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.

0

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30

40

50

60

70

80

90

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.

0

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20

30

40

50

60

70

80

90

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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2007

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2009

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2009

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2009

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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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2000

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2000

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2002

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2002

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2002

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2002

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2002

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2002

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2002

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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


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1990

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1990

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1990

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1990

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1991

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1991

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1991

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1991

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1991

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1991

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1991

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1991

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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


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1981

.Jan

1981

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1981

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1981

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1981

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1981

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1983

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1983

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1983

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1983

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1983

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1983

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1983

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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


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1979

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1979

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1979

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1979

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1979

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1979

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1980

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1980

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1980

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1980

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1980

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1980

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1980

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1980

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1980

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1980

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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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1973

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1973

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1975

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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


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1969

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1969

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1969

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1969

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1969

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1969

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1971

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Peak of the expansion in December 1969

Trough of the recession in November 1970


an expansion

Signal with a lag of one month the start of

a recession

50% threshold


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.

0102030405060708090

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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.

0102030405060708090

100

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



1. The probabilities for February, March and April were computed on February 7, 2014.

Source: The Forecasting Advisor.

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2006

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2006

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2007

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2007

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2008

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2009

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2009

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2010

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2010

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2011

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2011

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2012

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2013

.Feb

2013

.Sep

2014

.Apr

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.

0

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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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2007

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2008

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2009

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2009

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2009

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2009

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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


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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1989

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1989

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1989

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1989

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1989

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1989

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1990

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1990

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1990

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1990

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1990

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1990

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1991

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1991

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1991

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1991

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1991

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1991

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Peak of the expansion in March1990

Trough of the recession in March

1991


the expansion


the recession


50% threshold

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1981

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1981

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1981

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1981

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1981

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1981

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1982

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1982

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1982

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1982

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1982

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1982

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1983

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1983

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1983

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1983

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1983

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1983

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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


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1979

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1979

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1979

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1979

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1979

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1980

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1980

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1980

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1980

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1980

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1980

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1980

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1980

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1980

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1980

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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


expansion


recession

50% threshold


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1973

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1973

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1973

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1973

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1973

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1973

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1974

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1974

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1975

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1975

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Figure 6: Probability for Canada of Being in a Recession : 19751 (probability, %)


December 1974 Trough of the recession in March 1975

50% threshold


the expansion


recession


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




1. The probabilities for February, March and April were computed on February 14, 2014.


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2014

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Probability for Canada Being in a Recession1 (%)


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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1964 1970 1976 1982 1988 1994 2000 2006 2012

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

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2011

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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)


Peak of the bull market in August 2000

Trough of the bear market in October 2002


Signal of a shift to a bull market

50% threshold


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



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




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)


Peak of the bull market in August 1987

Trough of the bear market in December 1987



50% threshold


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




Peak of the bull market in November 1980

Trough of the bear market in July 1982

Signal a cyclical shift to a market



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



Peak of the bull market in September 1976

Trough of the bear market in March 1978





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





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





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



Peak of the bull market in January 1966



Signal a shift to a bull market2



50% threshold

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)


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



Real GDP Growth in the Primary Industry (%)


-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



Real GDP Growth in the Manufacturing Industry (%)


-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



Real GDP Growth in the Goods Sector (%)


-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



Real GDP Growth in the Services Sector (%)


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



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



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



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



Employment Growth in All Industry (%)


-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



Employment Growth in the Primary Industry (%)


-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



Employment Growth in the Manufacturing Industry (%)


-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



Employment Growth in the Goods Sector (%)


-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


Employment Growth in the Services Sector (%)


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



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



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



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