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 60.68% per annum.
- ACN price at the close of February 20, 2025 was $384.84 and was lower than the bottom border of the primary price channel by $1,139.55 (74.75%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 4.47% per annum.
- ACN price at the close of February 20, 2025 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: March 26, 2021
End date: January 12, 2022
a = 5.0222
b = 0.0013
s = 0.0328
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 60.68%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0328) – 1
= 14.00%
March 26, 2021 calculations
Top border of price channel:
Exp(Y276)
= Exp(a + b × X276 + 2 × s)
= Exp(a + b × 399 + 2 × s)
= Exp(5.0222 + 0.0013 × 399 + 2 × 0.0328)
= Exp(5.6062)
= $272.11
Bottom border of price channel:
Exp(Y276)
= Exp(a + b × X276 – 2 × s)
= Exp(a + b × 399 – 2 × s)
= Exp(5.0222 + 0.0013 × 399 – 2 × 0.0328)
= Exp(5.4751)
= $238.68
January 12, 2022 calculations
Top border of price channel:
Exp(Y478)
= Exp(a + b × X478 + 2 × s)
= Exp(a + b × 691 + 2 × s)
= Exp(5.0222 + 0.0013 × 691 + 2 × 0.0328)
= Exp(5.9856)
= $397.67
Bottom border of price channel:
Exp(Y478)
= Exp(a + b × X478 – 2 × s)
= Exp(a + b × 691 – 2 × s)
= Exp(5.0222 + 0.0013 × 691 – 2 × 0.0328)
= Exp(5.8546)
= $348.82
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 60.68% per annum.
- ACN price at the close of February 20, 2025 was $384.84 and was lower than the bottom border of the primary price channel by $1,139.55 (74.75%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: March 26, 2021
End date: February 20, 2025
a = 5.5914
b = 0.0001
s = 0.1042
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 4.47%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1042) – 1
= 51.72%
March 26, 2021 calculations
Top border of price channel:
Exp(Y276)
= Exp(a + b × X276 + 2 × s)
= Exp(a + b × 399 + 2 × s)
= Exp(5.5914 + 0.0001 × 399 + 2 × 0.1042)
= Exp(5.8477)
= $346.43
Bottom border of price channel:
Exp(Y276)
= Exp(a + b × X276 – 2 × s)
= Exp(a + b × 399 – 2 × s)
= Exp(5.5914 + 0.0001 × 399 – 2 × 0.1042)
= Exp(5.4308)
= $228.33
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(5.5914 + 0.0001 × 1,826 + 2 × 0.1042)
= Exp(6.0187)
= $411.03
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.5914 + 0.0001 × 1,826 – 2 × 0.1042)
= Exp(5.6018)
= $270.91
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 4.47% per annum.
- ACN 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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