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 May 16, 2024 was $308.00 and was lower than the bottom border of the primary price channel by $764.94 (71.29%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 2.24% per annum.
- ACN price at the close of May 16, 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: March 26, 2021
End date: January 12, 2022
a = 4.6710
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(Y468)
= Exp(a + b × X468 + 2 × s)
= Exp(a + b × 679 + 2 × s)
= Exp(4.6710 + 0.0013 × 679 + 2 × 0.0328)
= Exp(5.6188)
= $275.57
Bottom border of price channel:
Exp(Y468)
= Exp(a + b × X468 – 2 × s)
= Exp(a + b × 679 – 2 × s)
= Exp(4.6710 + 0.0013 × 679 – 2 × 0.0328)
= Exp(5.4878)
= $241.72
January 12, 2022 calculations
Top border of price channel:
Exp(Y670)
= Exp(a + b × X670 + 2 × s)
= Exp(a + b × 971 + 2 × s)
= Exp(4.6710 + 0.0013 × 971 + 2 × 0.0328)
= Exp(5.9983)
= $402.73
Bottom border of price channel:
Exp(Y670)
= Exp(a + b × X670 – 2 × s)
= Exp(a + b × 971 – 2 × s)
= Exp(4.6710 + 0.0013 × 971 – 2 × 0.0328)
= Exp(5.8672)
= $353.25
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 60.68% per annum.
- ACN price at the close of May 16, 2024 was $308.00 and was lower than the bottom border of the primary price channel by $764.94 (71.29%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: March 26, 2021
End date: May 16, 2024
a = 5.6374
b = 0.0001
s = 0.1063
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 2.24%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1063) – 1
= 52.97%
March 26, 2021 calculations
Top border of price channel:
Exp(Y468)
= Exp(a + b × X468 + 2 × s)
= Exp(a + b × 679 + 2 × s)
= Exp(5.6374 + 0.0001 × 679 + 2 × 0.1063)
= Exp(5.8911)
= $361.80
Bottom border of price channel:
Exp(Y468)
= Exp(a + b × X468 – 2 × s)
= Exp(a + b × 679 – 2 × s)
= Exp(5.6374 + 0.0001 × 679 – 2 × 0.1063)
= Exp(5.4661)
= $236.53
May 16, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.6374 + 0.0001 × 1,826 + 2 × 0.1063)
= Exp(5.9606)
= $387.84
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.6374 + 0.0001 × 1,826 – 2 × 0.1063)
= Exp(5.5356)
= $253.55
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 2.24% per annum.
- ACN price at the close of May 16, 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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