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 23.35% per annum.
- BA price at the close of February 20, 2025 was $180.88 and was higher than the top border of the primary price channel by $5.93 (3.39%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 80.25% per annum.
- BA price at the close of February 20, 2025 was inside the secondary price channel.
- 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 BA 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: June 1, 2023
End date: December 13, 2024
a = 6.3245
b = -0.0007
s = 0.0853
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -23.35%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0853) – 1
= 40.65%
June 1, 2023 calculations
Top border of price channel:
Exp(Y825)
= Exp(a + b × X825 + 2 × s)
= Exp(a + b × 1,196 + 2 × s)
= Exp(6.3245 + -0.0007 × 1,196 + 2 × 0.0853)
= Exp(5.6236)
= $276.87
Bottom border of price channel:
Exp(Y825)
= Exp(a + b × X825 – 2 × s)
= Exp(a + b × 1,196 – 2 × s)
= Exp(6.3245 + -0.0007 × 1,196 – 2 × 0.0853)
= Exp(5.2824)
= $196.85
December 13, 2024 calculations
Top border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 + 2 × s)
= Exp(a + b × 1,757 + 2 × s)
= Exp(6.3245 + -0.0007 × 1,757 + 2 × 0.0853)
= Exp(5.2148)
= $183.97
Bottom border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 – 2 × s)
= Exp(a + b × 1,757 – 2 × s)
= Exp(6.3245 + -0.0007 × 1,757 – 2 × 0.0853)
= Exp(4.8736)
= $130.79
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 23.35% per annum.
- BA price at the close of February 20, 2025 was $180.88 and was higher than the top border of the primary price channel by $5.93 (3.39%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: September 30, 2024
End date: February 20, 2025
a = 2.2645
b = 0.0016
s = 0.0439
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0016) – 1
= 80.25%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0439) – 1
= 19.19%
September 30, 2024 calculations
Top border of price channel:
Exp(Y1,159)
= Exp(a + b × X1,159 + 2 × s)
= Exp(a + b × 1,683 + 2 × s)
= Exp(2.2645 + 0.0016 × 1,683 + 2 × 0.0439)
= Exp(5.0690)
= $159.02
Bottom border of price channel:
Exp(Y1,159)
= Exp(a + b × X1,159 – 2 × s)
= Exp(a + b × 1,683 – 2 × s)
= Exp(2.2645 + 0.0016 × 1,683 – 2 × 0.0439)
= Exp(4.8935)
= $133.42
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.2645 + 0.0016 × 1,826 + 2 × 0.0439)
= Exp(5.2999)
= $200.31
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.2645 + 0.0016 × 1,826 – 2 × 0.0439)
= Exp(5.1243)
= $168.06
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 80.25% per annum.
- BA price at the close of February 20, 2025 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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