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 61.54% per annum.
- ACN price at the close of November 19, 2024 was $353.95 and was lower than the bottom border of the primary price channel by $1,025.16 (74.33%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 3.25% per annum.
- ACN price at the close of November 19, 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 ACN 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 5, 2021
End date: January 12, 2022
a = 4.8955
b = 0.0013
s = 0.0329
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 61.54%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0329) – 1
= 14.05%
April 5, 2021 calculations
Top border of price channel:
Exp(Y343)
= Exp(a + b × X343 + 2 × s)
= Exp(a + b × 502 + 2 × s)
= Exp(4.8955 + 0.0013 × 502 + 2 × 0.0329)
= Exp(5.6209)
= $276.13
Bottom border of price channel:
Exp(Y343)
= Exp(a + b × X343 – 2 × s)
= Exp(a + b × 502 – 2 × s)
= Exp(4.8955 + 0.0013 × 502 – 2 × 0.0329)
= Exp(5.4894)
= $242.12
January 12, 2022 calculations
Top border of price channel:
Exp(Y540)
= Exp(a + b × X540 + 2 × s)
= Exp(a + b × 784 + 2 × s)
= Exp(4.8955 + 0.0013 × 784 + 2 × 0.0329)
= Exp(5.9914)
= $399.99
Bottom border of price channel:
Exp(Y540)
= Exp(a + b × X540 – 2 × s)
= Exp(a + b × 784 – 2 × s)
= Exp(4.8955 + 0.0013 × 784 – 2 × 0.0329)
= Exp(5.8600)
= $350.72
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 61.54% per annum.
- ACN price at the close of November 19, 2024 was $353.95 and was lower than the bottom border of the primary price channel by $1,025.16 (74.33%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 5, 2021
End date: November 19, 2024
a = 5.6162
b = 0.0001
s = 0.1036
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 3.25%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1036) – 1
= 51.37%
April 5, 2021 calculations
Top border of price channel:
Exp(Y343)
= Exp(a + b × X343 + 2 × s)
= Exp(a + b × 502 + 2 × s)
= Exp(5.6162 + 0.0001 × 502 + 2 × 0.1036)
= Exp(5.8674)
= $353.32
Bottom border of price channel:
Exp(Y343)
= Exp(a + b × X343 – 2 × s)
= Exp(a + b × 502 – 2 × s)
= Exp(5.6162 + 0.0001 × 502 – 2 × 0.1036)
= Exp(5.4528)
= $233.41
November 19, 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(5.6162 + 0.0001 × 1,826 + 2 × 0.1036)
= Exp(5.9832)
= $396.72
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.6162 + 0.0001 × 1,826 – 2 × 0.1036)
= Exp(5.5687)
= $262.08
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 3.25% per annum.
- ACN price at the close of November 19, 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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