Octopus Paul - Psychic Forecaster

It is amazing to see how chance can fool us!!! Look at the worldwide craze about octopus Paul. The eight legged creature got six successive predictions about Germany's games correct and is being heralded as a "psychic forecaster". Nobody (especially the journalists) seems to be asking the simple question - How often will that happen just at random? The answer is also easy to compute. The Octopus's prediction can be thought of as a string of heads and tails obtained from tosses of a fair coin. The probability that the string generated by the octopus matches the actual string is

= (1/ 2^6)= 1/64 = 0.015. That is the chance is about 1.5%. What we have seen is an occurrence of a low probability event and we are immediately driven to see a pattern!!! Fooled by Randomness!

How low can Sensex go this month?

The sudden fall in the BSE-Sensex has disturbed many a investor and the question foremost in their mind is: How low can this get? I try to answer this question quantitatively below.

Here are my predictions for the lowest value of Sensex for the period 4-Nov to 30-Nov.

Chance of Sensex closing below 15000 on someday within this period: 58%

Chance of Sensex closing below 14000 on someday within this period: 14%

Chance of Sensex closing below 13000 on someday within this period: 2%

Another question that investors are interested in are the chances of an upswing. The chances of these positive happenings are given below:

Chance of Sensex closing above 16000 on someday within this period: 55%

Chance of Sensex closing above 17000 on someday within this period: 17%

Chance of Sensex closing above 18000 on someday within this period: 4%

On NIFTY-2

Here are my predictions of the possible closing value of NIFTY for the next week:

Date P5 Q1 Med Q3 P95

5-Oct 4921 5042 5089 5136 5226

6-Oct 4870 5015 5093 5165 5291

7-Oct 4830 5003 5099 5190 5341

8-Oct 4795 4990 5104 5216 5394

9-Oct 4772 4980 5111 5234 5438

P5 = 5th percentile

Q1 = 25th percentile

Med = 50th percentile

Q3 = 75th percentile

P95 = 95th percentile

On NIFTY - 1

There is now a lot of speculation regarding whether NIFTY will cross 5000 or not. As per my calculations

(a) the chance that the closing value of NIFTY on 1-Oct-2009 will exceed 5000 is 33.5% and

(b) the chance that the closing value of NIFTY on 16-Oct-2009 will exceed 5000 is 41.7%

Deaths due to Swine Flu in India - Predictions for Sept 11 -15

The prediction of the number of deaths due to swine flu for the next five days is:

Date Forecast 95% Prediction Interval

11-Sep 154 (150, 158)

12-Sep 159 (155, 164)

13-Sep 164 (159, 169)

14-Sep 170 (164, 175)

15-Sep 175 (169, 181)

(The analysis is based on data available from http://www.swineflu-india.org/)

Y-o-Y quarterly GDP growth of India (2009-10)

Based on the data on Year-on-Year (Y-o-Y) quarterly growth of GDP (at constant 1999-2000 prices) over the period 1997-98 to 2008-09 my predictions for the Y-o-Y quarterly growth for 2009-10 (at constant 1999-2000 prices) are as follows:

Forecast (%) 95% prediction interval

Q1 6.0 (3.1, 8.9)

Q2 6.9 (3.1, 10.7)

Q3 7.2 (3.0, 11.5)

Q4 7.8 (3.2, 12.4)

Swine Flu in India - 8

My forecasts for the number of deaths due to swine-flu for the next five days are as follows

Date Forecast 95% prediction interval

6-Sep 126 (123, 129)

7-Sep 131 (128, 134)

8-Sep 136 (132, 139)

9-Sep 141 (137, 144)

10-Sep 145 (142, 149)

The data on the statewise mortality figures given in http://www.swineflu-india.org/ continues to show remarkable heterogenity in the apparent mortality rate. Gujarat has the highest apparent mortality rate (~9%), followed by Karanataka (~6%). In contrast Delhi has an apparent mortality of 0.4% while the same for Tamil Nadu is 0.6%.