chinese regression

8/6/2019 Chinese Regression

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ANALYSIS OF THEINFLUENCE OFECONOMIC

INDICATORS ONSTOCKPRICES USING

MULTIPLEREGRESSION

SYS 302Spring 2000

Professor Tony Smith

Yale ChangCarl YeungChris Yip


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TABLE OF CONTENTS

I. INTRODUCTION

A. Chosen Economic Variables

B. Assumptions on the Regression Model

II. ANALYSIS

A. Single Regression Models of TCB 500 Against Indicators

B. Preliminary Multiple RegressionC. Multicollinearity

D. Choosing Variables With the Stepwise Regression Model

E. Gauss-Markov Assumptions: Heteroscedasticity and Autocorrelation

F. Predictive Abilities of the Regression Models

III. CONCLUSION

A. Single Regression Discussion

B. Multiple Regression Discussion

IV. SUPPLEMENTS

A. Appendix A

B. Appendix B


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I. INTRODUCTION

Every month, anxious investors eagerly await the release of key economic

indicators such as the employment report, CPI, and even housing starts. It is not

uncommon for the Dow Jones Industrial Average and NASDAQ to swing more than a

hundred points when the numbers only slightly miss consensus estimates. Every indicator

is an important measure of some facet of the domestic economy, but do these numbers

really shape the movement of stock prices in the long run? Which indicators yield the

most influence on the equity market? Can a model consisting of these indicators be

constructed to accurately forecast the stock market? And are any single indicators a good

predictor of stock prices? As curious investors ourselves, we developed a statistical

model in an attempt to detect a trend between stock prices and such variables and

evaluated the predictive abilities of the model.

Data was obtained from The Conference Board Economic Indicator Package,

provided by Wharton Research Data Services (WRDS). Monthly time series data was

obtained for stock market prices and a selection of economic indicators over a span of

twenty years, from January 1979 to January 1999. This period was chosen because of the

relative stability of the economy, the nations minimal exposure to severe external shock

(i.e. wars), and the comprehensiveness of the data. The stock market index provided by

the Conference Board is the TCB 500 common stock index, which is not commonly

quoted; each data point represents the indexs closing price for the given month. This

index was employed in our analysis because it represents the stock market more fully

than the Dow Jones Industrial Average, which includes only thirty stocks. Furthermore, a


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comparison of the TCB 500 and the SP500 revealed that the two indices are almost

identical, as the single regression shows below:

SPX By TCB 500 Stock

S

P

X

0

100

300

500

600

800

900

1100

1300

0 100 300 500 700 900 1100 1300

500 Stock

Linear Fit

Linear FitSPX = 0.05124 + 1.00486 500 Stock

Summary of FitRsquare 0.997687RSquare Adj 0.997678Root Mean Square Error 12.80636Mean of Response 370.3486Observations (or Sum Wgts) 241

A time series graph comparing the two indices is also shown below:

SP 500 vs TCB 500

0

200

400

600

800

1000

1200

1400

time (1979-1999)

TCB 500 SP 500


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A. Chosen Economic Indicators

The variables included in our initial analysis compose only a portion of the complete set

of economic indicators released monthly. The list below is by no means exhaustive, and

each indicator was chosen to measure a distinct component of the economy.

1. Composite index of 10 leading indicators (1992 = 100)

Labor force, employment, and unemployment:

2. Average weekly hours, manufacturing. (hours)3. Average weekly initial claims, unemployment insurance (thousands)4. Civilian unemployment rate (pct.)

Sales, Orders, and Deliveries:

5. Manufacturers' new orders, consumer goods and materials (mil. chain 1992 $)6. Vendor performance, slower deliveries diffusion index (pct.)7. Manufacturing and trade sales (mil. Chain 1992 $)

Output, Production, and Capacity Utilization:

8. Capacity utilization rate, total industry (pct.)

Fixed Capital Investment:

9. Contracts and orders for plant and equipment (bil. chain 1992 $)10. Building permits for new private housing units (thousands)

Producer and Consumer Prices:11. Producer Price Index, finished goods (1982=100)12. CPI for all urban consumers, all items (1982-84=100)

Commodity Prices:

13. Index of sensitive materials prices (level, 1992=100)

Incln: Cattle hides (1982=100)Lumber and wood products (1982=100)Iron and steel scrap (1982=100)Copper base scrap (1982=100)

Aluminum base scrap (1982=100)Nonferrous scrap, NSA (1982=100)Raw cotton (1982=100)Domestic apparel wool (1982=100)

Personal Income:

14. Personal income less transfer payments (AR, bil. chain 1992 $)15. Index of consumer confidence (1985=100) COPYRIGHTED (The Conf Bd)


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16. Index of consumer expectations (1985=100) COPYRIGHTED (The Conf Bd)

Money, Credit, Interest Rates, and Stock Prices:

17. Money supply, M2 (bil. chain 1992 $)18. Interest rate spread, 10-year Treasury bonds less federal funds

19. Federal funds rate, NSA (pct.)

Exports and Imports:

20. Exports, excluding military aid shipments (mil. $) - General imports (mil. $) =Trade Balance

International Comparisions:21. Exchange value of U.S. dollar, NSA (Mar. 1973=100)


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B. Assumptions on the Regression Model

1. The basic assumption made on the data set was that the chosen economic

indicators exert significant, observable influence on the price changes in the stock

market. The relationship between the TCB 500 stock index level and the chosen

indicators was assumed to be linear and subject to random error.

2. The different economic variables chosen are not released on the same day within

a given month. For example, the employment survey is released the first Friday of

every month, while the CPI is released the Tuesday of the third week. We have

assumed that this difference in timing does not affect our correlation model.

3. The quarterly released indicator such as GDP and productivity were not included

in our model since the time series data is on a monthly scale. While figures such

as GDP undoubtedly play an important role in affecting stock prices, their

inclusion in the model would most likely produce inconsistencies.

4. We have assumed that the TCB 500 index is a good proxy for the equity market.

From the earlier discussion, we found that it does represent the S&P 500 index

well. However, it is often argued that the S&P 500 is not the best measure of

equity market movements since it is not mean and variance sufficient.

5. The Gauss-Markov model was notautomatically assumed. Unique tests were

conducted to examine the Gauss-Markov assumptions as well as

heteroscedasticity and autocorrelation in order to derive an acceptable model.


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II. ANALYSIS

A. Single Regression Models of TCB 500 Against Indicators

To begin our study, single regression models of the TCB 500 index were run

against each economic indicator to obtain a graphical interpretation of how well each

variable correlates with the stock market. The regression plots for each indicator are

attached at the end of the report as Appendix A. These plots show that the only indicators

which seem to display a smooth, consistent relationship with the TCB 500 index are the

following: index of ten leading indicators, manufacturing and trade sales, CPI, and

personal income. The polynomial fits of these four variables correlate surprisingly well

with the stock index, withR2 values of at least 0.95 (see Appdendix B). With this

information in mind, we proceeded to perform a preliminary multiple regression.

B. Preliminary Multiple Regression

While single regressions can be limited in their analysis, multiple regression

models simultaneously take into account the effects of each variable. A standard least

squares multiple regression was conducted, plotting the TCB 500 common stock index

against all economic indicators. The results of the multiple regression are shown below:

Response: 500 StockSummary of Fit

RSquare 0.987224RSquare Adj 0.985999Root Mean Square Error 31.25715Mean of Response 368.508Observations (or Sum Wgts) 241

Parameter EstimatesTerm Estimate Std Error t Ratio Prob>|t|Intercept -2845.606 879.1908 -3.24 0.001410 Leading Ind 52.003024 13.65247 3.81 0.0002Avg Wkly Hr -16.89806 11.42545 -1.48 0.1406


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UE Claims 0.2057853 0.128894 1.60 0.1118Mfrs New Orders -0.003696 0.001289 -2.87 0.0045Vendor Prfm -0.738489 0.716969 -1.03 0.3041Bldg Permit -0.162113 0.024568 -6.60


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On the other hand, not all of the variables are significant, such as the trade

balance, commodity prices, and the unemployment rate, which has ap-value of almost 1!

It seems illogical to claim that what is probably the most closely watched measure of

economic performance by Wall Street and the Fed has practically no effect on stock

prices. It is also strange that the coefficients for CPI and PPI have opposite signs even

though they both measure inflation. Similarly, the unemployment rate and unemployment

claims also have a negative correlation, as well as consumer confidence and consumer

expectations.

C. Multicollinearity

A possible explanation of these discrepancies might be multicollinearity, which

undermines the significance of the individual coefficients. To refine the model, a

correlation plot between the stock index and the economic indicators was drawn to

determine which variables are highly dependent:

Variable10

LeadingIndicies

AvgWkly Hr

UEClaims

MfrsNew

Orders

BldgPermit

M2IntrtRate

Spread

UERate

Capacity UtilRate

Mnfr &TradeSales

Cntrct&

OrdersPPI CPI

PersInc

CnsmrConf

CnsmrExpt

FFRate

TradeBalance

Ex ValueUSD

500Stock

10 LeadingInd

1 0.8968 -0.7549 0.8954 0.2309 0.9665 0.4231 -0.6713 0.326 0.9075 0.7075 0.8576 0.897 0.9349 0.5724 0.3774 -0.8185 -0.8714 -0.4352 0.8156

Avg Wkly Hr 0.8968 1 -0.812 0.9078 0.2123 0.8006 0.3059 -0.7067 0.5284 0.8699 0.6887 0.7707 0.8261 0.857 0.5383 0.2914 -0.7119 -0.797 -0.4955 0.7468

UE Claims -0.7549 -0.812 1 -0.7392 -0.4653 -0.6496 -0.1116 0.7539 -0.6826 -0.6369 -0.6018 -0.4328 -0.5041 -0.6095 -0.7254 -0.4463 0.4645 0.6852 0.3242 -0.5006

Mfrs NewOrders

0.8954 0.9078 -0.7392 1 0.1647 0.8062 0.1685 -0.7852 0.5157 0.9746 0.8769 0.8053 0.878 0.9393 0.6249 0.2774 -0.6625 -0.84 -0.5305 0.9115

Bldg Permit 0.2309 0.2123 -0.4653 0.1647 1 0.0964 0.1002 -0.1259 0.0688 0.0466 0.1329 -0.1604 -0.1047 -0.0072 0.5578 0.5351 -0.13 -0.3827 0.4352 0.0489

M2 0.9665 0.8006 -0.6496 0.8062 0.0964 1 0.4068 -0.6457 0.2577 0.8574 0.6436 0.8492 0.877 0.915 0.4702 0.268 -0.8064 -0.8025 -0.4777 0.7652

Intrt RateSpread

0.4231 0.3059 -0.1116 0.1685 0.1002 0.4068 1 0.1916 -0.2923 0.1944 -0.1141 0.4303 0.3864 0.2715 -0.1331 0.1745 -0.7336 -0.272 0.0488 0.114

UE Rate -0.6713 -0.7067 0.7539 -0.7852 -0.1259 -0.6457 0.1916 1 -0.8275 -0.7427 -0.8241 -0.4541 -0.5514 -0.7062 -0.6963 -0.1141 0.3413 0.6413 0.5733 -0.6377

Capacity Util

Rate

0.326 0.5284 -0.6826 0.5157 0.0688 0.2577 -0.2923 -0.8275 1 0.4024 0.5588 0.1118 0.2052 0.339 0.5033 -0.0114 -0.0743 -0.2785 -0.5108 0.249

Mnfr & TradeSales

0.9075 0.8699 -0.6369 0.9746 0.0466 0.8574 0.1944 -0.7427 0.4024 1 0.8606 0.8853 0.9428 0.9862 0.5383 0.2104 -0.6957 -0.8368 -0.5596 0.9541

Cntrct &Orders

0.7075 0.6887 -0.6018 0.8769 0.1329 0.6436 -0.1141 -0.8241 0.5588 0.8606 1 0.6052 0.6909 0.809 0.6707 0.1954 -0.4037 -0.7084 -0.4607 0.8572

PPI 0.8576 0.7707 -0.4328 0.8053 -0.1604 0.8492 0.4303 -0.4541 0.1118 0.8853 0.6052 1 0.9872 0.9299 0.2604 0.1755 -0.7474 -0.711 -0.4933 0.8176

CPI 0.897 0.8261 -0.5041 0.878 -0.1047 0.877 0.3864 -0.5514 0.2052 0.9428 0.6909 0.9872 1 0.9707 0.3325 0.1679 -0.7755 -0.7662 -0.5441 0.8765

Pers Inc 0.9349 0.857 -0.6095 0.9393 -0.0072 0.915 0.2715 -0.7062 0.339 0.9862 0.809 0.9299 0.9707 1 0.4912 0.2056 -0.7396 -0.8315 -0.5548 0.9282

Cnsmr Conf 0.5724 0.5383 -0.7254 0.6249 0.5578 0.4702 -0.1331 -0.6963 0.5033 0.5383 0.6707 0.2604 0.3325 0.4912 1 0.7214 -0.1388 -0.6671 -0.0033 0.5157

Cnsmr Expt 0.3774 0.2914 -0.4463 0.2774 0.5351 0.268 0.1745 -0.1141 -0.0114 0.2104 0.1954 0.1755 0.1679 0.2056 0.7214 1 -0.0825 -0.3832 0.3137 0.2276


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FF Rate -0.8185 -0.7119 0.4645 -0.6625 -0.13 -0.8064 -0.7336 0.3413 -0.0743 -0.6957 -0.4037 -0.7474 -0.7755 -0.7396 -0.1388 -0.0825 1 0.6338 0.4345 -0.6009

TradeBalance

-0.8714 -0.797 0.6852 -0.84 -0.3827 -0.8025 -0.272 0.6413 -0.2785 -0.8368 -0.7084 -0.711 -0.7662 -0.8315 -0.6671 -0.3832 0.6338 1 0.2154 -0.7889

Ex Value USD -0.4352 -0.4955 0.3242 -0.5305 0.4352 -0.4777 0.0488 0.5733 -0.5108 -0.5596 -0.4607 -0.4933 -0.5441 -0.5548 -0.0033 0.3137 0.4345 0.2154 1 -0.4427

500 Stock 0.8156 0.7468 -0.5006 0.9115 0.0489 0.7652 0.114 -0.6377 0.249 0.9541 0.8572 0.8176 0.8765 0.9282 0.5157 0.2276 -0.6009 -0.7889 -0.4427 1

From this correlation plot,the composite index of 10 leading indicators shows muchhigher correlation with the following individual variables than with the stock index:

Average weekly hours, mfg. (hours)Manufacturers' new ordersManufacturing and trade salesVendor performanceBuilding permits for new private housing units (thous.)Index of stock prices, 500 common stocks, NSA (1941-43=10)

Money supply, M2 (bil. chain 1992 $)Interest rate spread, 10-year Treasury bonds less federal fundsTrade balancePersonal savingsPPICPI

Given the large number of dependent variables with such high correlations, further

economic research was conducted on these indicators; we later discovered that the index

of ten leading indicators actually includes many of the above variables. Most importantly,

the index of leading indicators includes the TCB 500 common stock index. As a result, a

second correlation plot was performed without the index of leading indicators:

Variable500

StocksAvg

Wkly HrUE

Claims

MfrsNew

Orders

BldgPermit

M2IntrtRate

Spread

UERate

Capacity UtilRate

Mnfr &TradeSales

Cntrct&

OrdersPPI CPI

PersInc

CnsmrConf

CnsmrExpt

FFRate

TradeBalance

ExValueUSD

VendorPrfm

ComdPrices

500 Stock 1 0.7468 -0.5006 0.9115 0.0489 0.7652 0.114 -0.6377 0.249 0.9541 0.8572 0.8176 0.8765 0.9282 0.5157 0.2276 -0.6009 -0.7889 -0.4427 0.0922 0.5992

Avg WklyHr

0.7468 1 -0.812 0.9078 0.2123 0.8006 0.3059 -0.7067 0.5284 0.8699 0.6887 0.7707 0.8261 0.857 0.5383 0.2914 -0.7119 -0.797 -0.4955 0.4503 0.6374

UE Claims -0.5006 -0.812 1 -0.7392 -0.4653 -0.6496 -0.1116 0.7539 -0.6826 -0.6369 -0.6018 -0.4328 -0.5041 -0.6095 -0.7254 -0.4463 0.4645 0.6852 0.3242 -0.575 -0.5003

Mfrs NewOrders

0.9115 0.9078 -0.7392 1 0.1647 0.8062 0.1685 -0.7852 0.5157 0.9746 0.8769 0.8053 0.878 0.9393 0.6249 0.2774 -0.6625 -0.84 -0.5305 0.3409 0.7227

BldgPermit

0.0489 0.2123 -0.4653 0.1647 1 0.0964 0.1002 -0.1259 0.0688 0.0466 0.1329 -0.1604 -0.1047 -0.0072 0.5578 0.5351 -0.13 -0.3827 0.4352 0.4549 -0.208

M2 0.7652 0.8006 -0.6496 0.8062 0.0964 1 0.4068 -0.6457 0.2577 0.8574 0.6436 0.8492 0.877 0.915 0.4702 0.268 -0.8064 -0.8025 -0.4777 0.1857 0.4911

Intrt RateSpread

0.114 0.3059 -0.1116 0.1685 0.1002 0.4068 1 0.1916 -0.2923 0.1944 -0.1141 0.4303 0.3864 0.2715 -0.1331 0.1745 -0.7336 -0.272 0.0488 0.2906 -0.1127

UE Rate -0.6377 -0.7067 0.7539 -0.7852 -0.1259 -0.6457 0.1916 1 -0.8275 -0.7427 -0.8241 -0.4541 -0.5514 -0.7062 -0.6963 -0.1141 0.3413 0.6413 0.5733 -0.2084 -0.7191

CapacityUtil Rate

0.249 0.5284 -0.6826 0.5157 0.0688 0.2577 -0.2923 -0.8275 1 0.4024 0.5588 0.1118 0.2052 0.339 0.5033 -0.0114 -0.0743 -0.2785 -0.5108 0.3459 0.6462


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Mnfr &TradeSales

0.9541 0.8699 -0.6369 0.9746 0.0466 0.8574 0.1944 -0.7427 0.4024 1 0.8606 0.8853 0.9428 0.9862 0.5383 0.2104 -0.6957 -0.8368 -0.5596 0.187 0.7112

Cntrct &Orders

0.8572 0.6887 -0.6018 0.8769 0.1329 0.6436 -0.1141 -0.8241 0.5588 0.8606 1 0.6052 0.6909 0.809 0.6707 0.1954 -0.4037 -0.7084 -0.4607 0.1874 0.6949

PPI 0.8176 0.7707 -0.4328 0.8053 -0.1604 0.8492 0.4303 -0.4541 0.1118 0.8853 0.6052 1 0.9872 0.9299 0.2604 0.1755 -0.7474 -0.711 -0.4933 0.0671 0.6231

CPI 0.8765 0.8261 -0.5041 0.878 -0.1047 0.877 0.3864 -0.5514 0.2052 0.9428 0.6909 0.9872 1 0.9707 0.3325 0.1679 -0.7755 -0.7662 -0.5441 0.1159 0.6529

Pers Inc 0.9282 0.857 -0.6095 0.9393 -0.0072 0.915 0.2715 -0.7062 0.339 0.9862 0.809 0.9299 0.9707 1 0.4912 0.2056 -0.7396 -0.8315 -0.5548 0.1453 0.6813

CnsmrConf

0.5157 0.5383 -0.7254 0.6249 0.5578 0.4702 -0.1331 -0.6963 0.5033 0.5383 0.6707 0.2604 0.3325 0.4912 1 0.7214 -0.1388 -0.6671 -0.0033 0.3686 0.4724

CnsmrExpt

0.2276 0.2914 -0.4463 0.2774 0.5351 0.268 0.1745 -0.1141 -0.0114 0.2104 0.1954 0.1755 0.1679 0.2056 0.7214 1 -0.0825 -0.3832 0.3137 0.3991 0.1384

FF Rate -0.6009 -0.7119 0.4645 -0.6625 -0.13 -0.8064 -0.7336 0.3413 -0.0743 -0.6957 -0.4037 -0.7474 -0.7755 -0.7396 -0.1388 -0.0825 1 0.6338 0.4345 -0.2797 -0.2685

TradeBalance

-0.7889 -0.797 0.6852 -0.84 -0.3827 -0.8025 -0.272 0.6413 -0.2785 -0.8368 -0.7084 -0.711 -0.7662 -0.8315 -0.6671 -0.3832 0.6338 1 0.2154 -0.3013 -0.4527

Ex ValueUSD

-0.4427 -0.4955 0.3242 -0.5305 0.4352 -0.4777 0.0488 0.5733 -0.5108 -0.5596 -0.4607 -0.4933 -0.5441 -0.5548 -0.0033 0.3137 0.4345 0.2154 1 -0.0591 -0.6624

VendorPrfm

0.0922 0.4503 -0.575 0.3409 0.4549 0.1857 0.2906 -0.2084 0.3459 0.187 0.1874 0.0671 0.1159 0.1453 0.3686 0.3991 -0.2797 -0.3013 -0.0591 1 0.1372

ComdPrices

0.5992 0.6374 -0.5003 0.7227 -0.2018 0.4911 -0.1127 -0.7191 0.6462 0.7112 0.6949 0.6231 0.6529 0.6813 0.4724 0.1384 -0.2685 -.0.4527 -0.6624 0.1372 1

Based on the above grid, multicollinearity was still found among other variables, as

shown by the highlighted values above. As a result, the following indicators were also

removed: manufacturing new orders, manufacturing and trade sales, personal income,

and PPI. The final correlation plot is shown below:

Variable500

StockAvg Wkly

HrUE

ClaimsBldg

PermitM2

Intrt RateSpread

UE RateCapacityUtil Rate

Cntrct &Orders

CPICnsmrConf

CnsmrExpt

FFRate

TradeBalance

Ex ValueUSD

VendorPrfm

ComdPrices

500 Stock 1 0.7468 -0.5006 0.0489 0.7652 0.114 -0.6377 0.249 0.8572 0.8765 0.5157 0.2276 -0.6009 -0.7889 -0.4427 0.0922 0.5992

Avg Wkly Hr 0.7468 1 -0.812 0.2123 0.8006 0.3059 -0.7067 0.5284 0.6887 0.8261 0.5383 0.2914 -0.7119 -0.797 -0.4955 0.4503 0.6374

UE Claims -0.5006 -0.812 1 -0.4653 -0.6496 -0.1116 0.7539 -0.6826 -0.6018 -0.5041 -0.7254 -0.4463 0.4645 0.6852 0.3242 -0.575 -0.5003

Bldg Permit 0.0489 0.2123 -0.4653 1 0.0964 0.1002 -0.1259 0.0688 0.1329 -0.1047 0.5578 0.5351 -0.13 -0.3827 0.4352 0.4549 -0.208

M2 0.7652 0.8006 -0.6496 0.0964 1 0.4068 -0.6457 0.2577 0.6436 0.877 0.4702 0.268 -0.8064 -0.8025 -0.4777 0.1857 0.4911

Intrt RateSpread

0.114 0.3059 -0.1116 0.1002 0.4068 1 0.1916 -0.2923 -0.1141 0.3864 -0.1331 0.1745 -0.7336 -0.272 0.0488 0.2906 -0.1127

UE Rate -0.6377 -0.7067 0.7539 -0.1259 -0.6457 0.1916 1 -0.8275 -0.8241 -0.5514 -0.6963 -0.1141 0.3413 0.6413 0.5733 -0.2084 -0.7191

Capacity UtilRate

0.249 0.5284 -0.6826 0.0688 0.2577 -0.2923 -0.8275 1 0.5588 0.2052 0.5033 -0.0114 -0.0743 -0.2785 -0.5108 0.3459 0.6462

Cntrct &Orders

0.8572 0.6887 -0.6018 0.1329 0.6436 -0.1141 -0.8241 0.5588 1 0.6909 0.6707 0.1954 -0.4037 -0.7084 -0.4607 0.1874 0.6949

CPI 0.8765 0.8261 -0.5041 -0.1047 0.877 0.3864 -0.5514 0.2052 0.6909 1 0.3325 0.1679 -0.7755 -0.7662 -0.5441 0.1159 0.6529

Cnsmr Conf 0.5157 0.5383 -0.7254 0.5578 0.4702 -0.1331 -0.6963 0.5033 0.6707 0.3325 1 0.7214 -0.1388 -0.6671 -0.0033 0.3686 0.4724

Cnsmr Expt 0.2276 0.2914 -0.4463 0.5351 0.268 0.1745 -0.1141 -0.0114 0.1954 0.1679 0.7214 1 -0.0825 -0.3832 0.3137 0.3991 0.1384

FF Rate -0.6009 -0.7119 0.4645 -0.13 -0.8064 -0.7336 0.3413 -0.0743 -0.4037 -0.7755 -0.1388 -0.0825 1 0.6338 0.4345 -0.2797 -0.2685

Trade Balance -0.7889 -0.797 0.6852 -0.3827 -0.8025 -0.272 0.6413 -0.2785 -0.7084 -0.7662 -0.6671 -0.3832 0.6338 1 0.2154 -0.3013 -0.4527

Ex Value USD -0.4427 -0.4955 0.3242 0.4352 -0.4777 0.0488 0.5733 -0.5108 -0.4607 -0.5441 -0.0033 0.3137 0.4345 0.2154 1 -0.0591 -0.6624

Vendor Prfm 0.0922 0.4503 -0.575 0.4549 0.1857 0.2906 -0.2084 0.3459 0.1874 0.1159 0.3686 0.3991 -0.2797 -0.3013 -0.0591 1 0.1372

Comd Prices 0.5992 0.6374 -0.5003 -0.208 0.4911 -0.1127 -0.7191 0.6462 0.6949 0.6529 0.4724 0.1384 -0.2685 -0.4527 -0.6624 0.1372 1


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12

The table shows that much of the multicollinearity problem has been eliminated

through the removal of five indicators: index of leading indicators, manufacturing new

orders, manufacturing and trade sales, personal income, and PPI.However,it is important

to realize the impossibility of completely removing multicollinearity since all of the

indicators are related in some way through macroeconomic principles. Although the

removal of variables will slightly diminishR2, and hence the predictability of the model,

our objective is to find the best combination of the most significant and influential

independent indicators in the regression model. Although considerable correlation still

exists among certain variables, further removal of variables would prevent a thorough

analysis of the influence of these indicators on the stock market.

D. Choosing Variables With the Stepwise Regression Model

After the filtering of certain variables, a stepwise regression was conducted to further

narrow down the most significant indicators and to yield the highest adjustedR2 value,

indicating highest predictability. The results of the first stepwise regression (Step model

1) are shown below:

Response: 500 StockStepwise Regression Control

Prob to Enter 0.250Prob to Leave 0.250

DirectionCurrent Estimates

SSE DFE MSE RSquare RSquare Adj Cp AIC

884727.99 228 3880.386 0.9472 0.9444 9.256008 2004.185

Lock Entered Parameter Estimate nDF SS "F Ratio" "Prob>F"X X Intercept 2030.66465 1 0 0.000 1.0000

_ X Avg Wkly Hr 28.4736768 1 9987.642 2.574 0.1100 _ _ UE Claims ? 1 39.81886 0.010 0.919 _ X Bldg Permit -0.083008 1 27995.25 7.215 0.0078 _ X M2 -0.3213083 1 209604.7 54.016 0.00 _ X Intrt Rate Spread -32.04761 1 147559.4 38.027 0.0000 _ X UE Rate -58.964848 1 43864.13 11.304 0.0009 _ X Capacity Util Rate -29.704393 1 121007.9 31.184 0.0000


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_ X Cntrct & Orders 0.01546194 1 388882.6 100.218 0.0000 _ X CPI 7.55712093 1 308604.9 79.529 0.000 _ X Cnsmr Conf 1.37104117 1 7634.109 1.967 0.1621 _ X Cnsmr Expt 1.51430471 1 11304.35 2.913 0.0892 _ X FF Rate -19.827616 1 88482.79 22.803 0.0000 _ _ Trade Balance ? 1 533.1804 0.137 0.711 _ _ Ex Value USD ? 1 285.0882 0.073 0.7870

_ _ Vendor Prfm ? 1 26.21451 0.007 0.934 _ X Comd Prices -4.8035508 1 124197.3 32.006 0.0000

Step History

Step Parameter Action "Sig Prob" Seq SS RSquare Cp p1 CPI Entered 0.0000 12866812 0.7683 746.62 22 Cntrct & Orders Entered 0.0000 2028176 0.8894 234.53 33 Capacity Util Rate Entered 0.0000 464129.7 0.9171 118.88 44 Intrt Rate Spread Entered 0.0001 91356.8 0.9226 97.728 55 Avg Wkly Hr Entered 0.0000 104074.3 0.9288 73.348 66 Comd Prices Entered 0.0018 48692.8 0.9317 63.005 77 M2 Entered 0.0159 28276.16 0.9334 57.838 88 UE Rate Entered 0.0000 93389.68 0.9389 36.166 9

9 Cnsmr Expt Entered 0.0010 47220.86 0.9418 26.197 1010 FF Rate Entered 0.0001 62452.44 0.9455 12.367 1111 Avg Wkly Hr Removed 0.5487 1431.699 0.9454 10.73 1012 Bldg Permit Entered 0.0749 12548.41 0.9462 9.549 1113 Avg Wkly Hr Entered 0.1237 9302.653 0.9467 9.1911 1214 Cnsmr Conf Entered 0.1621 7634.109 0.9472 9.256 13

The above stepwise regression shows that much of the multicollinearity problem has been

eliminated; for example, the unemployment rate now has a significantp-value, and

consumer confidence and expectation are no longer negatively correlated. However,

average weekly hours, consumer confidence, and consumer expectations are still included

in the model even though they exhibit highp-values. A possible explanation is that their

inclusion in the model contributes to a higher adjustedR2 value. After testing with

various combinations of the variables, the final stepwise regression model (step model 2)

is shown below:

Response: 500 StockStepwise Regression Control

Prob to Enter 0.250Prob to Leave 0.250

DirectionCurrent Estimates

SSE DFE MSE RSquare RSquare Adj Cp AIC914213.16 231 3957.633 0.9454 0.9433 10.72975 2006.086

Lock Entered Parameter Estimate nDF SS "F Ratio" "Prob>F"


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X X Intercept 2744.42601 1 0 0.000 1.0000 _ _ Avg Wkly Hr ? 1 1431.699 0.361 0.5487 _ _ UE Claims ? 1 1904.568 0.480 0.489 _ _ Bldg Permit ? 1 12548.41 3.201 0.074 _ X M2 -0.3164773 1 217531.8 54.965 0.00 _ X Intrt Rate Spread -30.072942 1 139643.7 35.285 0.0000 _ X UE Rate -68.853244 1 109618.3 27.698 0.0000

_ X Capacity Util Rate -26.328913 1 167767 42.391 0.0000 _ X Cntrct & Orders 0.01518301 1 482884.6 122.013 0.0000 _ X CPI 8.62389599 1 838177.3 211.788 0.000 _ _ Cnsmr Conf ? 1 216.337 0.054 0.815 _ X Cnsmr Expt 2.16589636 1 163006.5 41.188 0.0000 _ X FF Rate -15.707916 1 75646.95 19.114 0.0000 _ _ Trade Balance ? 1 0.215112 0.000 0.994 _ _ Ex Value USD ? 1 1169.58 0.295 0.5878 _ _ Vendor Prfm ? 1 64.92614 0.016 0.898 _ X Comd Prices -4.6080835 1 139365.5 35.214 0.0000

Although the above model has a slightly lower adjustedR2 value than the previous

stepwise model (0.9433 < 0.9444), the entered indicators all show highly significantp-

values ofp < 0.0001.

Using the set of indicators obtained from the results of the stepwise regression,

the standard least squares multiple regression was performed again to create a final linear

model (Model A). The regression is shown below:

Response: 500 StockSummary of FitRSquare 0.945412RSquare Adj 0.943285Root Mean Square Error 62.90972Mean of Response 368.508Observations (or Sum Wgts) 241

Parameter EstimatesTerm Estimate Std Error t Ratio Prob>|t|Intercept 2744.426 483.8281 5.67


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UE Rate 1 1 109618.27 27.6979


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200.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

Normal Quantile

The above plot shows that the residuals are extremely close to being normally distributed;

therefore, the first Gauss-Markov assumption is valid for this regression model.

Next, for the new model to be accepted, possible violations of the constant-

variance assumption must be tested for. The whole model test and the residual plot of the

multiple regression are shown below:

Whole-Model Test

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500 Stock Predicted

Analysis of VarianceSource DF Sum of Squares Mean Square F RatioModel 9 15833148 1759239 444.5179Error 231 914213 3958 Prob>FC Total 240 16747362


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17

The whole model test plot shows that the data points are more scattered at higher

values of thex-axis, but the variances are not significantly increasing; there are no

predictedy values that terribly miss the mark. Similarly, the residual plot does not show

any significant trend of increasing variance, although the residuals appear more scattered

at higher values ofx. Thus, the model can be accepted as fitting the constant variance

assumption, meaning that the increase in values of the economic indicators does not

produce overall increasing variance in the TCB 500.

Although the residual plot shows no significantly discrepant values, the residuals

seem to display a slightly cyclical pattern. So to test for autocorrelation in our model, the

Durbin-Watson test was conducted. The results are as follows:

Durbin-WatsonDurbin-Watson Number of Obs. AutoCorrelation0.5751493 241 0.7038

For a one-sided test at = 0.05, the Durbin-Watson values fork= 11 and n = 200 are dL

= 1.65 and dU= 1.89 (W.H. Green,Econometric Analysis). This shows that our data

contains serious autocorrelation problems. This is not surprising because the data consists

R

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500 Stock Predicted


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of time series statistics that include business cycles and economic fluctuations. There are

two alternatives to solving the autocorrelation problem: 1) perform a two-stage

estimation procedure to modify the data by weighted differencing or 2) add additional

variables which can account for the apparent autocorrelation effect. Although the second

alternative is generally a superior approach, all of thex-variables used in our regressions

are economic indicators and therefore unavoidably reflect business fluctuations; if we add

any more of the variables that we eliminated, we would end up with our preliminary

model and still not be able to correct autocorrelation. Therefore, the two-stage estimation

procedure was performed, and the no-intercept regression of the residuals are shown

below:

Response: Residual 500 StockSummary of Fit

RSquare ?RSquare Adj ?Root Mean Square Error 44.27803Mean of Response 0.136608Observations (or Sum Wgts) 240

Parameter Estimates

Term Estimate Std Error t Ratio Prob>|t|Intercept Zeroed 0 0 ? ?Lag Residuals 0.6921693 0.04757 14.55 FLag Residuals 1 1 415083.08 211.7183


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Observations (or Sum Wgts) 240



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After the two-stage estimation, the new value ofd, 0.953, is still much less than

the critical value, and significant autocorrelation still exists (autocorrelation = 0.5008).

However, a tradeoff must be made between the value ofdandR2; while dincreased from

0.692 to 0.952, R2 has dropped to 0.861 from 0.954 (Model A) in the transformed

multiple regression. The whole-model test plot of the transformed regression

correspondingly shows that the fit has become poorer. The federal funds rate and

commodity prices also showed a large decrease in theirp-values. This estimation

procedure could have been carried out with more lags, but collinearity would start to

become a problem since the lagged residuals are correlated with each other.

The tested model therefore does not satisfy the third Gauss-Markov assumption,

which states that the residual deviations are mutually independent. Because the

autocorrelation problem could not be eliminated to an acceptable extent, this model

would most likely not make an accurate forecasting tool.

F. Predictive Abilities of the Regression Models

Finally, to test the predictive abilities of our regression analyses, we used the models

obtained before and after the two-stage estimation (Model A and Model Atransformed) to

predict the values of the TCB 500 within the time range of our data. The actual values

from WRDS and the values from both prediction models correlated very well as shown

by the time series graphs below:


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Predicted TCB 500 VS Actual TCB 500 (1977-1999)

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Predicted TCB 500by modelReal TCB 500

Predicted Transformed TCB500 vs Actual

Transformed TCB500 stocks (1977-1999)

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time (1977-1999)

Actual TCB 500

Predicted TCB 500

We then gathered actual data on our indicators for a period outside the data range we

used to derive the models. As the graph below shows, the predicted trend is terribly off

the mark for the time period 1967-1977. We have found that the farther we depart from

our original data range, the larger the variances. Our regression model even predicted

negative values for the TCB 500! This highlights the fact that our model only works well


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within the range of our original data and performs poorly in forecasting data outside this

range.

Model Prediction VS. Real TCB 500 from (1967-1977)

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index

value

Model Prediction

Real TCB 500 value


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IV. CONCLUSION

I. Single RegressionFrom our initial single regression plots, the four indicators that demonstrated the

strongest correlation with stock price were the index of ten leading indicators,

manufacturing and trade sales, CPI, and personal income. This result is not surprising: the

leading indicators are a broad measure of the economy and should move in sync with the

stock market; manufacturing and trade sales are a good indicator of overall economic

activity and output, similar to GDP, and therefore should correspond with stock prices;

the CPI measures the price level which generally increases with rising aggregate demand;

and the more income an individual has, the more stocks he/she is likely to buy.

II. Multiple Regression

In the final multiple regression model (model A), the nine remaining economic

indicators were: M2 money supply,interest rate spread, unemployment rate, capacity

utilization rate, manufacturing contracts and orders, CPI, consumer expectations, the

federal funds rate, and commodity prices. All of these indicators were highly significant,

withp < 0.0001, and they accounted for approximately 94.5% of the variance. The model

is shown again below:

Response: 500 StockSummary of Fit




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Intrt Rate Spre -30.07294 5.062709 -5.94


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significant than variables such as the trade balance, which would be assumed to have

bigger importance and more impact on the entire economy.

Multicollinearity was substantial in our preliminary multiple regression since all

the indicators are related according to economic theory; as more variables were

eliminated in the refinement process, theR2 value in our modeldecreased slightly in

return for more significantp-values and more logical coefficients. In fact, CPI was the

only one of the four quality variables from single regression analysis to remain in the

final set of indicators. This was the result of the removal of highly dependent variables.

In addition, those four indicators had goodpolynomialfits with stock prices, but the

multiple regression was based on linear relationships.

While the TCB 500 stock index was predicted fairly well by our data within the

same time range, it seems futile to attempt to forecast the stock market outside the range

using our set of economic indicators. It is surprising that given all of the measures of

economic performance that we used, a successful prediction model failed to be

developed. This could be partly due to high autocorrelation problems in the model, but

more importantly, it suggests that many other factors contribute to the movement of the

equity market than just the economic indicators.


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IV. SUPPLEMENTS:

APPENDIX A: Single Regression Plots, TCB 500 Against All

Indicators

APPENDIX B: Polynomial Line Fit For Leading Indicators,

Manufacturing and Trade Sales, CPI, and

Personal Income


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APPENDIX B

500 Stock By 10 Leading Ind

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Polynomial Fit degree=6

Polynomial Fit degree=6500 Stock = 1.561e7 611383 10 Leading Ind + 6226.79 10 Leading Ind 2 + 50.4847 10 Leading Ind^3

1.47785 10 Leading Ind^4 + 0.01071 10 Leading Ind^5 0.00003 10 Leading Ind^6Summary of Fit


Analysis of VarianceSource DF Sum of Squares Mean Square F RatioModel 6 15941455 2656909 771.4502

Error 234 805906 3444 Prob>FC Total 240 16747362 |t|Intercept 15611913 7426678 2.10 0.036610 Leading Ind -611383.1 391548.6 -1.56 0.119810 Leading Ind^2 6226.7869 9018.339 0.69 0.490610 Leading Ind^3 50.484734 122.3188 0.41 0.680210 Leading Ind^4 -1.477852 1.039863 -1.42 0.156610 Leading Ind^5 0.0107058 0.005017 2.13 0.033910 Leading Ind^6 -0.000026 0.00001 -2.59 0.0103

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APPENDIX B

500 Stock By Mnfr & Trade Sales

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Mnfr & Trade Sales


Polynomial Fit degree=6500 Stock = -195090 + 2.32132 Mnfr & Trade Sales 0.00001 Mnfr & Trade Sales^2 + 2.9e-11 Mnfr & Trade

Sales^3 4e-17 Mnfr & Trade Sales^4 + 2.9e-23 Mnfr & Trade Sales^5 8.9e-30 Mnfr & Trade Sales^6Summary of Fit


Analysis of VarianceSource DF Sum of Squares Mean Square F Ratio

Model 6 16472623 2745437 2338.343Error 234 274738 1174 Prob>FC Total 240 16747362 |t|Intercept -195090.1 113131.5 -1.72 0.0859Mnfr & Trade Sales 2.321316 1.194856 1.94 0.0532Mnfr & Trade Sales^2 -0.000011 0.000005 -2.16 0.0317Mnfr & Trade Sales^3 2.86e-11 1.2e-11 2.38 0.0182Mnfr & Trade Sales^4 -4.01e-17 1.55e-17 -2.59 0.0101Mnfr & Trade Sales^5 2.945e-23 1.05e-23 2.80 0.0055Mnfr & Trade Sales^6 -8.87e-30 2.96e-30 -3.00 0.0030

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APPENDIX B

500 Stock By CPI

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CPI


Polynomial Fit degree=6500 Stock = 17244.2 1207.26 CPI + 34.3338 CPI 2 0.50537 CPI^3 + 0.00406 CPI 4 0.00002 CPI^5 + 2.85e-

8 CPI^6Summary of Fit



Model 6 16569482 2761580 3632.854Error 234 177879 760 Prob>FC Total 240 16747362 |t|Intercept 17244.23 16028.91 1.08 0.2831CPI -1207.261 883.2916 -1.37 0.1730CPI^2 34.333804 19.95 1.72 0.0866CPI^3 -0.505366 0.236511 -2.14 0.0337CPI^4 0.0040617 0.001553 2.62 0.0095CPI^5 -0.000017 0.000005 -3.15 0.0018CPI^6 2.8484e-8 7.6e-9 3.75 0.0002

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APPENDIX B

500 Stock By Pers Inc

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Pers Inc


Polynomial Fit degree=6500 Stock = -523578 + 733.695 Pers Inc 0.42589 Pers Inc^2 + 0.00013 Pers Inc^3 2.26e-8 Pers Inc^4 + 2.1e-

12 Pers Inc^5 7.8e-17 Pers Inc^6Summary of Fit



Model 6 16522641 2753773 2867.479Error 234 224721 960 Prob>FC Total 240 16747362 |t|Intercept -523578.5 194766.6 -2.69 0.0077Pers Inc 733.69489 266.0705 2.76 0.0063Pers Inc^2 -0.425889 0.150455 -2.83 0.0050Pers Inc^3 0.0001311 0.000045 2.91 0.0040Pers Inc^4 -2.256e-8 7.548e-9 -2.99 0.0031Pers Inc^5 2.059e-12 6.7e-13 3.08 0.0024Pers Inc^6 -7.78e-17 2.46e-17 -3.16 0.0018

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chinese regression

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