1Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

I nt roduc t I onIt is both human nature and a useful exercise to compare something of current interest to past experience, offering potentially valuable insights as we attempt to anticipate and adjust to an uncertain future. In economics, practitioners often seek to characterize different time periods and environments as “regimes,” thereby facilitating side-by-side analysis.

During the second half of the 1990s, for example, the U.S. economy was experiencing robust economic growth without igniting inflationary pressure, while the unemployment rate remained low. This period was often compared to the 1960s, and was characterized as a “Goldilocks” economic regime: not too hot, nor too cold, but just right. Fast forward to the past year, and the question often asked (for example by Krugman (2008)) was, “Are we going back to the 1930s?” Depression is clearly considered as a regime. As more aggressive quantitative easing action was taken, some started to wonder if we would see a return to the “stagflation” of the 1970s, during which both inflation and economic stagnation occurred simultaneously — yet another possible regime.

In characterizing the state of the economy, growth and prices are by far the most widely followed metrics. For example, periods of widespread economic growth are called expansions, while periods of broad contraction are called recessions. Similarly, periods of rising prices are called inflationary, while periods of declining prices are referred to as deflationary. However, at least in the United States, the definition of a recession is far more complicated and widely debated than just using the economic growth metric. It is generally agreed that the National Bureau of Economic Research (NBER) has become the authority in dating the turning point at which the U.S. economy has moved from expansion to recession and vice versa. As described in NBER’s Web site and discussed at length in Chauvet and Piger (2008), the number of variables considered by the NBER’s Business Cycle Dating Committee far exceeds economic growth alone. Unfortunately, many observers believe that this process is neither transparent nor reproducible.

The practice of categorizing individual time periods with economic “regimes” such as recession, depression and expansion is commonplace and has a strong influence on the return assumptions employed as inputs in asset allocation models. Unfortunately, methodologies used to determine whether a period belongs to a given regime vary in their effectiveness and can be inexact. In this paper, we offer an alternative, nonparametric approach that includes emphasizing current conditions rather than preset regime characteristics and drawing on probabilities to reflect the reality that no two economic periods are identical. We also include case studies to illustrate and apply our recommendations, which we believe are a valuable addition to current literature on the subject of economic regimes.

Hakan Kaya, Ph.D. Quantitative Investment Group Neuberger Berman

Wai Lee, Ph.D. Managing Director Quantitative Investment Group Neuberger Berman

Bobby Pornrojnangkool, Ph.D. Senior Vice President Quantitative Investment Group Neuberger Berman

August 2009

Regimes: Nonparametric Identification and ForecastingForthcoming in Journal of Portfolio Management Winter 2010

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

2Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Of course, NBER is not the only authority on characterizing economic conditions. Some economists pair up the two measures, growth and prices, to generate four phases of the economy, such as expansion with rising inflation, recession with falling inflation, and the like. Strongin, Petsch and Fenton (1997) divide the economy, entirely based on growth, in two ways: (1) above and below capacity and (2) rising above or falling below sustainable growth rates, such that a particular state of economy can be mapped into one of the four phases:

Phase 1: below potential and falling•

Phase 2: below potential and rising•

Phase 3: above potential and rising•

Phase 4: above potential and falling•

While this classification provides an intuitive and appealing conceptual framework, its implementation is challenging and prompts some reservations regarding the resulting inferences and conclusions. To name one obstacle — it requires estimates of potential or sustainable growth rate — which is subject to debate. Furthermore, as the authors note, the key analytical issue is dating the transitions between phases, especially in periods during which the economy appears to be in an up-and-down range rather than on a distinguishable path. In this way, the framework can remain as subjective as it is objective and analytical.

An important mandate of the investment industry is to make prudent investment decisions for clients. The analysis of regime switching, however, typically starts with dissecting and predefining the world in regimes such as those discussed in Strongin, Petsch and Fenton (1997). As such, the industry starts with history, then attempts to map the current period of interest into predefined historical regimes in order to generate return and risk forecasts to serve as inputs in making investment decisions. Based on our experience and observations in the industry, the majority of mapping is done through a combination of largely subjective visual inspection of charts, which is supplemented by simple order statistics. Nevertheless, borrowing terminology from economic theory, we consider the investment industry’s approach to regime switching to be “structural,” as it offers more insights into phases of the economy.

The concept of regimes has been part of mainstream financial theory for more than half of a century. The key financial security in a general equilibrium setting for the financial economy is a state-contingent claim, or what is commonly known as the Arrow-Debreu security. An Arrow-Debreu security pays one dollar if a particular state or regime of the world occurs at a particular point in time, and otherwise pays nothing. With a set of pre-defined regimes, probabilities of the regimes’ occurrence, and discount rates, it is not difficult to see that any financial security, traditional or derivative, with uncertain future payoffs that are conditional on the regimes, can be created and priced as a portfolio of Arrow-Debreu securities. As a result, Arrow-Debreu securities are fundamental building blocks in asset pricing theory. It can be shown that an economy with all regimes spanned by Arrow-Debreu securities will rule out any arbitrage opportunity, and the resulting market is said to be “complete.” While the theory of market completeness is sound, academia’s take on Arrow-Debreu securities remains largely theoretical. For more details, see Ingersoll (1987) and Merton (1994). For information on the feasibility and synthetic creation of these securities, see Chapter 16 in Merton (1994).

The key analytical issue is dating the transitions between phases, especially in periods during which the economy appears to be in an up-and-down range rather than on a distinguishable path.

Based on our experience and observations in the industry, the majority of mapping is done through a combination of largely subjective visual inspection of charts, which is supplemented by simple order statistics.

The key financial security in a general equilibrium setting for the financial economy is a state-contingent claim, or what is commonly known as the Arrow-Debreu security.

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

3Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Much of the academic literature focusing on the empirical implementation of regime switching models has been driven by econometrics. Among the most widely cited studies is the seminal work of Hamilton (1989). In general, studies following this direction relate or define regimes as statistical distributions. For example, Ang and Bekaert (2004) characterize regimes based on episodes of high volatility and unusually high correlations among international equity markets. Transition probabilities from one regime to another are then estimated and the resulting investment opportunity set that is conditional on regimes is then used as inputs to portfolio optimization in deriving optimal asset allocation decisions. The more recent study by Guidolin and Timmermann (2008) finds evidence that joint distribution of stock and bond returns can be characterized by four regimes: crash, slow growth, bull and recovery. Tu (2008) further demonstrates in a similar “bull/bear” Markov switching regime analysis that portfolio decisions in a model that ignores regime switching can result in substantial losses.

It is interesting to note that the academic approach to regime switching is primarily investment driven, focusing on optimal portfolio weights based on estimated transition probabilities among regimes and the resulting expected returns and risk measures. As these regime-switching asset allocation models do not explicitly focus on the structure of the economy, we consider such empirical work to provide “reduced form” models.

As we move further away from 2008 — arguably the most dramatic and challenging year ever for living investors — enduring a global recession, the topic of regime switching remains timely. This paper adds to the literature on several fronts. As discussed above, the existing works from both the industry and academia on regime switching start with a predefined set of regimes and then map the current period of interests into one of those choices. In this paper, we reverse the order of this process, so that the current period of interests, instead of the predefined regimes from history, becomes the focal point. In addition, we argue that every period in history is unique — no two are identical. As a result, regime identification should be probabilistic, so that each historical period can be assigned a probability of being in the same regime with the current period of interest. To some extent, the academic approach of estimating transition probabilities from one regime to another is consistent with our view that this should be approached as a statistical problem.

To that end, we first start with the current period of interests and try to look back in history to identify periods that are probabilistically close to the current period. In doing so, we first briefly review the technique called Locally Weighted Scatter Plot Smoothing (LOWESS), commonly known as Locally Weighted Regression and studied under nonparametric methods (Härdle (1994)). We present several case studies with different sets of what we call regime identifiers. In the first case, we use inflation and growth as identifiers. Through LOWESS, we report the 10 historical periods that have the highest probability of being the closest neighbor to the year 2008. Subsequent inflation and growth of these periods are then analyzed, and can be used as forecasts of subsequent economic activities. In the second case, we introduce asset returns (such as for stocks) as identifiers. If capital markets are forward-looking, we can argue that including asset returns as identifiers will better incorporate market expectations for some macroeconomic identifiers. In the third and last case, we demonstrate how to turn our approach into a regime-forecasting tool; for example, by using a set of variables believed to be considered by NBER in defining turning points, we make dating turning points into a repeatable process.

Existing works from both the industry and academia on regime switching start with a predefined set of regimes and then map the current period of interests. We reverse the order of this process, so that the current period of interests, instead of the predefined regimes from history, becomes the focal point.

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

4Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Loc aLLy WeIghted sc at ter pLot smoothI ng ( LoWess )LOWESS is a local polynomial kernel method developed by Cleveland (1979 and 1988) that robustly fits smoothing functions to data without any assumptions about the form or the shape of these functions. This is achieved by employing lower-order polynomial approximation in a close neighborhood of a point of concern x, where data points that are closer to x are given more importance according to their distance. In our case studies, this explanatory vector x contains macro factors such as inflation and growth that summarize the snapshot of the economy during a particular period of time.

The response, or dependent variable of interest, denoted by y, can be a measure of future macro variables or market returns. In our case studies, y includes inflation, growth and stock returns, among others. Given n observations of y

i (i = 1…n) and k dimensional

independent variables xi= (x

i1,…,x

ik)

(i = 1…n) in the neighborhood of a point x, the aim

is to find the coefficients β of a pth order polynomial P by minimizing

where w(xi,x)

is the weight given to the ith closest neighbor. Here the weight function is

defined with respect to the nth nearest neighbor: Let ρ(x,xi) denote the distance of x

i to x,

and let d(x) denote the distance of nth nearest xi to x, then we have

A lower-order polynomial is desired in order not to introduce variance, especially at boundaries. To keep the analysis simple and transparent, in all of our examples we employ 0th order polynomials. In other words, the regression estimate boils down to taking the weighted average of the n nearest response variables in the neighborhood.

The distance function ρ(x,xi) can be chosen in a variety of ways. If independent variables

are categorical (such as deciles, high/low, etc.) then the city block distance can be intuitive. Otherwise, Euclidean norm can be a sensible choice. More complex distance measures (for example, Mahalanobis measure) can provide additional benefits such as taking into account the covariance between explanatory variables at the expense of introducing additional parameters. In these cases, it may be suggested that a robust principal component analysis is carried out, and data are projected onto the first few principal components, which can then be used as orthogonal explanatory variables. Principal components can also be useful as a tool to reduce the dimension of the design space.

Another important point is the proper scaling of data. In a multivariate analysis, when we have independent variables in different scales, we first need to scale the data before applying any distance measure. To this end, one can either normalize the observations by subtracting their means and dividing by their standard deviation, or by transforming the data to the unit interval by either scaling them with their range or by calculating their empirical percentile levels. In our examples, we followed the latter approach.

Another benefit of this framework is that a priori relative ranking of factors is possible. To this end, when measuring distances between points, one can introduce weights, ν

l,, for

LOWESS is a local polynomial kernel method developed by Cleveland (1979 and 1988) that robustly fits smoothing functions to data without any assumptions about the form or the shape of these functions.

2

1),;(),(Min

n

iiii pxPyxxw

otherwise0)1,0[1)(

)(),(),(

33 uuuK

xdxxKxxw i

i

Another important point is the proper scaling of data. In a multivariate analysis, when we have independent variables in different scales, we first need to scale the data before applying any distance measure.

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

5Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

each independent variable. In the Euclidian case, the distance function between points x = (x

1,…,x

k) and z = (z

1,…,z

k) can be represented as

For example, if the analyst believes market returns track inflation more effectively, then he/she can give more weight to market variables relative to other independent factors. If no ranking preference is present among indicators, ν’s can be set to 1 to recover the usual Euclidian measure.

data se tOur analysis requires a substantial time series of financial and macroeconomic data. This is necessary because regimes, depending on their definition, may last from a few months to a decade or more, and the longer they get, the fewer data points we have for analysis. Due to this limitation, we ruled out a number of macroeconomic indicators such as manufacturing and trade inventories and sales, and personal income less transfer payments, which appear in NBER’s Web site as turning point identifiers.

We compiled data on inflation, industrial production, S&P 500 total returns, nonfarm payrolls and corporate and long-term government bonds. Our S&P 500 and long-term corporate and government bond monthly total returns are from the period of January 1926 through May 20091. Inflation, industrial production and nonfarm payrolls data were obtained from the St. Louis FRED database: Consumer Price Index year-over-year percentage change for all urban consumers (January 1913 – May 2009)2; Industrial Production Index year-over-year percentage change (January 1919 – May 2009)3; Nonfarm Payrolls Index year-over-year percentage change (January 1939 – May 2009)4.

The frequency of the raw data is monthly. However, in order to capture regimes, we aggregate data to an annual frequency, creating monthly overlapping time series of annual geometric returns of S&P 500 and government bonds, and calculating year-over-year changes in the trend-restored CPI, industrial production, and nonfarm payrolls data.

Im pLementat IonLet us denote by the vector x

T the current state of the economy. We first calculate the

weighted distances of each monthly state vector xt (t = 1,2,…,T-1) to x

T and rank them

in ascending order. The distances, as denoted by ρ(xT,x

t), are measured in scaled data

(percentiles) as described above. Because we do not have a priori preference for an economic variable, we always equally weight the components of x

t when measuring the

distances to xT.

Second, we apply a filter to rule out periods that follow each other. If a period ending at time t is selected, any other periods ending in t ± 3 years are dropped from the ranked data to ensure periods belonging to the same regime do not overwhelm the neighborhood during local regression. This way, we always maintain at least two years between selected yearly periods.

1 Source: Ibbotson Associates2 Source: Board of Governors of the Federal Reserve System (CPIAUCNS)3 Source: U.S. Department of Labor’s Bureau of Labor Statistics (INDPRO)4 Source: Bureau of Labor Statistics (PAYEMS)

k

llll zxvzx

1

2),(

Our analysis requires a substantial time series of financial and macroeconomic data, because regimes may last from a few months to a decade or more.

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

6Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Having compiled a neighborhood consisting of 10 nearest periods, we then analyze what happened subsequently. For example, if the year 1930 is the period that most resembles the current period, 2008, we will be interested in knowing what happened during the one-to-three-year period after 1930. Did the inflation increase/decrease or were there corrections in the stock/bond market afterward? We calculate these types of consequent macroeconomic states, and then run weighted regressions for each of these returns or identifiers. Here, the weights are assigned by the tricube kernel and can be thought of as the reoccurrence probability of the associated regime.

These weights can also be used to calculate recession probabilities. For instance, if, in the neighborhood, there are a number of periods associated by NBER with a recession, then the sum of the weights of these recession periods gives us the recession probability for the current environment.

Below we exhibit our results in three cases. First, we will use inflation and industrial production as regime identifiers. Next, we will add asset returns to the analysis, and finally include nonfarm payroll enrollment to proxy NBER’s analysis.

case 1: Inflation and growth as regime IdentifiersWhat defines a regime? If we choose to answer this question in a macroeconomic context, then typically the “usual suspects” are inflation and growth. Payrolls, wages, trades, sales, inventories and many other variables possibly correlate and/or integrate in inflation and growth in low frequencies, thus giving us grounds to simply define a regime with respect to these two indicators.

The question we would like to answer is how the year 2008 compares to previous periods in history in terms of inflation and industrial production growth. The shaded section in Table 1, on the following page, shows the year-over-year percentage changes in CPI and in industrial production. It also has the associated percentiles for the actual values. For example, a 0.09% year-over-year increase in CPI corresponds to the 14th percentile. Similarly -8.86% year-over-year industrial production growth corresponds to the 8th percentile. These two measures, both in actual and in percentile units, tell us that 2008, although not the worst, is one of the worst years in history.

Table 1 also lists 10 periods in history that are closest to 2008 with respect to a weighted Euclidean measure of component percentiles. Here, we equally weighted these indicators when calculating distances. As a result, for example, the period from July 1953 to July 1954 resembles 2008 the most. We also note that there was a recession between July 1953 and May 1954 which partly covers this similar period.

Table 1 further provides us with the tricube kernel-driven probabilities assigned to each of these 10 periods. The first two periods are given almost the same probabilities (13.1%), and these probability measures decrease as periods become less similar (0.14% for the 10th closest neighbor).

As discussed on the prior page, we can also define a recession measure by simply summing the probabilities assigned to recession periods. In Table 1, nine out of 10 similar periods correspond to recessions. The sum of probabilities of these periods equals 96%.

What defines a regime? In a macroeconomic context, the “usual suspects” are inflation and growth.

The question we would like to answer is how the year 2008 compares to previous periods in history in terms of inflation and industrial production growth.

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

7Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Source: Quantitative Investment Group. For illustrative purposes only.

Having identified the similar periods, we may be interested in what happened as a consequence of these periods. Table 2 tabulates the annualized geometric returns of stock and bond markets and annualized changes in the CPI and the industrial production in the subsequent one to three years. For example, after the July 1953 – July 1954 period, S&P 500 returned 47.35% next year, and 20.58% annualized in the next three years. Similarly, CPI decreased 0.37% in the next year and increased at an annualized mean rate of 1.71% in the next three years. In this same period, the industrial production clearly reverted to the mean by achieving 14.56% and 6.68% annualized mean rates in the next one-to-three-years.

Table 2 also shows the summary statistics of the market returns and regime identifiers. Each column in the probability-weighted average row shows the estimate of a weighted polynomial regression of order 0 with kernel calculated weights. In other words, this regression is equivalent to taking the weighted average of the respective column.

For example, the regression estimate for the yearly S&P 500 return can be read as 19.87%. Its associated standard error is 31.41%. For comparison purposes, this table also lists the historical (grand) minimum, maximum and average of each column, calculated using periods that are not included in these 10 similar periods. It is clear that when compared to these averages, the model is pointing to higher-than-expected stock returns and lower-than-expected government bond returns in the year after 2008. Furthermore, lower-than-expected CPI growth and higher-than-expected industrial production are predicted.

tabLe 1: regIme IdentIfIers of current Versus cLosest recessIon

perIods

Regime Regime Identifiers:

Weight % 50% 50%

Rank Probability Start Date End DateCPI

Actual %CPI

PercentileINDPRO Actual %

INDPRO Percentile Recession Periods

Current Dec-07 Dec-08 0.09 14.24 -8.86 8.481 13.10 Jul-53 Jul-54 0.37 15.15 -8.56 8.69 Jul 1953 to May 19542 13.10 Jan-29 Jan-30 0.00 14.04 -7.17 10.61 Aug 1929 to Mar 19333 13.07 May-48 May-49 -0.42 11.82 -6.88 11.01 Nov 1948 to Oct 19494 12.81 Jan-37 Jan-38 0.71 17.27 -26.09 2.12 May 1937 to Jun 19385 12.29 Apr-60 Apr-61 1.01 20.61 -3.65 16.06 Feb 1960 to Feb 19616 12.16 Jan-01 Jan-02 1.14 22.32 -4.16 15.05 Mar 2001 to Nov 20017 11.45 Jan-32 Jan-33 -10.30 1.72 -11.31 6.87 Aug 1929 to Mar 19338 8.25 Apr-44 Apr-45 1.70 32.12 -4.98 13.94 Feb 1945 to Oct 19459 3.64 May-85 May-86 1.48 28.79 0.56 28.9910 0.14 Dec-25 Dec-26 -1.12 9.09 2.47 41.01 Oct 1926 to Nov 1927

Probability of Recession 96.40%

It is clear that when compared to these averages, the model is pointing to higher-than-expected stock returns and lower-than-expected government bond returns in the year after 2008. Furthermore, lower-than-expected CPI growth and higher-than-expected industrial production are predicted.

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

8Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Source: Quantitative Investment Group. The historical performance shown is for illustrative purposes and is not meant to forecast, imply or guarantee future performance.

In Figure 1, we plot the time series of estimated recession probabilities. For each month starting in 1972, we rerun the model using data up until that month and calculate the neighboring weights. The sum of the weights of the neighbors, which are associated with recession periods, are then defined to be that month’s recession probability. In this figure, the height of the bars represents recession probability and shaded areas show the NBER defined recession periods. We have also placed up and down arrows at NBER announcement dates regarding peaks and troughs, respectively.

Figure 1 shows that, although not perfectly matching the NBER dates, the recession probabilities calculated as above rises over 50% and decreases below 50% before announcement dates. We also see that, especially in the mid-1980s, there are two periods in which the model gives false alarms.

tabLe 2: cLosest regImes and subsequent market and economIc

enVIronment

Regime % Annualized Returns % Annualized Regime Identifiers S&P 500 Corp Bond Gov Bond CPI INDPRO

Rank Prob % Start Date End Date 1 Year 3 Years 1 Year 3 Years 1 Year 3 Years 1 Year 3 Years 1 Year 3 YearsCurrent Dec-07 Dec-08

1 13.10 Jul-53 Jul-54 47.35 20.58 0.40 -2.50 -3.36 -2.75 -0.37 1.68 14.56 6.682 13.10 Jan-29 Jan-30 -25.86 -28.19 9.52 7.19 3.97 5.72 -7.28 -9.41 -21.24 -16.833 13.07 May-48 May-49 42.41 27.64 2.34 1.12 4.29 0.94 -0.42 3.38 13.97 8.394 12.81 Jan-37 Jan-38 20.47 3.44 5.96 4.38 5.53 4.94 -1.42 -0.24 18.55 18.965 12.29 Apr-60 Apr-61 2.91 10.25 7.08 4.64 3.55 2.61 1.33 1.21 11.26 7.766 12.16 Jan-01 Jan-02 -23.02 3.24 14.57 10.38 15.01 9.63 2.56 2.47 2.71 2.607 11.45 Jan-32 Jan-33 68.96 33.33 7.34 9.60 1.00 4.58 2.30 2.25 25.50 17.718 8.25 Apr-44 Apr-45 31.74 6.38 4.02 1.31 5.84 1.70 3.32 9.53 -26.23 -3.639 3.64 May-85 May-86 21.12 12.78 5.70 9.21 5.49 8.08 3.78 4.27 4.62 3.86

10 0.14 Dec-25 Dec-26 37.48 21.83 7.44 4.50 8.94 4.08 -2.29 -0.96 -4.82 1.32Prob Weighted Average 19.87 9.55 6.40 4.70 4.42 3.60 -0.09 1.04 5.96 5.33Average 22.35 11.13 6.44 4.98 5.03 3.95 0.15 1.42 3.89 4.68Median 26.43 11.52 6.52 4.57 4.89 4.33 0.48 1.96 7.94 5.27Max 68.96 33.33 14.57 10.38 15.01 9.63 3.78 9.53 25.50 18.96Min -25.86 -28.19 0.40 -2.50 -3.36 -2.75 -7.28 -9.41 -26.23 -16.83Prob Weighted Stdev 31.41 17.92 4.12 4.20 4.84 3.56 3.21 4.69 16.41 10.74Stdev 30.34 17.20 3.91 4.19 4.79 3.57 3.32 4.78 16.89 10.27Grand Average 12.06 10.69 6.08 5.93 5.86 5.55 3.03 3.11 3.82 3.55Grand Min -67.57 -42.35 -18.17 -6.90 -17.10 -6.03 -11.36 -9.99 -33.66 -22.56Grand Max 162.88 43.34 46.74 23.85 54.41 25.42 17.96 11.25 62.04 25.39

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

9Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Source: Quantitative Investment Group. For illustrative purposes only.

case 2: Inflation, growth and asset returns as regime IdentifiersSome may argue that because markets are forward-looking, they discount back all relevant information about the future state of the economy. Therefore, we can expect that prices or returns can identify the current regime, and hence can be used for tracking macroeconomic variables.

In what follows, we rerun the same analysis as in Case 1 but now with the addition of market return data. Here, one can employ a number of assets, or use a portfolio of assets, such as a 60/40 stock/bond mix, as an identifier. Volatility and/or correlation figures can also be related to regimes.

Instead of speculating with regard to what constitutes the best identifier, we simply use yearly S&P 500 total returns as the additional identifier in this section. We avoid the bonds due to their dependence on political agendas. For example, during the Reagan years of the mid-1980s, we experienced high bond returns as a result of a program to alleviate the pain of the early-80s recessions.

In Table 3, we see that most of the recessionary periods picked by the model overlap with the ones in Table 1. Although, in this case, we have eight recession periods (compared to ten in Table 1), the recession probability increases to 99.6%.

Some may argue that because markets are forward looking, they discount back all relevant information about the future state of the economy. Therefore, we can expect that prices or returns can identify the current regime, and hence can be used for tracking macroeconomic variables.

fIgure 1: recessIon probabILItIes WIth IdentIfIers cpI and

IndustrIaL productIon

0.0

0.2

0.4

0.6

0.8

1.0

Aug-09Jun-05Jun-01Jun-97Jun-93Jun-89Jun-85Jun-81Jun-77Jun-73

Recession ProbabilityNBER Recession Periods

Dec 2007 Peak

Nov 2001 Trough

Mar 2001 Peak

Mar 1991 Trough

Jul 1990 Peak

Nov 1982 Trough

Jul 1981 Peak

Jul 1980 Trough

Jan 1980 Peak

CPI Y-o-Y Ch 50.00INDPRO Y-o-Y 50.00

Identifier Weight (%)

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

10Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Source: Quantitative Investment Group. For illustrative purposes only.

Did the inclusion of S&P 500 change the forecasts? Table 4 shows that, although in absolute amounts the forecasts measured by probability-weighted average changed, the direction did not change. The model still predicts a mean reversion in S&P 500 returns and underperformance in government bond returns. Corporate bond returns are very much in line with historical averages. On the macro side, we can see from Table 4 that a low CPI growth rate of 0.07% is predicted, compared to a higher-than-average industrial production growth rate.

Source: Quantitative Investment Group. The historical performance shown is for illustrative purposes and is not meant to forecast, imply or guarantee future performance.

tabLe 3: regIme IdentIfIers of current Versus cLosest recessIon

perIods

Regime Regime Identifiers:Weight % 33% 33% 33%

Rank Probability Start Date End DateS&P 500 Actual %

S&P 500 Percentile

CPI Actual %

CPI Percentile

INDPRO Actual %

INDPRO Percentile Recession Periods

Current Dec-07 Dec-08 -37.00 2.02 0.09 14.24 -8.86 8.481 22.60 Nov-31 Nov-32 -25.27 4.44 -10.76 0.91 -10.92 7.47 Aug 1929 to Mar 19332 20.58 Oct-00 Oct-01 -24.89 4.65 2.10 37.47 -5.23 13.64 Mar 2001 to Nov 20013 17.93 Dec-59 Dec-60 0.46 27.58 1.35 26.16 -6.16 11.92 Feb 1960 to Feb 19614 14.24 Aug-37 Aug-38 -20.05 6.67 -2.80 5.15 -23.13 2.53 May 1937 to Jun 19385 9.92 Jun-48 Jun-49 -9.48 14.75 -0.83 9.29 -8.26 9.29 Nov 1948 to Oct 19496 5.58 Feb-53 Feb-54 7.14 38.48 1.50 28.89 -6.00 12.53 Jul 1953 to May 19547 5.20 Dec-56 Dec-57 -10.79 13.23 2.86 51.21 -6.83 11.11 Aug 1957 to Apr 19588 3.60 Nov-28 Nov-29 -10.48 13.64 0.58 16.26 0.37 27.68 Aug 1929 to Mar 19339 0.29 Jul-92 Jul-93 8.67 41.52 2.74 48.59 2.25 39.6010 0.06 Sep-97 Sep-98 9.06 42.42 1.48 28.69 4.60 55.05

Probability of Recession 99.60%

Did the inclusion of S&P 500 change the forecasts? In absolute amounts the forecasts measured by probability weighted average changed, direction did not change.

tabLe 4: cLosest regImes and subsequent market and economIc

enVIronment

Regime % Annualized Returns: % Annualized Regime Identifiers S&P 500 Corp Bond Gov Bond CPI INDPRO

Rank Prob % Start Date End Date 1 Year 3 Years 1 Year 3 Years 1 Year 3 Years 1 Year 3 Years 1 Year 3 YearsCurrent Dec-07 Dec-08

1 22.60 Nov-31 Nov-32 58.66 31.57 9.11 11.47 2.40 5.11 0.00 1.48 16.13 16.332 20.58 Oct-00 Oct-01 -15.11 3.91 8.06 8.80 6.21 6.62 2.01 2.39 2.03 2.133 17.93 Dec-59 Dec-60 26.89 12.45 4.82 4.96 0.97 2.99 0.67 1.21 12.53 7.564 14.24 Aug-37 Aug-38 -2.93 0.60 1.97 4.59 6.16 5.16 -2.15 1.78 19.07 21.855 9.92 Jun-48 Jun-49 34.42 29.64 1.72 0.89 2.32 0.40 -0.42 3.38 17.60 8.126 5.58 Feb-53 Feb-54 47.52 23.35 0.45 -0.55 0.45 0.09 -0.75 0.96 7.72 6.977 5.20 Dec-56 Dec-57 43.37 17.27 -2.22 1.84 -6.11 1.45 1.75 1.60 5.37 2.478 3.60 Nov-28 Nov-29 -16.91 -27.56 11.05 5.69 4.44 4.24 -5.34 -9.05 -22.51 -16.999 0.29 Jul-92 Jul-93 5.19 15.62 -1.62 5.46 -3.00 5.14 2.73 2.79 5.63 4.9410 0.06 Sep-97 Sep-98 27.79 2.04 -5.92 4.72 -8.32 4.87 2.59 2.87 3.70 0.99Prob Weighted Average 22.30 14.45 5.33 6.32 2.96 4.08 0.05 1.45 10.69 9.32Average 20.89 10.89 2.74 4.79 0.55 3.61 0.11 0.94 6.73 5.44Median 27.34 14.03 1.85 4.84 1.65 4.55 0.33 1.69 6.67 5.96Max 58.66 31.57 11.05 11.47 6.21 6.62 2.73 3.38 19.07 21.85Min -16.91 -27.56 -5.92 -0.55 -8.32 0.09 -5.34 -9.05 -22.51 -16.99Prob Weighted Stdev 28.47 14.44 3.66 3.83 3.06 2.13 1.68 2.14 8.90 8.52Stdev 26.76 17.36 5.45 3.57 4.96 2.26 2.48 3.60 11.94 10.25Grand Average 12.06 10.69 6.08 5.93 5.86 5.55 3.03 3.11 3.82 3.55Grand Min -67.57 -42.35 -18.17 -6.90 -17.10 -6.03 -11.36 -9.99 -33.66 -22.56Grand Max 162.88 43.34 46.74 23.85 54.41 25.42 17.96 11.25 62.04 25.39

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

11Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Source: Quantitative Investment Group. For illustrative purposes only.

Figure 2 above replicates Figure 1 with the addition of S&P 500 returns as an identifier. We can observe that with S&P 500 returns, the model aligns better with the starts and ends of NBER recessions. However, although diminished in size, the mid-1980s false alarm still persists.

Because returns introduce more volatility, Figure 2 is more rugged than Figure 1. However, one can apply a few months moving average to smooth the probability data. By this way, while still keeping correct identifications in NBER recession periods, one can remove the false alarms in mid-1980s and mid-1990s.

case 3: quantifying the nber turning points dating processAccording to NBER’s Web site, one of the indicators watched in dating business cycles is nonfarm payrolls data, which consist of the total number of paid U.S. workers (excluding employees involved in farming-related areas). Because of their political implications, such data can be linked to the Federal Reserve’s actions on interest rates: On one hand, an increase in these data means rising employment, which may result in higher inflation and, hence, increases in interest rates. On the other hand, a decrease may suggest a route towards recession and lead to possible interest rate cuts.

In Table 5, we list the 10 neighboring “regimes” closest to 2008. Because the nonfarm payroll data started in 1940, earlier years have been dropped from the analysis. Even with the exclusion of the Great Depression and other recessionary periods in the 1920s and

fIgure 2: recessIon probabILItIes IdentIfIers cpI, IndustrIaL

productIon and s&p 500

0.0

0.2

0.4

0.6

0.8

1.0

Aug-09Jun-05Jun-01Jun-97Jun-93Jun-89Jun-85Jun-81Jun-77Jun-73

Recession ProbabilityNBER Recession Periods

Dec 2007 Peak

Nov 2001 Trough

Mar 2001 Peak

Mar 1991 Trough

Jul 1990 Peak

Nov 1982 Trough

Jul 1981 Peak

Jul 1980 Trough

Jan 1980 Peak

S&P 500 Year 33.33CPI Y-o-Y Ch 33.33INDPRO Y-o-Y 33.33

Identifier Weight (%)

According to NBER, one of the indicators watched in dating business cycles is nonfarm payrolls data.

An increase in these data means rising employment, which may result in higher inflation and, hence, increases in interest rates. On the other hand, a decrease may suggest a route towards recession and lead to possible interest rate cuts.

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

12Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

30s, the model finds many other recessionary periods, leading to a recession probability for 2008 that is quite high.

Source: Quantitative Investment Group. For illustrative purposes only.

Table 6 confirms that our projection for outperformance in stocks and underperformance in government bonds remain the case. Again, CPI growth is predicted to be near zero for 2009 and industrial production is expected to grow at an above-average rate. The included nonfarm payroll growth rate is below normal for the 2009 and about normal for the next three years.

Source: Quantitative Investment Group. The historical performance shown is for illustrative purposes and is not meant to forecast, imply or guarantee future performance.

tabLe 5: regIme IdentIfIers of current Versus cLosest

Regime Regime Identifiers: Weight % 25% 25% 25% 25%

RankProb % Start Date End Date

S&P 500 Actual

S&P 500 Percentile

CPI Actual

CPI Percentile

INDPRO Actual

INDPRO Percentile

NONFARM Actual

NONFARM Percentile Recession Periods

Current Dec-07 Dec-08 -37.00 0.72 0.09 4.44 -8.86 3.96 -2.20 6.481 21.29 Jun-48 Jun-49 -9.48 11.64 -0.83 1.44 -8.26 4.80 -2.90 3.72 Nov 1948 to Oct 19492 21.25 Jan-01 Jan-02 -16.14 4.44 1.14 12.97 -4.16 10.92 -1.40 10.92 Mar 2001 to Nov 2001 3 19.77 Dec-52 Dec-53 -0.98 22.93 0.75 8.64 -4.78 9.96 -0.90 14.17 Jul 1953 to May 19544 18.75 Dec-59 Dec-60 0.46 25.09 1.35 17.29 -6.16 7.68 -0.80 14.65 Feb 1960 to Feb 19615 13.96 Dec-56 Dec-57 -10.79 10.20 2.86 44.54 -6.83 6.72 -1.00 13.57 Aug 1957 to Apr 19586 3.85 Oct-43 Oct-44 13.02 51.26 1.71 24.37 1.64 34.09 -2.30 6.247 0.62 Aug-91 Aug-92 7.95 38.54 3.10 49.70 2.57 40.94 0.60 26.778 0.43 Aug-69 Aug-70 -11.39 9.12 5.26 75.87 -3.83 11.52 -0.10 20.77 Dec 1969 to Dec 19709 0.07 Jul-81 Jul-82 -13.39 6.12 6.24 81.87 -6.37 7.32 -2.30 6.24 Jul 1981 to Nov 198210 0.02 Dec-85 Dec-86 18.47 64.59 1.09 11.76 1.45 32.17 1.90 43.10

Probability of Recession 96%

tabLe 6: cLosest regImes and subsequent market and economIc

enVIronment

Regime % Annualized Returns: % Annualized Regime Identifiers: S&P 500 Corp Bond Gov Bond CPI INDPRO NONFARM

Rank Probability Start Date End Date 1 Year 3 Years 1 Year 3 Years 1 Year 3 Years 1 Year 3 Years 1 Year 3 Years 1 Year 3 YearsCurrent Dec-07 Dec-08

1 21.29 Jun-48 Jun-49 34.42 29.64 1.72 0.89 2.32 0.40 -0.42 3.38 17.60 8.12 3.10 3.372 21.25 Jan-01 Jan-02 -23.02 3.24 14.57 10.38 15.01 9.63 2.56 2.47 2.71 2.60 -0.20 0.503 19.77 Dec-52 Dec-53 52.62 28.85 5.39 -0.44 7.18 -0.04 -0.75 0.84 3.54 6.60 -0.70 2.144 18.75 Dec-59 Dec-60 26.89 12.45 4.82 4.96 0.97 2.99 0.67 1.21 12.53 7.56 2.10 2.205 13.96 Dec-56 Dec-57 43.37 17.27 -2.22 1.84 -6.11 1.45 1.75 1.60 5.37 2.47 -0.60 0.846 3.85 Oct-43 Oct-44 36.35 11.49 4.41 2.03 7.99 4.01 2.23 8.62 -30.76 -5.68 -7.50 2.107 0.62 Aug-91 Aug-92 15.14 13.82 16.22 8.64 22.79 10.06 2.73 2.72 2.78 4.56 2.10 2.608 0.43 Aug-69 Aug-70 25.51 11.92 17.28 8.91 18.19 7.67 4.51 4.83 0.03 6.16 0.60 2.859 0.07 Jul-81 Jul-82 59.40 27.12 28.85 21.20 20.14 18.09 2.43 3.35 3.01 3.99 1.00 2.9210 0.02 Dec-85 Dec-86 5.23 17.36 -0.27 8.67 -2.72 8.01 4.34 4.40 7.23 3.34 3.10 2.66

Prob Weighted Average 25.58 18.05 5.49 3.68 4.97 3.15 0.80 2.23 6.96 5.19 0.52 1.89Average 27.59 17.32 9.08 6.71 8.58 6.23 2.01 3.34 2.40 3.97 0.30 2.22Median 30.65 15.55 5.10 6.80 7.58 5.84 2.33 3.03 3.28 4.27 0.80 2.40Max 59.40 29.64 28.85 21.20 22.79 18.09 4.51 8.62 17.60 8.12 3.10 3.37Min -23.02 3.24 -2.22 -0.44 -6.11 -0.04 -0.75 0.84 -30.76 -5.68 -7.50 0.50Prob Weighted Stdev 26.72 10.31 5.54 3.99 6.87 3.68 1.32 1.59 9.56 3.21 2.23 1.04Stdev 24.11 8.68 9.79 6.41 10.07 5.61 1.77 2.27 12.79 3.94 3.08 0.91Grand Average 12.06 10.69 6.08 5.93 5.86 5.55 3.94 3.96 3.98 3.47 2.20 2.04Grand Min -67.57 -42.35 -18.17 -6.90 -17.10 -6.03 -2.91 0.12 -33.66 -9.70 -7.60 -2.54Grand Max 162.88 43.34 46.74 23.85 54.41 25.42 17.96 11.25 31.67 22.39 16.30 10.39

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

13Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Source: Quantitative Investment Group. For illustrative purposes only.

In a comparison to Figure 1 and 2, Figure 3 above shows that recession probabilities now match the starting points of NBER recessions more accurately. However, especially after the 1990s, we observe that the probabilities do not decrease as quickly after recessions. This is because the recovery in nonfarm payroll data is slower than in earlier recessions (see Figure 4). This suggests that inclusion of second-order lags may be useful in capturing information about growth/decline periods as well as the value levels within a series.

fIgure 3: recessIon probabILItIes WIth IdentIfIers cpI, IndustrIaL

productIon, s&p 500 and nonfarm payroLLs

0.0

0.2

0.4

0.6

0.8

1.0

Aug-09Jun-05Jun-01Jun-97Jun-93Jun-89Jun-85Jun-81Jun-77Jun-73

Recession ProbabilityNBER Recession Periods

Dec 2007 Peak

Nov 2001 Trough

Mar 2001 Peak

Mar 1991 Trough

Jul 1990 Peak

Nov 1982 Trough

Jul 1981 Peak

Jul 1980 Trough

Jan 1980 Peak

S&P 500 Year 25.00CPI Y-o-Y Ch 25.00

INDPRO Y-o-Y 25.00NONFARM 25.00

Identifier Weight (%)

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

14Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Source: U.S. Department of Labor: Bureau of Statistics. For illustrative purposes only.

conc Lus IonLow frequency macroeconomic forecasting that includes dating business cycles and identifying regime changes has received increasing attention from investors and policymakers. As a result, today, we have at our disposal a variety of approaches that seek to address the regime identification issue as well as its impact on asset allocation.

To tackle this problem, traditional analyses in the literature have employed complex econometric tools in which unobserved state variables augment autoregressive processes to better approximate the nonlinearities in the data. Given their “black-box” nature and the difficulty of replication due to subjective prior distributions and lack of global optimization routines for parameter estimations, these models have been limited to academic use.

On the other hand, as noted above, the mainstream industry approach to the regime problem has been structural. Investment advisers tended to rely on charts and visual inspection to extract patterns from historical episodes. The lack of scientific evidence and a track record to support regime-related propositions has been a major disadvantage, although the analyses and accompanying explanations have often seemed quite convincing.

In this paper, our aim was to offer an alternative quantitative procedure which is practical and which can be tailored for a variety of purposes in macroeconomic analysis. To this end, we employed a kernel method called locally weighted scatter plot smoothing. This method allowed us to rank historical periods that statistically resemble a current period according to their similarity measured by a weighted distance. These similar periods in history then can constitute the support for future extrapolations.

We demonstrated the procedure in a number of cases. First, inflation and growth were used as regime identifiers. Second, we added asset returns to extract the message in information-discounted market prices. Finally, we included a lagging indicator watched by NBER to measure the performance in a turning-point dating process.

fIgure 4: totaL nonfarm payroLLs

-10

-5

0

5

10

15

20

20102000199019801970196019501930 1940

Perc

ent

Ch

ang

e fr

om

a Y

ear

Ag

o

Change in Non-Farm PayrollsNBER Recession Periods

Identifying regime changes has received increasing attention from investors and policymakers. As a result, we have at our disposal a variety of approaches that seek to address the regime identification issue as well as its impact on asset allocation.

Given their “black-box” nature and the difficulty of replication due to subjective prior distributions and lack of global optimization routines for parameter estimations, these models have been limited to academic use.

In this paper, our aim was to offer an alternative quantitative procedure which is practical and which can be tailored for a variety of purposes in macroeconomic analysis. To this end, we employed a kernel method called locally weighted scatter plot smoothing.

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

15Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

Further research can be focused in a number of directions. For example, one might employ additional time-dependent weights in local regressions to introduce dynamic adaptation. In our context, this could make the 1930s era less similar to the current period as policymakers have more tools to fight recessions. Another approach, for business cycle dating purposes, would be to generate a routine for the supervised training of the model — i.e., the weights in the distance measure could be optimized to match NBER turning points.

ac knoWLedgmentWe would like to thank the Teacher Retirement System of Texas Strategic Partnership Network for initiating this research project. We are grateful for helpful comments from John Mulvey and the members of the Quantitative Investment Group at Neuberger Berman. This article reflects the views of the authors and does not reflect the official views of the authors’ employer, Neuberger Berman.

referenc es :Ang, Andrew, and Geert Bekaert, “How Regimes Affect Asset Allocation,” Financial Analyst Journal, Vol. 60, No. 2, Mar./Apr. 2004: 86 – 99.

Chauvet, Marcelle, and Jeremy Piger, “A Comparison of the Real-Time Performance of Business Cycle Dating Methods,” Journal of Business and Economic Statistics, 26, 2008: 42 – 49.

Cleveland, William S., and Susan J. Devlin, “Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting,” Journal of the American Statistical Association, Vol. 83, No. 403, Sep. 1988: 596 – 610. http://www.jstor.org/stable/2289282

Cleveland, W. S., “Robust locally weighted regression and smoothing scatter plots”, J. Amer. Statist. Assoc. 74(368): 829 – 836.

Guidolin, Massimo, and Allan G. Timmermann, “Asset Allocation Under Multivariate Regime Switching,” Journal of Economic Dynamics and Control, Vol. 31, No. 11, 2007: 3503 – 3544.

Hamilton, James D., “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle,” Econometrica, Vol. 57, No. 2, March 1989: 351 – 384

Härdle, Wolfgang, Applied Nonparametric Regression (Econometric Society Monographs), 1992, Cambridge University Press.

Ingersoll, Jonathan E., Theory of Financial Decision Making, Rowman & Littlefield, Maryland, 1987.

Krugman, Paul, The Return of Depression Economics and the Crisis of 2008, W. W. Norton, 2008.

Merton, Robert C., Continuous-Time Finance, Blackwell Publishers, Cambridge, MA, 1994.

Strongin, Steve, Melanie Petsch, and Colin Fenton, “Global Equity Portfolios and the Business Cycle,” Global Portfolio Analysis, Goldman Sachs working paper, April 7, 1997.

Tu, Jun, “Is Regime Switching in Stock Returns Important in Asset Allocations?” EFA 2008 Athens Meetings Paper, June 2008. Available at SSRN: http://ssrn.com/abstract=1028445.

regImes: nonparametrIc IdentIfIcatIon and forecastIng (continued)

16Note: Opinions expressed herein are subject to change without notice. Past performance is not indicative of future results.

CONTACT INFORMATION

Hakan Kaya, Ph.D.212.476.5667hakan.kaya@nb.com

Wai Lee, Ph.D.212.476.5668wai.lee@nb.com

Bobby Pornrojnangkool, Ph.D.212.426.5673bobby.pornrojnangkool@nb.com

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