stock market valuation. What is the best way to forecast the inflation rate? How reliable is inflation forecasting?
The following discussion provides the CXO Advisory Group LLC forecasts for U.S. total and core (excluding food and energy) inflation rates, along with the method for constructing the forecast and the rationale for the methodology.
This forecast is a key input for our Real Earnings Yield Model of the U.S. stock market. Forecast granularity (monthly) is therefore important. Also, accuracy over the short-term (a few months), which may influence trading decisions, is much more important than accuracy over the long-term (many months or years).
We update this discussion monthly as the Bureau of Labor Statistics (BLS) releases new Consumer Price Index data.
Forecast - Methodology - Rationale for Methodology - Forecast Flyoff
The inflation rate (based on non-seasonally adjusted Consumer Price Index - CPI-U) is an important input to our Real Earnings Yield (REY) Model of the S&P 500 index. The following chart shows our forecast for the 12-month trailing, non-seasonally adjusted total and core inflation rates over the next year by month. The error bars indicate confidence intervals of one standard deviation above and below the total inflation rate forecast based on all backtested forecasts for 2000-2005.
These forecasts, along with the S&P 500 operating earnings projection from Standard and Poor's, drive REY Model projections.
We rely on simple technical analysis to forecast the inflation rate. By technical analysis, we mean prediction based only on past Consumer Price Index (CPI) and associated inflation rate data rather than prediction based on external fundamentals such as trends in commodity prices, employment levels and wages.
As background, the following chart shows how the non-seasonally adjusted CPI varies by calendar month for two intervals, 1960-2005 and 1990-2005. The shorter, more current period indicates that changes in the inflation rate vary systematically across the calendar year, lower during May-July and November-December than the rest of the year. (See our blog entry of 11/14/05 for thoughts on a connection between inflation seasonality and stock market calendar effects.) The longer sample confirms only a less pronounced November-December anomaly. Assuming that the seasonality in the more current period persists, the inflation rate for a particular month during the next 12 months is likely related more to past inflation rate behavior during that same calendar month than to inflation rates during other past months.
How much historical data should we use in forecasting the inflation rate? Using too little history risks statistical significance. Using too much history risks comparability with current conditions and exposure of new trends. Is more recent historical data more important than older data? A change in trend is evident only in the newest data.
To answer these questions, we perform empirical tests over both the periods used above. The tests involve constructing 12-month inflation rate forecasts for January-December of each year in the sample using from two to six years of historical data, either unweighted or weighted so that more recent years are more important. We then compare each annual forecast with the actual inflation rates during the same year by calculating the Pearson correlation, the cumulative error across all 12 months and the cumulative absolute error across all 12 months. Then we calculate the means of these statistics across all annual forecasts within the sample.
The following table summarizes results for the more current 1990-2005 sample, ranking tests according to increasing mean annual absolute error. It shows, that the lowest mean annual absolute error between forecasted and actual inflation rates results from using just two years of historical data, with the more recent year weighted more heavily than the older. More specifically for this case, to estimate the inflation rate for next December, average the inflation rates for the last two Decembers, weighting the most recent past December more heavily.
The next table summarizes results for the longer 1960-2005 sample, again ranking tests according to increasing mean annual absolute error. Again, two years of weighted historical data yields the smallest mean annual absolute error.
We choose for our inflation rate forecast three years of historical data, with most recent data weighted more heavily than older data (the test shaded in light yellow in the tables above). This selection is a compromise between higher correlation and lower error. So, for example, we estimate the inflation rate for next September by extrapolating the changes in CPI from the three most recent Septembers, weighting newer historical data more heavily than older data.
The following chart shows the changes in total CPI by month over the past three years. These changes are the raw data for our total inflation rate forecast. Similarly, we use historical core inflation data to forecast the core inflation rate.
We generate error bars for total inflation rate forecasts by applying this methodology to each month in the period January 2000 through June 2005 and calculating the standard deviations of the differences between forecasted inflation rates and the actual inflation rates for each of forecast months 1 through 12. See our blog entry of 7/10/06 for details on this error analysis.
In summary, as indicated by empirical results, we are using a relatively small amount of historical data to forecast the inflation rate, with more recent data weighted more heavily. The empirical results suggest that catching trend changes is an important aspect of forecasting inflation. Note that an empirical approach is susceptible to data snooping bias.
For discussions about using:
instead of non-seasonally adjusted total inflation to predict future total inflation, see our blog entries of 7/6/06, 12/15/06 and 1/20/07. See also the April 2006 research paper entitled "Core Inflation as a Predictor of Total Inflation by Neil Khettry and Loretta Mester of the Federal Reserve Bank of Philadelphia, which concludes:
"...[C]ore CPI inflation...performs better as an out-of-sample predictor of total CPI inflation than the total CPI, the CPI less energy, and the Cleveland Fed’s weighted median CPI. The CPI less energy was a close second in terms of predicting future total CPI inflation. This suggests...focus on core CPI inflation rather than total CPI inflation over short time horizons. Based on our results, we cannot make a similar conclusion for the PCE...
"[H]owever, ...results on inflation prediction vary considerably across studies, depending on the forecasting model, time period, and measures of inflation used. Thus, we cannot conclude that one particular alternative measure of inflation does a substantially better job at predicting inflation across all time horizons or sample periods."
Our focus is the effect of inflation on investor valuation of stocks, which arguably involves behavioral aspects more appropriate for the volatile total CPI. However, the focus of the Federal Reserve Board of Governors on core measures may be attracting investor attention.
For some thoughts about the long-term inflation trend as driven by changes in workforce productivity and government deficit spending, see our blog entries of 1/2/06 and 1/3/06, respectively.
The following three research papers describe attempts to adjust technical forecasts of inflation using a wide range of fundamental factors:
In an April 2000 paper entitled "The Unreliability of Inflation Indicators", Stephen Cecchetti, Rita Chu and Charles Steindel compare the inflation-forecasting power of 19 potential indicators with that of historical inflation data autoregression. The 19 indicators include commodity prices, financial indicators and economic indicators. They conclude that: "No single indicator in our simple statistical framework clearly and consistently improved autoregressive projections. The indicators we found to be reasonably well correlated with overall price inflation either are inherently difficult to forecast independently of inflation or bear an inverse relationship to inflation that seems to defy all logic."
In an April 2003 paper that asks "Are there any reliable leading indicators for U.S. Inflation and GDP Growth?", Anindya Banerjee, Massimiliano Marcellino and Igor Masten confirm and extend the work in the above paper by looking at complex combinations of potential indicators and more extensive datasets to predict future inflation. They conclude that single-indicator models work best but "...the indicators can hardly beat the autoregressions more than 50% of the time, which provides support for the [autoregression] model as a robust forecasting device..." And, "...overall the paper provides yet another indication of the goodness and robustness of simple autoregressive models for forecasting [inflation]."
In a September 2003 paper entitled "Forecasting U.S. Inflation by Bayesian Model Averaging", Jonathan Wright in contrast concludes that inflation forecasts derived from either (1) the equal-weighted outputs of a large number of different inflation forecasting models or (2) a Bayesian (empirically weighted) average of these outputs substantially outperform a simple autoregression. He demonstrates this outperformance via outputs from a set of 93 simple inflation forecasting models.
In summary, using historical inflation rate data to predict future inflation is simple and probably as effective as any reasonably manageable approach. There is no easy, accurate method.
Since April 2005, we have compared our total inflation rate forecast (CXO) with those offered online by the Financial Trend Forecaster (FTF) and BMO Nesbitt Burns (BMO). The FTF Moore Inflation Predictor provides a technical forecast of the inflation rate by month for the next 12 months that apparently combines elements of trend-following and reversion to mean. FTF updates monthly as new CPI becomes available. The United States Economic Outlook from BMO offers a forecast of the inflation rate (year-over-year change in the CPI) by quarter for more than a year ahead. BMO updates weekly (but generally alters the inflation forecast only once a month).
The following chart compares the three inflation rate one-month-ahead forecasts since April 2005 with each other and with the actual inflation rate over the same period. The FTF forecast has generally been the most volatile, shifting most dramatically up and down from month to month. The chart also shows the most recently published forecasts for all three sources. All three forecasts now incorporate actual inflation rate data for the month of July 2008.
Based on 40 months of accumulated data, there is not much difference in the one-month-ahead accuracy statistics among the three forecasts. Average monthly errors are in the range -0.08% to +0.10%, and standard deviations of monthly errors are in the range 0.46% to 0.51%. See our blog entry of 8/20/08 for flyoff details at the 40-month mark.
After eight months of the fly-off, we switched from from the FTF inflation forecast to our own as an input for the REY Model. We made this change to reduce the volatility and improve the usefulness of the REY Model output. Switching to our own inflation rate forecast also allows quick reaction to new CPI data.
After 14 months of the fly-off, we modified the CXO methodology. During the first 14 months, we employed four years of unweighted historical data to construct forecasts. We now use three years of weighted historical data as described above.
All of the forecasts are sensitive to monthly surprises in the actual inflation rate. In other words, a one-month surprise in actuals significantly wags the 12-month predictions, indicating that the forecasts are not very good.
See our blog entry of 2/7/07 for the results of an abbreviated flyoff between the simple CXO methodology and an artificial intelligence model.
