Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 28.86% per annum.
- K price at the close of September 17, 2024 was $80.64 and was higher than the top border of the primary price channel by $13.85 (20.74%).
- The secondary trend is increasing.
- The growth rate of the secondary trend is 832.90% per annum.
- K price at the close of September 17, 2024 was inside the secondary price channel.
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 K 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: September 5, 2023
End date: June 25, 2024
a = 2.8759
b = 0.0007
s = 0.0285
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 28.86%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0285) – 1
= 12.08%
September 5, 2023 calculations
Top border of price channel:
Exp(Y997)
= Exp(a + b × X997 + 2 × s)
= Exp(a + b × 1,448 + 2 × s)
= Exp(2.8759 + 0.0007 × 1,448 + 2 × 0.0285)
= Exp(3.9389)
= $51.36
Bottom border of price channel:
Exp(Y997)
= Exp(a + b × X997 – 2 × s)
= Exp(a + b × 1,448 – 2 × s)
= Exp(2.8759 + 0.0007 × 1,448 – 2 × 0.0285)
= Exp(3.8249)
= $45.83
June 25, 2024 calculations
Top border of price channel:
Exp(Y1,199)
= Exp(a + b × X1,199 + 2 × s)
= Exp(a + b × 1,742 + 2 × s)
= Exp(2.8759 + 0.0007 × 1,742 + 2 × 0.0285)
= Exp(4.1431)
= $63.00
Bottom border of price channel:
Exp(Y1,199)
= Exp(a + b × X1,199 – 2 × s)
= Exp(a + b × 1,742 – 2 × s)
= Exp(2.8759 + 0.0007 × 1,742 – 2 × 0.0285)
= Exp(4.0291)
= $56.21
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 28.86% per annum.
- K price at the close of September 17, 2024 was $80.64 and was higher than the top border of the primary price channel by $13.85 (20.74%).
Secondary Trend
Start date: June 26, 2024
End date: September 17, 2024
a = -6.7017
b = 0.0061
s = 0.0679
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0061) – 1
= 832.90%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0679) – 1
= 31.22%
June 26, 2024 calculations
Top border of price channel:
Exp(Y1,200)
= Exp(a + b × X1,200 + 2 × s)
= Exp(a + b × 1,743 + 2 × s)
= Exp(-6.7017 + 0.0061 × 1,743 + 2 × 0.0679)
= Exp(4.0981)
= $60.23
Bottom border of price channel:
Exp(Y1,200)
= Exp(a + b × X1,200 – 2 × s)
= Exp(a + b × 1,743 – 2 × s)
= Exp(-6.7017 + 0.0061 × 1,743 – 2 × 0.0679)
= Exp(3.8264)
= $45.90
September 17, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(-6.7017 + 0.0061 × 1,826 + 2 × 0.0679)
= Exp(4.6059)
= $100.07
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-6.7017 + 0.0061 × 1,826 – 2 × 0.0679)
= Exp(4.3342)
= $76.27
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 832.90% per annum.
- K price at the close of September 17, 2024 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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