Forecasting Business and Stock Market Cycles and Industry ... · About Us Founded in January 2013....
Transcript of Forecasting Business and Stock Market Cycles and Industry ... · About Us Founded in January 2013....
Forecasting Business and Stock Market Cycles and Industry Growth
Robert Lamy www.theforecastingadvisor.com
Presentation at the Department of Finance Canada
February 20th, 2014
About Us Founded in January 2013.
Develop models to forecast reversals in the stock market cycle in the U.S, reversals in the business cycle in the U.S. and Canada, and real GDP and employment growth by industry in Canada.
Five monthly Reports:
− Outlook on the business cycle in the U.S. for next three months
− Outlook on the business cycle in Canada for next three months
− Outlook on the stock market cycle in the U.S. for next two months
− Real GDP outlook for 35 industries in Canada for current and next year
− Employment outlook for 32 industries in Canada for current and next year.
A research paper is associated with each Report. The research papers can be obtained free from the website.
U.S. Business Cycle Model
Model The U.S. business cycle is characterised by two phases: expansion and recession.
The static probit modeling approach is used to calculate the probability of a reversal in the U.S. business cycle between expansion and recession phases. Lagged values of the state of the business cycle or (and) lagged values of the probability function is (are) not included in the model.
The model is estimated with monthly data from January 1962 and it includes a number of U.S. economic indicators, such as building permits, initial claims, consumer sentiment, and the yield curve.
The predicted outcome for the business cycle is determined using the usual 50% threshold:
- When the economy is an expansion, the model predicts a reversal to a recession if the probability is equals to or exceeds 50%.1 Otherwise, the model predicts that the expansion will continue.
- When the economy is a recession, the model predicts a reversal to an expansion if the probability is equals to or falls below 50%.1 Otherwise, the model predicts that the recession will continue.
Figure 1 (next slide) illustrates the monthly evolution of the probability of the U.S. being in a recession (identified by the blue line) along with the recession periods (grey shaded areas).
1. It is possible that an increase (decline) in the probability to above (below) 50% could be explained by a limited number of the model’s predictive variables. When the model signals of a reversal in the business cycle, the source of the change in the probability is investigated in order to reduce the risk of a false alarm.
Source: The Forecasting Advisor. 1. The in-sample probability were computed with the one-month ahead probit model. Shaded areas indicate recessions, as
dated by the NBER.
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100
1962M01 1968M01 1974M01 1980M01 1986M01 1992M01 1998M01 2004M01 2010M01
Figure 1: Probability of the U.S. Being in a Recession1: January 1962 - December 2013 (probability, %)
Source: The Forecasting Advisor. Shaded areas indicate recessions.
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100
1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 2012
U.S. business cycle model Yield curve Yield curve & stock market returns
Figure 2: Probability of the U.S. Being in a Recession: U.S. Business Cycle Model Versus Two Well-Know Specifications (probability, %)
50% threshold
Model McFadden R-square
Model 0.89
Alternative probit models: Yield curve Yield curve + stock market returns Kauppi & Saikkonen (2008) Wright (2006) Nyberg (2013) Kauppi (2008)
0.32 0.40
0.20 to 0.582 0.22 to 0.50
0.29 to 0.842 0.23 to 0.682
Prediction Evaluation (Success rate based on the 50% rule) In-Sample3 Out-of-Sample4
Predicted / Total Recession Months 78 / 83 (94%)
24 / 24 (100%)
Predicted / Total Expansion Months 529 / 536 (99%)
251 / 259 (97%)
Table 1 Some Key Probit Estimation Output for the
U.S. Business Cycle Model 1
1. The results for the U.S. business cycle model are from the one-month ahead probability model. 2. The highest values are obtained with autoregressive and dynamic and autoregressive probit models. 3. Based on an estimation period of January 1962 to July 2013. 4. Based on an estimation period of January 1962 to December 1989. The out-of-sample starts in January 1990.
Business Cycle Reference Dates2
Lead (-) / Lag(+) in Predicting the Start
of the Recession (in months)
Lead(-) / Lag(+) in Predicting the Start
of the Expansion (in months) Peak Trough
December 1969 November 1970 +1 0
November 1973 March 1975 +1 0
January 1980 July 1980 -2 0
July 1981 November 1982 -1 -1
July 1990 March 1991 0 +1
March 2001 November 2001 -1 +1
December 2007 June 2009 -1 0
Average -0.43 +0.14
Table 2 Performance of the Model in Predicting the Reversals
in the Business Cycle in the U.S. since 19621
1. The results are based on the one-month ahead probability model. 2. The reference dates are from the NBER.
Source: The Forecasting Advisor. 1. In-sample probabilities from the one-month ahead probability model.
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2007
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50% threshold
Figure 3: Probability of the U.S. Being in a Recession: 2008-2009 Episode1 (%)
Peak of the expansion in December 2007
Trough of the recession in June 2009
Signal with a lead of one month the start of
a recession
Signal with no lead/lag the start of an
expansion
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2002
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2002
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2002
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2002
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.Oct
2002
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2002
.Dec
Figure 4: Probability of the U.S. Being in a Recession: 2001 Episode1 (%)
Peak of the expansion in March 2001
Trough of the recession in
November 2001
Signal with a lag of one month the start of an
expansion
Signal with a lead of one month the start of a
recession
50% threshold
Source: The Forecasting Advisor. 1. In-sample probabilities from the one-month ahead probability model.
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1990
.Jan
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.May
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.Jul
1991
.Aug
1991
.Sep
1991
.Oct
1991
.Nov
1991
.Dec
Figure 5: Probability of the U.S. Being in a Recession: 1990-1991 Episode1 (%)
Peak of the expansion in
July 1990
Trough of the recession in March 1991
Signal with a lag of one month the start of an
expansion
Signal with no lead/lag the start of a recession
50% threshold
Source: The Forecasting Advisor. 1. In-sample probabilities from the one-month ahead probability model.
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1981
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.Dec
Figure 6: Probability of the U.S. Being in a Recession: 1981-1982 Episode1 (%)
Peak of the expansion in
July 1981 Trough of the recession
in November 1982
Signal with a lead of one month the start of an
expansion
Signal with a lead of one month the start of a
recession
50% threshold
Source: The Forecasting Advisor. 1. In-sample probabilities from the one-month ahead probability model.
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1979
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.Nov
Figure 7: Probability of the U.S. Being in a Recession: 1980 Episode1 (%)
Peak of the expansion in January 1980
Trough of the recession in July 1980
Signal with no lead/lag the start of
an expansion
Signal with a lead of two months the start
of a recession
50% threshold
Source: The Forecasting Advisor. 1. In-sample probabilities from the one-month ahead probability model. .
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Figure 8: Probability of the U.S. Being in a Recession: 1973-1975 Episode1 (%)
Peak of the expansion in November 1973
Trough of the recession in March 1975
Signal with no lead/lag the start of an
expansion
Signal with a lag of one month the start
of a recession
50% threshold
Source: The Forecasting Advisor. 1. In-sample probabilities from the one-month ahead probability model.
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Figure 9: Probability of the U.S. Being in a Recession: 1969-1970 Episode1 (%)
Peak of the expansion in December 1969
Trough of the recession in November 1970
Signal with no lead/lag the start of
an expansion
Signal with a lag of one month the start of
a recession
50% threshold
Source: The Forecasting Advisor. 1. In-sample probabilities from the one-month ahead probability model.
Out-of-Sample Forecasting Performance
Source: The Forecasting Advisor. 1. The out-of-sample probabilities are computed with coefficients of the model estimated from January1962 to December 1989. In-sample probabilities are computed from January 1962 to December 2012. * The shaded areas correspond to recessions.
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1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012
Recession periods* In-sample probability Out-of-sample probability
Figure 10: Probability of the U.S. Being in a Recession: In- and Out-of-Sample Probabilities from January 1990 to December 20121 (%)
50% threshold
Source: The Forecasting Advisor. 1. The out-of-sample probabilities are computed with coefficients of the model estimated from January1962 to December 1989. In-sample probabilities are computed from January 1962 to December 2012. * The shaded areas correspond to recessions.
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1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012
US business cycle model Yield curve Yield curve & stock market returns
Figure 11: Probability of the U.S. Being in a Recession: Out-of-Sample Probabilities from Three Models1 (%)
50% threshold
Outlook on the Business Cycle in the U.S.
Model's Forecast
Phase of the Business Cycle
Actual Outlook1
January 2014
February 2014
March 2014
April 2014
Expansion
Probability of Being in a Recession 0.0% 0.0% 0.0%
Predicted Outcome for the Business Cycle
Expansion to continue
Expansion to continue
Expansion to continue
1. The probabilities for February, March and April were computed on February 7, 2014.
Source: The Forecasting Advisor.
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2013
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2013
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2014
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Probability of the U.S. Being in a Recession (%)
Peak of expansion in
December 2007
Trough of recession in June 2009
Probabilities of 0% for February, March and April do
not suggest an oncoming recession
50% threshold
Signal a reversal to a recession Signal a reversal
to an expansion
Canadian Business Cycle Model
1. It is possible that one or very few explanatory variables of the model could explain the probability from rising from below to above 50%. In the future, when the model will give a signal of a reversal in the business cycle, the source of the change will be investigated in order to reduce as much as possible the risk of a making false signal.
Model In the model, the Canadian business cycle is characterised by two phases: an expansion or a recession.
The static probit modeling approach is used to calculate the probability of a reversal in the Canadian business cycle between expansion and recession phases. Lagged values of the state of the business cycle or (and) lagged values of the probability function is (are) not included in the model.
The model includes a number of economic indicators for Canada, such as building permits, new orders, consumer confidence, and the yield curve.
The probability is calculated for a forecast horizon of one to three months. - For example, on September 17, 2013, we calculated a probability for the months of August,
September, and October. The predicted outcome for the state of the economy is determined using the usual 50% threshold:
- When an expansion exists, the model predicts a reversal to a recession if the probability is equal or greater than 50%.1 Otherwise, the model predicts that the expansion will continue.
- When a recession exists, the model predicts a reversal to an expansion if the probability is equal or less than 50%.1 Otherwise, the model predicts that the recession will continue.
Figure 1 (next slide) illustrates the monthly evolution of the probability for Canada of being in a recession (identified by the blue line) along with the recession periods (grey shaded areas) since January 1962.
Source: The Forecasting Advisor. Last data point: December 2012. 1. One-month ahead probability. * See Table 1 for the reference dates for the business cycle. The shaded areas correspond to the recessions.
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1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 2012
Figure 1: Probability for Canada of Being in a Recession1: 1962-2012 (probability, %)
50% threshold
Business Cycle Reference Dates2
Lead (-) / Lag(+) in Predicting the Start
of the Recession (in months)
Lead(-) / Lag(+) in Predicting the Start of the Expansion
(in months) Peak Trough
December 1974 March 1975 0 0
January 1980 June 1980 0 0
June 1981 October 1982 0 -1
March 1990 March 19913 0 0
October 2008 May 2009 0 0
Average 0 -0.2
Table 1 Forecasting the Reversals in
the Business Cycle in Canada since 19621
1. The results are based on the one-month ahead probability model. 2. The reference dates for the business cycle are from the C.D. Howe Institute (see Cross, P. and Bergevin, P., “Turning Points:
Business Cycles in Canada since 1926”, Commentary No. 366, October 2012. 3. We assumed that the 1990-1991 recession ended in March 1991 as quarterly real GDP began to recover in the second quarter of
1991, albeit at a modest pace, and total employment grew between the economic trough of March 1991 and most of the rest of 1991. Moreover, Cross (1996) stated that the recession ended in the first quarter of 1991.
In-Sample Forecasting Performance
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Figure 2: Probability for Canada of Being in a Recession : 2008-20091 (probability, %)
Peak of the expansion in October 2008
Trough of the recession in May 2009
Signal with no lead/lag the start of
the expansion Signal with no lead/lag
the start of the recession
50% threshold
Source: The Forecasting Advisor. 1. One-month ahead probability.
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Figure 3: Probability for Canada of Being in a Recession : 1990-19911 (probability, %)
Peak of the expansion in March1990
Trough of the recession in March
1991
Signal with no lead/lag the start of
the expansion
Signal with no lead/lag the start of
the recession
Source: The Forecasting Advisor. 1. One-month ahead probability.
50% threshold
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Figure 4: Probability for Canada of Being in a Recession : 1981-19821 (probability, %)
Peak of the expansion in June 1981
Trough of the recession in October1982
50% threshold
Signal with a lead of one month the start
of the expansion
Signal with no lead/lag the start of the
recession
Source: The Forecasting Advisor. 1. One-month ahead probability.
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Figure 5: Probability for Canada of Being in a Recession : 19801 (probability, %)
Peak of the expansion in January 1980
Trough of the recession in June
1980
Signal with no lead/lag the start of the
expansion
Signal with no lead/lag the start of the
recession
50% threshold
Source: The Forecasting Advisor. 1. One-month ahead probability.
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Figure 6: Probability for Canada of Being in a Recession : 19751 (probability, %)
Peak of the expansion in
December 1974 Trough of the recession in March 1975
50% threshold
Signal with no lead/lag the start of
the expansion
Signal with no lead/lag the start of the
recession
Source: The Forecasting Advisor. 1. One-month ahead probability.
Out-of-Sample Forecasting Performance
Source: The Forecasting Advisor. 1. The out-of-sample probabilities are computed with coefficients of the model estimated from January1962 to December 1999. In-sample probabilities are computed from January 1962 to December 2012.
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2000 2002 2004 2006 2008 2010 2012
In-sample probability
Out-of-sample probability
Figure 7: Probability for Canada of Being in a Recession: In- and Out-of-Sample Probabilities from January 2000 to December 20121 (probability, %)
50% threshold
Outlook on the Business Cycle in Canada
Model's Forecast
Phase of the Business Cycle
Actual Outlook1
December 2013
January 2014
February 2014
March 2014
Expansion
Probability of Being in a Recession 0.0% 0.0% 0.0%
Predicted Outcome for the Business Cycle
Expansion to continue
Expansion to continue
Expansion to continue
1. The probabilities for February, March and April were computed on February 14, 2014.
Source: The Forecasting Advisor.
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Probability for Canada Being in a Recession1 (%)
Peak of the expansion in
October 2008 Trough of the recession in May 2009
Probabilities of 0% for January, February and March do not
suggest an oncoming recession
50% threshold
Signal in November a reversal to a
recession
Signal in May a reversal to an
expansion
U.S. Stock Market Cycle Model
Introduction
In contrast to forecasting the business cycle, there is only two studies to the best of our knowledge that have looked at the issue of forecasting the state of the stock market cycle in the U.S.
The first study is from Chen (2009) and he evaluated the information content of various economic indicators in forecasting U.S. bear markets. With a static probit model, he showed that the yield curve and the inflation rate are the best predictors. Other good predictors are the unemployment rate, short-term interest rates, and industrial production.
The second study is from Nyberg (2013). His results showed that the state of the U.S. stock market cycle is predictable in- and out-of-sample, but only when the lagged values of the state of the stock market cycle or (and) lagged values of the probability function is (are) included in the model. In other words, the autoregressive and dynamic autoregressive probit models outperform a static probit model in forecasting U.S. bear and bull markets.
The model The U.S. stock market is benchmarked with the S&P 500 index and the stock market is
characterised by two phases: a bull or a bear market.
The traditional probit modeling approach is used to calculate the probability of a reversal in the stock market cycle between bear and bull phases. Lagged values of the state of the stock market cycle or (and) lagged values of the probability function is (are) not included in the model.
The model, which is estimated with monthly data from January 1964, includes a number of U.S. economic indicators, such as production, the unemployment rate and the inflation rate.
The predicted outcome for the U.S. stock market is determined using the usual 50% threshold: - When a bull market exists, the model predicts a reversal to a bear market if the probability is
equal to or exceeds 50%.1 Otherwise, the model predicts that the bull market will continue. - When a bear market exists, the model predicts a reversal to a bull market if the probability is
equal to or falls below 50%.1 Otherwise, the model predicts that the bear market will continue.
Figure 1 (next slide) illustrates the monthly evolution of the probability of the S&P 500 index being in a bear market (blue line), the bear market periods (grey shaded areas) and the level of the S&P 500 (red line) since January 1964.
1. It is possible that an increase (decline) in the probability to above (below) 50% could be explained by a limited number of the model’s explanatory variables. In the future, when the model signals a reversal in the state of the stock market cycle, the source of the change in the probability will be investigated in order to reduce the risk of a false alarm.
Sources: Federal Reserve Bank of St-Louis Fred Database (S&P 500 index) and The Forecasting Advisor (probability). 1. In-sample probabilities from the one-month ahead regression probit model. * See Table 1 for reference dates for the stock market cycle.
3.0
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Bear market periods* Probability (left scale) S&P 500 Index (right scale)
Figure 1: Probability of the S&P 500 Index Being in a Bear Market1: 1964-2012 probability, in % log of S&P 500
50% threshold
Model McFadden R-square
U.S. Stock Market Cycle Model 0.79
Alternative probit models: Chen (2009) Nyberg (2013)
0.006 to 0.1032
0.041, 0.135, 0.4123, 0.8073
Prediction Evaluation (Success rate based on the 50% rule) In-Sample4 Out-of-Sample5
Predicted / Total Bear Market Months 126 / 139 (91%)
35 / 43 (81%)
Predicted / Total Bull Market Months 446 / 456 (98%)
82 / 89 (92%)
Table 1 Some Key Probit Estimation Output for the
U.S. Stock Market Cycle Model 1
1. The results are from the one-month ahead probability model. 2. Based on the static probit model approach. 3. The last two values comes from an autoregressive and a dynamic/autoregressive probit model. 4. Based on an estimation period of January 1962 to July 2013. 5. Based on an estimation period of January 1962 to December 1999. Out-of-sample from January 2000 to December 2010.
Actual start of the
bull market1
Signal of a shift to a
bull market2
# of months before (-) or after (+) the actual start of a
bull market Nov. 1966 Nov. 1966 0
Jul. 1970 Sep. 1970 +2
Jan. 1975 Jan. 1975 0
Apr. 1978 Dec. 1977 -4
Aug. 1982 May 1982 -3
Jan. 1988 Feb. 1988 +1
Nov. 1990 Dec. 1990 +1
Nov. 2002 Jun. 2002 -5
Apr. 2009 Apr. 2009 0
Average -0.9
Table 2 Performance of the Model in Forecasting the Reversals
to Bear and Bull Markets in the S&P 500 Index since 1966
1. There are no official reference dates for the start and the end of bear markets for the S&P 500 price index. A bear market is generally defined as a decline of about 20% or more spread in a broad market index over a period of at least two months (see Tables 2 and 3 at the end of the document for the duration and percentage change in all the bear and bull markets since 1966). The dates reported in Table 1 correspond to those available in the economic literature.
2. The signals were determined using the usual 50% threshold.
Actual start of the
bear market1
Signal of a shift to a
bear market2
# of months before (-) or after (+) the actual start of a
bear market Feb. 1966 Apr. 1966 +2
Jan. 1969 Dec. 1968 -1
Feb. 1973 Oct. 1972 -4
Oct. 1976 Sep. 1976 -1
Dec. 1980 Dec. 1980 0
Sep. 1987 Nov. 1987 +2
Jul. 1990 Jul. 1990 0
Sep. 2000 Jul. 2000 -2
Nov. 2007 Sep. 2007 -2
Average -0.7
In-Sample Forecasting Performance
6007008009001 0001 1001 2001 3001 4001 5001 600
0102030405060708090
100
2004
.Dec
2005
.Mar
2005
.Jun
2005
.Sep
2005
.Dec
2006
.Mar
2006
.Jun
2006
.Sep
2006
.Dec
2007
.Mar
2007
.Jun
2007
.Sep
2007
.Dec
2008
.Mar
2008
.Jun
2008
.Sep
2008
.Dec
2009
.Mar
2009
.Jun
2009
.Sep
2009
.Dec
2010
.Mar
2010
.Jun
2010
.Sep
2010
.Dec
2011
.Mar
2011
.Jun
2011
.Sep
2011
.Dec
Probability (left scale)S&P 500 (right scale)
Figure 2: Probability of the S&P 500 Index Being in a Bear Market,1 2007-2009 (probability, %) (index)
Peak of the bull market in October 2007
Trough of the bear market in March 2009
Signal a shift to a bear market
Signal a shift to a bull market
50% threshold
Sources: Federal Reserve Bank of St-Louis Fred Database (S&P 500 index) and The Forecasting Advisor (probability). 1. In-sample probabilities from the one-month ahead probability model.
6007008009001 0001 1001 2001 3001 4001 5001 600
0102030405060708090
100
2000
.Jan
2000
.Mar
2000
.May
2000
.Jul
2000
.Sep
2000
.Nov
2001
.Jan
2001
.Mar
2001
.May
2001
.Jul
2001
.Sep
2001
.Nov
2002
.Jan
2002
.Mar
2002
.May
2002
.Jul
2002
.Sep
2002
.Nov
2003
.Jan
2003
.Mar
2003
.May
2003
.Jul
2003
.Sep
2003
.Nov
Probability (left scale)
S&P 500 (right scale)
Figure 3: Probability of the S&P 500 Index Being in a Bear Market,1 2000-2002 (probability, %) (index)
Peak of the bull market in August 2000
Trough of the bear market in October 2002
Signal a shift to a bear market
Signal of a shift to a bull market
50% threshold
Sources: Federal Reserve Bank of St-Louis Fred Database (S&P 500 index) and The Forecasting Advisor (probability). 1. In-sample probabilities from the one-month ahead probability model.
200225250275300325350375400425450
0102030405060708090
100
1989
.Jan
1989
.Mar
1989
.May
1989
.Jul
1989
.Sep
1989
.Nov
1990
.Jan
1990
.Mar
1990
.May
1990
.Jul
1990
.Sep
1990
.Nov
1991
.Jan
1991
.Mar
1991
.May
1991
.Jul
1991
.Sep
1991
.Nov
1992
.Jan
Probability (left scale)
S&P 500 (right scale)
Figure 4: Probability of the S&P 500 Index Being in a Bear Market,1 1990 (probability, %) (index)
Peak of the bull market in June 1990
Trough of the bear market in October 1990
Signal a shift to a bull market
Signal a shift to a bear market
50% threshold
Sources: Federal Reserve Bank of St-Louis Fred Database (S&P 500 index) and The Forecasting Advisor (probability). 1 In-sample probabilities from the one-month ahead probability model.
150175200225250275300325350375400
0102030405060708090
100
1986
.Oct
1986
.Nov
1986
.Dec
1987
.Jan
1987
.Feb
1987
.Mar
1987
.Apr
1987
.May
1987
.Jun
1987
.Jul
1987
.Aug
1987
.Sep
1987
.Oct
1987
.Nov
1987
.Dec
1988
.Jan
1988
.Feb
1988
.Mar
1988
.Apr
1988
.May
1988
.Jun
1988
.Jul
1988
.Aug
1988
.Sep
1988
.Oct
Probability (left scale)S&P 500 (right scale)
Figure 5: Probability of the S&P 500 Index Being in a Bear Market,1 1987 (probability, %) (index)
Peak of the bull market in August 1987
Trough of the bear market in December 1987
Signal a shift to a bull market
Sources: Federal Reserve Bank of St-Louis Fred Database (S&P 500 index) and The Forecasting Advisor (probability). 1. In-sample probabilities from the one-month ahead probability model.
50% threshold
Signal a shift to a bear market
8090100110120130140150160170180
0102030405060708090
100
1980
.Jan
1980
.Mar
1980
.May
1980
.Jul
1980
.Sep
1980
.Nov
1981
.Jan
1981
.Mar
1981
.May
1981
.Jul
1981
.Sep
1981
.Nov
1982
.Jan
1982
.Mar
1982
.May
1982
.Jul
1982
.Sep
1982
.Nov
1983
.Mar
1983
.May
1983
.Jul
1983
.Sep
Probability (left scale)
S&P 500 (right scale)
Figure 6: Probability of the S&P 500 Index Being in a Bear Market,1 1980-1982 (probability, %) (index)
Peak of the bull market in November 1980
Trough of the bear market in July 1982
Signal a cyclical shift to a market
Signal a shift to a bear market
Sources: Federal Reserve Bank of St-Louis Fred Database (S&P 500 index) and The Forecasting Advisor (probability). 1. In-sample probabilities from the one-month ahead probability model.
50% threshold
There was no shift to a bear market in early 1980 but the U.S. was in a recession and the S&P 500 fell by a total of 11% in March and April 1980.
86889092949698100102104106
0102030405060708090
100
1976
.Jan
1976
.Mar
1976
.May
1976
.Jul
1976
.Sep
1976
.Nov
1977
.Jan
1977
.Mar
1977
.May
1977
.Jul
1977
.Sep
1977
.Nov
1978
.Jan
1978
.Mar
1978
.May
1978
.Jul
1978
.Sep
1978
.Nov
Probability (left scale)
S&P 500 (right scale)
Peak of the bull market in September 1976
Trough of the bear market in March 1978
Signal a shift to a bear market
Signal a shift to a bull market
Sources: Federal Reserve Bank of St-Louis Fred Database (S&P 500 index) and The Forecasting Advisor (probability). 1. In-sample probabilities from the one-month ahead probability model.
Figure 7: Probability of the S&P 500 Index Being in a Bear Market,1 1976-1978 (probability, %) (index)
50% threshold
405060708090100110120130140
0102030405060708090
100
1972
.Jan
1972
.Apr
1972
.Jul
1972
.Oct
1973
.Feb
1973
.May
1973
.Aug
1973
.Nov
1974
.Feb
1974
.May
1974
.Aug
1974
.Nov
1975
.Feb
1975
.May
1975
.Aug
1975
.Nov
Probability (right scale)
S&P 500 (left scale)Peak of the bull market in January 1973
Trough of the bear market in December 1975
Signal a shift to a bull market
Signal a shift to a bear market
Sources: Federal Reserve Bank of St-Louis Fred Database (S&P 500 index) and The Forecasting Advisor (probability). 1. In-sample probabilities from the one-month ahead probability model.
Figure 8: Probability of the S&P 500 Index Being in a Bear Market,1 1973-1975 (probability, %) (index)
50% threshold
This is a false alarm of a shift to a bear market. The US economy has been growing strongly for many months during that period and labour market conditions were strong.
405060708090100110120130140
0102030405060708090
100
1968
.Jan
1968
.Mar
1968
.May
1968
.Jul
1968
.Sep
1968
.Nov
1969
.Jan
1969
.Mar
1969
.May
1969
.Jul
1969
.Sep
1969
.Nov
1970
.Jan
1970
.Mar
1970
.May
1970
.Jul
1970
.Sep
1970
.Nov
Probability (right scale)
S&P 500 (left scale)
Peak of the bull market in December 1968
Trough of the bear market in June 1970
Signal a shift to a bull market
Signal a shift to a bear market
Sources: Federal Reserve Bank of St-Louis Fred Database (S&P 500 index) and The Forecasting Advisor (probability). 1. In-sample probabilities from the one-month ahead probability model.
Figure 9: Probability of the S&P 500 Index Being in a Bear Market,1 1969-1970 (probability, %) (index)
50% threshold
60
65
70
75
80
85
90
95
100
105
110
0
10
20
30
40
50
60
70
80
90
100
1965
.Jan
1965
.Mar
1965
.May
1965
.Jul
1965
.Sep
1965
.Nov
1966
.Jan
1966
.Mar
1966
.May
1966
.Jul
1966
.Sep
1966
.Nov
1967
.Jan
1967
.Mar
1967
.May
Probability (left scale)
S&P 500 (right scale)
Peak of the bull market in January 1966
Trough of the bear market in October 1966
Signal a shift to a bear market
Signal a shift to a bull market2
Sources: Federal Reserve Bank of St-Louis Fred Database (S&P 500 index) and The Forecasting Advisor (probability). 1. In-sample probabilities from the one-month ahead probability model.
Figure 10: Probability of the S&P 500 Index Being in a Bear Market,1 1966 (probability, %) (index)
50% threshold
Out-of-Sample Forecasting Performance
Sources: Federal Reserve Bank of St-Louis Fred Database (S&P 500 index) and The Forecasting Advisor (probability). 1. One-month ahead probability. 2. The out-of-sample probabilities were computed with coefficients estimated from January 1964 to December 1999 and the in-sample probabilities with coefficients estimated from January 1964 to December 2012.
02004006008001 0001 2001 4001 6001 8002 000
0102030405060708090
100
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Bear market periods In-sample probability (left scale)Out-of-sample probability (left scale) S&P 500 (right scale)
Figure 11: Probability of the S&P 500 Index Being in a Bear Market1: In- and Out-of-Sample Probabilities from January 2000 to December 20102
(probability, %) (index)
50% threshold
1. The probabilities were computed on February 7, 2014.
Outlook on the Stock Market Cycle in the U.S.
Model's Forecast
State of the Stock Market
Actual Outlook1
January 2014 February 2014 March 2014
Bull market
Probability of Being in a Bear Market 0.0% 0.3%
Predicted Outcome for the Stock Market
Bull market will continue
Bull market will continue
6007509001 0501 2001 3501 5001 6501 8001 9502 100
0102030405060708090
100
2005
.Jan
2005
.Jun
2005
.Nov
2006
.Apr
2006
.Sep
2007
.Feb
2007
.Jul
2007
.Dec
2008
.May
2008
.Oct
2009
.Mar
2009
.Aug
2010
.Jan
2010
.Jun
2010
.Nov
2011
.Apr
2011
.Sep
2012
.Feb
2012
.Jul
2012
.Dec
2013
.May
2013
.Oct
2014
.Mar
Probability (left scale) S&P 500 Index (right scale)
October 2007 peak
March 2009 trough
Probabilities of 0.0% for February and March do not suggest a reversal to a bear
market
50% threshold
Probability of the S&P 500 Index Being in a Bear Market1 (%) (index)
Source: The Forecasting Advisor.
Signal a reversal to a bear market
Signal a reversal to a bull market
Forecasting Canadian Real GDP and Employment by Industry
Robert Lamy The Forecasting Advisor www.theforecastingadvisor.com
Forecasting Real GDP by Industry in Canada
Description
The general form of the GDP equation by industry is presented below:
GDPit = f ( Dt-i
, EXRt, Vt, GDPit-1 )
where
• GDPi is the value of real gross domestic product (GDP) for the industry i • D is a vector of long-term determinants of real GDP in the industry i, such
as foreign/domestic economic activity. • EXR is the Canada-US real exchange rate • V is a vector of short-term determinants of real GDP for the industry i, such
as the rate of growth in foreign/domestic economic activity • GDPi is the value of real GDP for the industry i at time t-1
For the goods-producing sector, there is an equation for each of the following industry:
– Agriculture, forestry, fishing, and trapping (NAICS 11); Oil and gas extraction and mining (NAICS 21)
– Utility (NAICS 22); Construction (NAICS 23) – Food (NAICS 311); Beverage and tobacco products (NAICS 312) – Textile, clothing and leather (NAICS 313, 314, 315, 316) – Wood product (NAICS 321); Paper (NAICS 322) – Printing (NAICS 323) – Petroleum and coal product (NAICS 324); Chemical (NAICS 325) – Plastic and rubber products (NAICS 326); – Non-metallic mineral products (NAICS 327) – Primary metal (NAICS 331); Fabricated metal product (NAICS 332) – Machinery (NAICS 333); – Computer and electronic product (NAICS 334) – Electrical equipment and appliance (NAICS 335) – Automotive industry (NAICS 3361, 3362, 3363) – Other transportation equipment (NAICS 3364, 3365, 3366, 3369) – Furniture (NAICS 337, 339)
For the services-producing sector, there is an equation for each of the following industry:
– Wholesale trade (NAICS 41); Retail trade (NAICS 44, 45) – Transportation and warehousing (NAICS 48, 49) – Information and cultural industries (NAICS 51) – Finance and insurance, real estate, rental and leasing (NAICS 52, 53) – Professional, scientific, and technical services (NAICS 54) – Management and administration and support (NAICS 55, 56) – Educational services (NAICS 61); Heath care and social services (NAICS 62) – Arts, entertainment, and recreation (NAICS 71) – Accommodation and food services (NAICS 72) – Public administration (NAICS 91); Other services (NAICS 81)
The equations generate a projection of GDP for each of the thirty-five industries for the current year and the following year.
Sector Impact of 1% Increase in
Foreign and Domestic Economic Activity
Impact of 10% Appreciation of the
Canadian Dollar against the U.S. Dollar
Goods sector 0.9% -3.4%
Primary 0.5% 0.0%
Construction1 0.8% 0.0%
Manufacturing 1.0% -6.5%
Services sector 0.8% 0.0%
All Industry 0.9% -1.1%
Properties Impact of a Change in Demand and the Exchange Rate on Real GDP by Sector and Industry
1. Includes the utility industry.
-4
-2
0
2
4
6
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Forecasting Performance
Real GDP Growth in All Industry (%)
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
-10-8-6-4-202468
10
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Forecasting Performance
Real GDP Growth in the Primary Industry (%)
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
-16
-12
-8
-4
0
4
8
12
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Forecasting Performance
Real GDP Growth in the Manufacturing Industry (%)
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
-12-10
-8-6-4-202468
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Forecasting Performance
Real GDP Growth in the Goods Sector (%)
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
-2
0
2
4
6
8
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Forecasting Performance
Real GDP Growth in the Services Sector (%)
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
Real GDP Growth in Oil and Gas and Mining Industry: In-Sample Forecasting Performance (%)
-10-8-6-4-202468
101214
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
Real GDP Growth in Motor Vehicle Industry: In-Sample Forecasting Performance (%)
-40
-30
-20
-10
0
10
20
30
40
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
Real GDP Growth in the Retail Trade Industry: In-Sample Forecasting Performance (%)
-8-6-4-202468
10
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
Forecasting Employment by Industry in Canada
Core Drivers
In the long-term, employment by industry is determined by a number of economic variables, such as :
– Foreign and domestic economic activity – Canada-U.S. exchange rate – World commodity prices
In the short-term, employment by industry is influenced by the changes in the variables listed above plus economic uncertainty (proxy by the change in the unemployment rate).
Description
The general form of the employment equation by industry is presented below:
Eit = f ( Dt-i
, EXRt, Vt, Eit-1 )
where
• Ei is employment in the industry i • D is a vector of long-term determinants of employment in the industry i,
such as foreign/domestic economic activity • EXR is the Canada-U.S. real exchange rate • V is a vector of short-term determinants of employment in the industry i,
such as the rate of growth in foreign/domestic economic activity • Ei is employment in the industry i at time t-1
For the goods-producing sector, there is an equation for each of the following industry: – Agriculture, forestry, fishing, and trapping (NAICS 11); – Mining, quarrying, and oil and gas extraction (NAICS 21) – Utility (NAICS 22); Construction (NAICS 23) – Food and beverage and tobacco product manufacturing (NAICS 311, 312) – Textile mills, textile product mills, clothing and leather allied product manufacturing (NAICS 313,
314, 315, 316) – Wood product manufacturing (NAICS 321); Paper manufacturing (NAICS 322) – Printing and related support activities (NAICS 323) – Petroleum and coal product manufacturing (NAICS 324); Chemical manufacturing (NAICS 325) – Plastic and rubber products manufacturing (NAICS 326) – Non-metallic mineral product manufacturing (NAICS 327) – Primary metal manufacturing (NAICS 331); – Fabricated metal product manufacturing (NAICS 332) – Machinery manufacturing (NAICS 333); – Computer and electronic product manufacturing (NAICS 334) – Electrical equipment and appliance manufacturing (NAICS 335) – Motor vehicle and parts manufacturing (NAICS 3361, 3362, 3363) – Other transportation equipment manufacturing (NAICS 3364, 3365, 3366, 3369) – Furniture and miscellaneous manufacturing (NAICS 337, 339)
For the services-producing sector, there is an equation for each of the following industry:
– Trade (NAICS 41, 44, 45) – Transportation and warehousing (NAICS 48, 49) – Information and cultural industries and arts, entertainment, and recreation (NAICS 51, 71) – Finance and insurance, real estate, rental and leasing (NAICS 52, 53) – Professional, scientific, and technical services (NAICS 54) – Management and administration and support (NAICS 55, 56) – Educational services (NAICS 61); Heath care and social services (NAICS 62)
Accommodation and food services (NAICS 72) – Public administration (NAICS 91); Other services (NAICS 81)
The equations generate a projection of employment for each of the thirty-two industries for the current year and the following year.
Sector Impact of 1% Increase in
Foreign and Domestic Economic Activity
Impact of 10% Appreciation of the
Canadian Dollar against the U.S. Dollar
Goods sector 0.4% -4.7%
Primary 0.0% -2.3%
Construction1 0.9% 0.0%
Manufacturing 0.3% -7.4%
Services sector 0.4% 0.0%
All industry 0.4% -1.2%
Properties Impact of a Change in Demand and the Exchange Rate on Employment by Sector and Industry
1. Includes the utility industry.
-2
-1
0
1
2
3
4
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Forecasting Performance
Employment Growth in All Industry (%)
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
-10-8-6-4-202468
10
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Forecasting Performance
Employment Growth in the Primary Industry (%)
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
-10-8-6-4-202468
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Forecasting Performance
Employment Growth in the Manufacturing Industry (%)
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
-8
-6
-4
-2
0
2
4
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Forecasting Performance
Employment Growth in the Goods Sector (%)
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
-1
0
1
2
3
4
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
Actual Dynamic simulationStatic simulation
Forecasting Performance
Employment Growth in the Services Sector (%)
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
Employment Growth in Oil and Gas and Mining Industry: In-Sample Forecasting Performance (%)
-20
-15
-10
-5
0
5
10
15
20
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
Employment Growth in Automotive Industry: In-Sample Forecasting Performance (%)
-30
-20
-10
0
10
20
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
Employment Growth in the Trade Industry: In-Sample Forecasting Performance (%)
-3
-2
-1
0
1
2
3
4
5
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
ActualDynamic simulationStatic simulation
Sources: Statistics Canada (actual data) and The Forecasting Advisor (simulation).
Thanks!