1. N-tuple S&P Patterns Across Decades, 1950s to 2011
A. G. (Tassos) Malliaris
Mary Malliaris
LOYOLA UNIVERSITY CHICAGO
The Korea Institute of Finance and
The Athenian Policy Forum Conference
Seoul, Korea
June 16-18, 2013

2. Purpose
To investigate the Up and Down movements of the S&P 500 from 1950 through 2011
And to use that information to forecast the direction tomorrow of the S&P 500

3. Data Daily closing prices from 1/3/1950 to 7/19/2011
Over 15,000 observations
were transformed into Up [U] or Down [D] by comparing today’s value to yesterday’s
Up and Down movements were recorded from 1 up to 7 days

4. Up [U] and Down [D] movements per decade, 1950 through 2011.

5. Two-Day Patterns Across Decades

6. Three-Day Patterns

7. Four to Seven-Day patterns
Strings were formed, for example, UDDU through DUDUDDU
From 16 to 128 patterns [too many to display on a slide]
Columns also created counting the number of Up movements within a string

8. Number of Ups in Two Days

9. Number of Ups in Three Days

10. Number of Ups in Four Days

11. Number of Ups in Five Days

12. Forecasting
Training set: data from January 1950 through December 2009 [15,087 rows].
Validation set: January 2010 through mid-September 2011 [387 rows]
Training set patterns were used as inputs for models that were then used to predict the Validation set

13. Forecasting Methodologies
Pattern Forecasts with 1 to 7 Days
Decision Tree
Neural Network
Random Forecasts

14. The Forecast Decision by Pattern, an Example
Training set 4-day patterns
Count
DDUD
760
DDUU
1050
Validation Set Pattern Up through Today
Most Likely Move Tomorrow
DDU U
Suppose that DDU has occurred. Past history tells us that, for the next day, DDUU is more likely to occur than DDUD. So, for tomorrow, we will forecast Up when the three days before tomorrow have the pattern DDU.

15. Decision Tree Forecasts
Decision Tree Methodology: C5.0
Software Package: SPSS Modeler
Target: Tomorrow’s Direction
Inputs: : the up-down patterns from one to seven days, the number of up days in 1 to five days, and the closing value today

16. Decision Tree Variable Importance
This Modeler technique also ranks the input variables in terms of importance, with more important variables occurring higher up on the tree.
The variables ranked highest in importance to the forecast were
the direction today
the closing value today
the 7-day pattern [for example UDUUDDU]
number of Up movements in the last three days.

17. Neural Network Forecasts
Neural Network Methodology: Back Propagation; two hidden layers
Software Package: SPSS Modeler
Target: Tomorrow’s Direction
Inputs included: the up-down patterns from one to seven days, the number of up days in 1 to five days, and the closing value today

18. Neural Network Variable Importance
SPSS Modeler also ranks the input variables in terms of their importance to the neural network
The variables ranked highest in importance with this methodology were
the patterns in the 4 day through 7 day strings
the number of Ups in the past three days
the closing value

19. Comparing Methods by Calculating Gain or Loss Daily Gain/Loss Summed Over 387 Days
Change in Index
Actual Direction
Predicted Direction
Amount of Gain/Loss -5
Down 5 Up

20. Random Forecast
A random number was generated for each day in the validation set
If the random value was less than .5 then Down was predicted, otherwise the forecast was Up.
The amount of gain/loss was calculated over the Validation set
This was repeated 100,000 times

21. RANDOM WALK SIMULATIONS Total gains/losses for 100,000 simulated random forecasts for 387 days

22. Number of correct directional forecasts for each methodology
Down Up
Number Correct
2 Day String 72
123
195
3 Day String 41
164
205
4 Day String
Decision Tree 43
168
211
5 Day String 45
167
212
7 Day String 48
6 Day String 40
178
218
1 Day String
219
Neural Net 61
161
222

23. Total amount gained or lost per strategy, and comparison to the random simulations
Type of Forecast
Total Amount Gained/Lost
Amount as Std Deviations in the Random Distribution
2 Day String
-21.08
-0.087
Decision Tree
168.16
0.715
3 Day String
174.34
0.742
4 Day String
1 Day String
193.96
0.825
7 Day String
306.92
1.303
5 Day String
307.22
1.305
6 Day String
335.84
1.426
Neural Net
393.4
1.67

24. Conclusions
The number of up movements is greater than down movements across the decades.
Patterns of Up and Down movement from the past can be useful for forecasting future movement
The highest gain from simple patterns came from using the 6-day strings
The neural network, a more complex methodology, yielded the greatest gain