Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 41.07% per annum.
- BP price at the close of March 3, 2015 was $41.74 and was higher than the top border of the primary price channel by $3.78 (9.96%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 331.50% per annum.
- BP price at the close of March 3, 2015 was lower than the bottom border of the secondary price channel by $1.45 (3.36%). This indicates a possible reversal in the secondary trend direction.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of BP price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: April 29, 2014
End date: January 23, 2015
a = 6.2026
b = -0.0014
s = 0.0389
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0014) – 1
= -41.07%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0389) – 1
= 16.83%
April 29, 2014 calculations
Top border of price channel:
Exp(Y1,045)
= Exp(a + b × X1,045 + 2 × s)
= Exp(a + b × 1,517 + 2 × s)
= Exp(6.2026 + -0.0014 × 1,517 + 2 × 0.0389)
= Exp(4.0827)
= $59.31
Bottom border of price channel:
Exp(Y1,045)
= Exp(a + b × X1,045 – 2 × s)
= Exp(a + b × 1,517 – 2 × s)
= Exp(6.2026 + -0.0014 × 1,517 – 2 × 0.0389)
= Exp(3.9272)
= $50.76
January 23, 2015 calculations
Top border of price channel:
Exp(Y1,231)
= Exp(a + b × X1,231 + 2 × s)
= Exp(a + b × 1,786 + 2 × s)
= Exp(6.2026 + -0.0014 × 1,786 + 2 × 0.0389)
= Exp(3.6930)
= $40.17
Bottom border of price channel:
Exp(Y1,231)
= Exp(a + b × X1,231 – 2 × s)
= Exp(a + b × 1,786 – 2 × s)
= Exp(6.2026 + -0.0014 × 1,786 – 2 × 0.0389)
= Exp(3.5375)
= $34.38
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 41.07% per annum.
- BP price at the close of March 3, 2015 was $41.74 and was higher than the top border of the primary price channel by $3.78 (9.96%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 5, 2015
End date: February 18, 2015
a = -3.5065
b = 0.0040
s = 0.0192
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0040) – 1
= 331.50%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0192) – 1
= 7.96%
January 5, 2015 calculations
Top border of price channel:
Exp(Y1,218)
= Exp(a + b × X1,218 + 2 × s)
= Exp(a + b × 1,768 + 2 × s)
= Exp(-3.5065 + 0.0040 × 1,768 + 2 × 0.0192)
= Exp(3.6139)
= $37.11
Bottom border of price channel:
Exp(Y1,218)
= Exp(a + b × X1,218 – 2 × s)
= Exp(a + b × 1,768 – 2 × s)
= Exp(-3.5065 + 0.0040 × 1,768 – 2 × 0.0192)
= Exp(3.5373)
= $34.38
February 18, 2015 calculations
Top border of price channel:
Exp(Y1,248)
= Exp(a + b × X1,248 + 2 × s)
= Exp(a + b × 1,812 + 2 × s)
= Exp(-3.5065 + 0.0040 × 1,812 + 2 × 0.0192)
= Exp(3.7902)
= $44.27
Bottom border of price channel:
Exp(Y1,248)
= Exp(a + b × X1,248 – 2 × s)
= Exp(a + b × 1,812 – 2 × s)
= Exp(-3.5065 + 0.0040 × 1,812 – 2 × 0.0192)
= Exp(3.7136)
= $41.00
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 331.50% per annum.
- BP price at the close of March 3, 2015 was lower than the bottom border of the secondary price channel by $1.45 (3.36%). This indicates a possible reversal in the secondary trend direction.
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